·Printed by K. N. Bhargava at the
Allahabad Oriental Press, Lucknow---1920
AND
Published by.
Swami N. S. Swayam Jyoti
Secretary,
The Rama Tirtha Publication League.
Lucknow,
1920,

·FOREWORD. The complete works of Swami Rama Tirtha have been puti shed in the four volumes of "In Woods of God-Realization, the fourth of which contains the article on Mathematics presented in this tract. This was the very first article written by Rama and specially for the Student Community The fourth volume having run short yet awaits republication, but in the meanwhile, for the benefit of the students specially, this article on Mathematics has been taken out of it and published by itself at nominal price. Further, to enhance its value and to make it more attrac. tive and useful a photo of Swami Rama as a professor, along with his life-sketch with fuller details of his studertlife is also given, The life-sketch has been rather hastily written to meet an urgent demand for the article but it is presented in an arranged form, specially bringing out those points in Rama's unique life as may serve to inspire and' guide many a poor student labouring under sore difficulties and may make his life's burden light and cheerfully borne. a The sketch is based mostly on the materials contained in Shri R, S. Narayana Swami's Urdu

·(ii)
edition of Swami Rama's life and the life and
appreciation of Rama in English by Mr. Puran,
from which several quotations have been
taken.
If this small tract is appreciated and received
warmly and eagerly by the public, as it should
it will encourage the Publishers to issue
a series of such handy booklets containing the
most useful articles of Swami Rama and other
saints and savants
Any suggestions for the improvement of the
series will be thankfully received.

·No text on this page.

·Swami RAMA TIRTHA.
PROF, TIRTHA RAM GOSWAMI M A
11896.)

·A BRIEF LIFE SKETCH OF Swami Rama Tirtha. (Specially IVritten). Swami Rama, previously known as Gyain Birth and Tirtha Rama, M A , was born Family. on Wednesday, the 22nd Octoer, 1873, on the day following the Diwali at (uraliwala a small village in the District of ujranwala; Punjab Born in the family of Fosain Brahmans, he was the direct descendant | Gosain Tulsi Das the famous author of the Jindi Ramayana and in the line of Rishi Vasish; ha, the Guru of Bhagwan Sri Rama Chandra. no His father Gosain Hirananda had peans of livelihood except what he received as ifts in his spiritual tours to Peshawar and Swat, Lis mother passed away when he was but a few ays old, and he was brought up by his elder rother Gosain Guru .Das and his old aunt. wami Rama was thus born under the lowly loof of a poor but noble Brahman family, He was brought up on cow's milk and mained very weak and thin .Childhood and during his childhood. His aunt, predictions. who was a model of goodness, hastity. and devotion, used to take the little ·(2) Rama along with her to temples and shrines where the worship offered, the recitations from the Puranas, the Mahabharat and the Bhagwat, and the blowing of the conches had a strange fascination and charm for him. So much so that he used to cry if he heard the conches blow in the neighbourhood, and no toys, 'no sweets, nothing indeed satisfied the baby short of its being taken to the place of worship As a child he was very attentive in listening to the recitations of the sacred lore and would rather forego his meals or even the much-loved studies than not go'to attend the 'Kathas He ruminated over the stories he had heard with a precocious mind, put questions and offered appropriate explanations, His village people bear testimony to his unusual intelligence, his contemplative nature and his love of solitude. Thus the devotional songs and stories and the sacred sound of the conches had early impressed the baby mind and sown the seeds of a intense longing for the Divine. Quite an uncommon child, it was predicted by astrologers that he was the coming genius of his race, the illuminator of faith, a traveller ·( 3 ) 3. of foreign lands, and-had danger of life by water in his 33rd year. This prediction came true literally While he was yet a baby, only two years old Rama was betrothed by his Early father to the infant daughter of Marriage. Pandit Rama Chandra of Viroki in the Tehsil Wazirabad of District gujranwala, and was married in his tenth year. It can only be imagined how this early marriage stood in 'the way of Rama's studies later on but at the time he was too young to make any protests, It points forcibly to one of the evil customs of our Hindu Society which not a few still follow in their ignorance and only succeed in putting a double burden of a student and house. hold life on the shoulders of their younger generations stunting their growth, undermining their health and intellect, and ruining their lives for good, It was through sheer strength of determi. nation and devotion and love for studies that Ramz successfully mct and overcame every obstacle put in his way. He became a student at the age of five. He was admitted into a Vernacular Student Priinary chool in the village Lile. Muraliwala ·r ( 4 ) Though tiny in size and simple in habits, (i) Pimary he had had a a splendid memory tducation, and was both intelligent and industrious. The Head Maulvi of the school was at times quite astonished at his intel. ligence and memory. At this early age in his 5th class, he had finished Gulistan and Bostan (thc tivo standard Persian books) besides the school books and had committed to memory a large number of Urdu poems. But he was not given to sports and games at all. The whole day was spent in study and in the evening as soon as he got leizure he used to go to Dharamshalla to hear the much loved recitations of the sacred books. On his return he took his evening nieals and recited before his admiring relations each and evcry word of what he had heard without any additions or alterations Whatever. After finishing the primary cducation he went with his father to the (ii) Secondary High School in Gujranwala, a Education ang Guru, distance of about 7 miles from his village. Being only ten years old he was there left by his father under the protection of his able and kind friend Bhagat Dhanna Ramji, who was consequently regarded by Rama and accepled in true faith and devotion as his Guru or Spiritual Guide. det ·(5) . He was admitted there in the special class to study English and after coming out successful was taken into the Middle class in 1886. He was now 1,2 years old and cherished an intense. devotion towards his Guru whom he wrote his first letter in Urdu from Viroki his father inlaw's place). In the course of his secondary and college education he exchanged more than a thousand letters with his Guru, many of which have been collected and printed in Urdu in the form of a book called Rama Patra They are highly interesting to read and show the great depth of devotion and faith and respectful atti. tude which he always had for his Guru though illiterate, In 1888 when fourteen and half years old, he passed his Entrance Examina- (iii) University tion from the Punjab University, Edacation. standing first in his school and (al Entrance. 38th in the University and gained a scholarship. But his father did not want him to read further and so he came to Lahore for admission into College quite against his father's will. Consequently, he had to sub. sist on the small sum of scholarship that he had' secured from the Municipal Committee, Gujranwala on account of his first position in the school ·( 6 ) already 'mentioned and was admitted in the Mission College, Lahore Lahora In his second year specially he worked so hard that he was very often ilt. It was not unoften that he kept himself absorbed in his studies from sunset to sunrise, Solitude, hard work, and ample tim: for his studies were what he loved dearly. As a result he stood first in F. A. in 1890 and also secured the Government (6) F.A. scholarship notwithstanding his conti. nuod illness and the fact that he had taken Sanskrit in F. A., as against Persian which he had studied up to Entrance. He continued his studies in the B A., Class in the same Mission College with (c) Trials and difficulties perfect faith in God and his in B. A. Guru and maintaining life on the scholarship he secured But when his father saw that he could maintain him. self without his help and 'was 'not willing to undertake any service according to his wishes, he felt very angry and took Rama's wife with him to Lahore and left her also in charge of poor Rama for a year or so without any kind of suppɔrt from himself: Gosain Rama nad now to face a number of difficulties, viz., the house reint, the cost of bɔ'ss, the college fee, the expenses for his wife and himself etc, etc. But such were 7 ·( 7 ) his undaunted courage to meet any difficulties and the supreme love of knowledge for its own sake that he could entirely forget the ordinary comforts and physical needs of daily life. He would forego an extra suit, an extra loaf or even a duy's meal for the oil of his mid. night lamp and would actually starve for days together without however, showing the least signs of suffering or sorrow on his face for he attended College regularly with a calm and peaceful appearance and kept to his studies as usual ! Once Gosain Rama happened to spend his scholarship in the purchase of (d) An incident. his text books and did not care at the time to make provision for other expenses, As a consequence he found out that what he had left was only a very triAling sum which could be spent during the month at the rate of only 3 pices or 9 pies per day. He was at first rather at a less what to do bua moment after said to him. self that God winted to test him, that at least beggars did pass their days on two or three pices a day and hence he should not fail under that trial Ramı, therefors, began to subsist on two pices worth of bread in the morning and only one pice in the evening. But soon after, one ·(S). cvening the shop keeper accosted him with the femarks that he took pulse frcc along with onc picc of bread ; that such a business could bring bim no profit and her.cc he could no more sell onc picc worth of broad to him Thcrcupon Rama resolved to partake of food only once a day until hc got moncy again. ns1 iic was a Thus with an iron will did he fight his way (-) Clinraclor coolly like a soldier day and sturient night and vin over field after field of knowicdge. Hunger and thirst cold and heat, could not tell upon this suprem: passion that hic felt towards knowlerige. typical student who lovcj lo study not with any hope of gaining worldly ends, but for satisfying the evergrowing thirst for knowicine which was firing his soul anew with every cw sun His daily studies were sanctified oblations on the altar of this 'havan kund" He was the patient architect of him elf from childhood to manhood. He built himself little by little, moment by momant and day by day. It may be said that perhaps , the whole career of his further life was sketched nlrendy beforo his mind's eye, beca:130 ovon in boy he was working ro grarely, so silently and en consciously for a definito mission. Ho had an angelic nature with a purity and innocence of life rarely inet with, ·(9) As a 'lndent he lired in extreme porerty. The dress of the boy.Roma consisted (1) Dress. of a shirt. a pair of Punjabee trousers and a small turban, each made of a cheap and very charse conniry cloth, the entire outfit costing about Rs 3. He nlways wore dative shoes even while studying in B. A., class and was rather in a fix what to do when he had to use the prescribed pair of boots in the Coprocation Hill. Once he lost one of his shoes in a drain while it was raining and the Dext day he went to college wilh the remaining shoe in one foot and an old used shoe of a female in the other. Afterwards he purchased a per pair for nine apons and three pies only. He had a soft hander.me face of a typical Aryan cnt. The yebro ryg, arched (g) Physical over a pair of spectacles covering appearance. deep black eyes, which showed the mysteries and fore of his soul. In contrast with a big, brond, prominent furehead, showing high intellectanl power there was feininius softness round his lips. When he was serious' the lower lip pressed against the upper op a sinal round chin. which betukened 'indomitable strength of will. But he was lashlul like a modest gri. Living as he did sh lho light of love, he looked transparently pute through bis small, frail, fair-coloured body. And yet, ulder Ibis CDagel ming bumble oprear.

·( 10 ) ance there lay hid a reinarkable man with some lofty aspirations and noble aims, which the Brahman body thought too sacred to be uttered. Now to return to onr narrative of his studies in tbe B. A, class, we find still (h) Greater greater trials awaiting for Gosain Trials, Rama. In the year in which he appeared for his B. A. examination there was such a confusion in the examination of English papers that some of the best boys failed to pass while the one who came out first as the boy whom the Principal was not going to send up at all. Poor Rama was also ono of those who failed and he failed by only three marks in English although he was first in the whole University in the aggregate of marks, There was a great agitation and discussion in the papers which resulted in the (0) New Rule passing if a new rule in the Uni. passed, versity, though nothing could be done for Rama, i came into force from the next year and provided for the re-examination of the answer-books of a body who failed by only five marks. Rama had, therefore, to accept., his hard lot, and to continue his studies in B. A., for ona year more. That very sear a state scholarship wag & warded for_the study of Mathematics in England ·í fr.) to a candidatë who was not over 21 years and had passed his B A., or M.A., in Mathematics, Thia was eligible for Rama but as he failed in B. A., he could no longer get it. Again, the scholarship, which he was hitherto getting, 'was also scopped owing to his failure in B A. This was a moment of sore trial for him and although he saw only gloominess all arouod yet his trust in God never forsook him and his courage never failed bim. He resolved all the more firmly to pass his B. A, examination and with tears in (3) Resolution his and Selfeyes he prayed to God in soli. Surrender. tude making a total self-surrrender of himself. From the depths of his grieved heart ca ne forth the well-kaown couplet:- स्वमेव माता च पिता त्वमेव । त्वमेव पन्ध शप्तता त्वमेव ॥ स्वमेव विद्या द्रविणं त्वमेव । त्वमेव सर्वं मम देवदेव ॥ Thou alone art my mother aud father, Thon alope my relation and friend, Thou art kuowledge, Thou art wealth, Thou art all, my God of gods ! The uext day, when he got himself admitted in B, A., again, he found !o bir () Vaexpected great surprise that the College help. sweetseller L, Jhandu Mall came full of sympathy and requested him to dine there. after daily at his house. Ramà, of course, accepted ·( 12 ) 1 the timely offer and invitation.' This generous sweetseller not only helped him with food but provided him with clothes also from time to time and also a free house to live in. Io times of great need he was helped with money and food by one of his relatives also namely P. Raghunath Mal, Assistant Surgeon who was also his teacher for soine time Not only this but the Principal called him and handed over a sum of Rs. 53 only saying that it was given to himn for Ramu by somebody. He hesitated to accept the whole sum but only hulf of it and entreated the Principal to spend the other half for some College purpose, or, to pay to Mr, Gilbertson the Professor. of Mathematics, who had been very generously paying up half of his College fee. But the Principal pressed him to accept it and he had to do so. Moreover, he undertook some private tuitions also, even giving free instructions to some in his hard pressed time, for he took a great delight in teaching. Thus he toiled on till the time was ripe to send the University fee of Rs. 30 only. God helps those_who_help themselves. Just when he was thinking about it and how to meet the difficulty, Mr. Gilbertson, who was extremely pleased with Rama's industry and intelligence called him apart and gave him something wrapped in a piece of paper, On goiog home he opened the little ·( 13 ) 5 1 packet and found to bis surprise the eract sm nf Rs. 30 only. In his test examination, he stood first gaining 60 marks more thnn were required (2) B. A. Test. for First Divi iva. ln Maubematics he grined 145 murks out of 15C. He had 80 mach self-confidence when he appenred in his B A. exrmination that in his Mathematics paper while he hnd a choice of doing any 9 questions ont of 13, he solved all of them and requested the examiner to select any nine, although the paper was a stiff one and other boys were able to do 3 or 4 questions only nt their best. In 1893, his success was the marked one, for he stood First in the Punjab Univers (mi B.A. Result sity ir, B. A. and in First Division, securing 310 marks. He niso gained two scholars ships, amounting to Rs. 60 per month besides a gold mednl, a gown, and other rewards. All this was the result of his perforo trust in God and firm! determination, He was nosy nineteen and a half years old when he entered for his M. A, in (n) J. A. Study. Mathematics in the Government College, Lahore, as there was then no M A, in the Mission College. He used to tench his class-fellows with so much pleasure that he used to leave off ·( 14 ) his own work at once, however bus ly engaged, if any of them asked him a question. While studying for his M, A,, he also acted as an honorary professor of Mathematics in the Forman Christian College, wbere be had himself studied, and worked for about two years thicking it to be his duty to discbarge the debt he owed to his Alma Mater. He used to study at least four or five books on the same subject He was the idol of all his teachers who were always very kind to him. When he passed his B. A., with distinction he had a chance to accept the Statescholarship for Civil Service but he only liked to be a teacher or preacher. In one of his letters to his Guru, dated the 9th (o) Daily routine February 1894, he writes about in M. A. bis daily routine as follows:- "I rise from bed at about 5 A, M. and study till 7 A, M, then go to answer the call. of nature, take my daily bath and exercise. Af:er that I go to Panditji (reading in the way), Thereafter an hour I take my food and go to college along with him in a conveyance, 0.2 retura from college I take milk in the way and after a few minutes stay at home I proceed to wards the river Rávi where I take a walk for about half an hour by its side. On my return I make a round of the city through its gardens and reaching home again walk up and down ·( 15 ) the roof of the upper storey of the house until it becomes dark. But you should not forget that I walk up and down never without studying from a book at the same time, On dusk I take my exercise and after it read till 7 p, m. Then I go to take my meals and to teach Prem, a student. On return I take exercise again and then study till about half past ten in the night and lastly go to beș. It is my experience that it is only when our stomach is in a healthy condition that we feel cheerful and buoyant, concentraled and keen in intellect and memory, and can offer our prayers to Him with a pure heart. I, for one, partake of food very sparingly and what I do eat I make it a point to digest it thoroughly," It may be remembered that being very studious, (p Food and Rama was, in his student life even Exercise. up to B. A. very weak in health often suffering from fever, headache and constipa-* tion of which he wrote to his Guru in some of his letters. But now he realized the value of open air exercise and light but nourishing food well digested. In his M A , in 1894, he took delight in taking pure milk so mnch that he wholly subsisted on it and took long walks, often of 30 miles without feeling tired. On the contrary he felt very healthy, light and clear in brain. He invented new and odd exercises but very effective at the same time.

·ſ 16 ) 6 One of them was to raise aud lower slonly a bed: s. ead (chár pái) wluch he could do 160 times and w licb tbe su ougest of the College boj s could not do more than 20 times, le rever used an umbrella even in the hottest sun or the rainiest duy, lu 1995, when Rama was about 20 years old, he ubiained his M. A., degree in (9) M; A. Result. Dlathematics with a very high percentage of marks, although the Marbematics papers that year were specially hard, the like of which (as Rama himself says) were never before set in any Indian University in N. A. Dr, WV. Bell, then Principal of the Government College Lahore, thought very highly of his exceptional attainments and wished him to go up for live coni: petitive Examination of tbe Provincial Civil Service. But Gosain Rama's own desire was to teach Alatbematics which he had acquired with an iufiuile amount of lubuur. He thought 10 those days of tak 1 g the State Scholarship-as it was his right that year and gowg to Cambudge for the Biue Ribbon. But he was destined to be'a greater mau in unotber line than a mere Senior Wrangler, and the scholarship was giveu tor young Mohamedao'. For sometime, after his M. A, in 1895, lie 5 Service and opened Private Classes in Mathe. Public work, matics for T, A., and, B. A., stu.

·( 17 ) dents on Rs. 10 and Rs. 15 each, per month, respectirely and besides these students one or two professors of the Colleges also caäe to study with him. All this was a very hard work and told upon his health. So he had to return to his home furari- Tala in Gujranwaln. After regnining health a fer months after he.came back to Lahore and becam. r member and later on the Secretary of the Educati n Committee of Sanatan Dhurma Saboa, In the meinwhile he leirat the art of Drawing in the Ved.c College, Lahore. Then near the end of 1895, he became the Second lister of Ameriorn Mis- (i, Sialkote. sion High School, Sialkote, on Rs 80 p. m. ind in a fex diys he became known am yg the bwys as one who could multiply by memo,; silin3 reiching t. millio 13, Miny a boy fr.in distant places fucked in his school and he was on such familiar terms with them that whatever they asked for he glue them withont hesitation, Any bry could according to his need go and drink m lk from the sucets seller on Ruumil's account. Thus he spent the whole of his pay on students and passecl a simple life ala'ng them full of mercy, sympathy and unselfishness. He also took part in the local Sanatan Dharma Sabhn and other religious bodies giving his inspiring lectures is at Lahure.

·( 18 ) In 1896, he also become the Superintendent of the Mission Boarding House, Sialkate, but only after a month or two, in the same year he got an appointment as Professor of Mathematios in the Forman Christian College, Lahore. He also noted as Reader for a short time in the Oriental College, Lahore. What (ii) Laliore, ever he got as bis pay of professorship he used to distribute almost tho whole of it at once among tho doserving persons and thus left for himself a very scanty and trifling sum mooth by month. He oared po$ for his own physio il self and its comforts, nor för wealth, or clothes, or materin! needs, but was being gradually transformed and culoured in wardly with true mental renunciation (Vairágya), He had an intense love for Bhagwad Gita and 6. Devotion to read and re-read it time after time Krishna. till be had dived deep into its ipner meanings and made himself one with it, His devotion to Shri Krishna dereloped to such an intensity that many a night found him weeping constantly in his separation so much so that his bed sheets were found all wet in the morning. He vould go to the Ravi side and remain absorbed in meditation till late in the night. All his holidays were spent in constant thought of his beloved Krishna and if .

·( 19 ) he lectured in Sanatan Dharma Sabha on 'Bhakti or 'Krishna' all the words that diopped from his lips were quito set with tears. At this stage of his spiritual derelopment he sery often beheld the cloud-coloured Krishna with a bamboo flute on his lips and dracing on the head of a cobra, face to fico, with his eyes open and his senses all about bimsolf. His Holiness Jagadguru Shri 1108 Shri Raj Rajeshwar Tirtha Swamiji, Shan. 7. (i) Jagad Guru's karacharya of Sharada Matha, reception and Dwarka, Kathiawar happened to Vedanta. comc in Lahore during these days. He was very proficient in Upnishads and Vedanta and was so learned in Sanskrit language and the Shastras that hc had no cqual. Goswami Rama had the occasion to receive him on behalf of the Sanatan Dharma Sabha and had full opportunity to enjoy his blessed company. His intense devotion to Krishna nos changed its direction and worked with an cqual force in search of self-realization as taught in Vedanta, He now began to make a thorough study of the Upnishads the Vadanta Sutras and other books on Vedanta, and determined to pass his summer vacation in llardwar and Rishikesh for spiritual exercises and deep meditation on Self, ·( 20 ) Hence in August 1897 he hired a house by the Ganges side in Hardwar and began to enjoy the bliss of deep meditation in solitude (realizing in practice what he studied about Vedanta in theory ) Thus by continued practice, his spiritual bliss developed to such a pitch that on (ii) Mental October 25th 1897, the Diwali day, Renunciation. it led him spontaneously to make a total self-surrender or renunciation of all ani he wrote to his father to the effect that Rama had on Diwali day gambled away his body for the Real Self, After this Rama was ever absorbed in contemplation of the Self or Atman and knew not day from night but the One Supreme Realization or the search after the Absolute Truth. At the same time in February 1878 in order to taste of the Sweet Nectar of (üi) Sahha, Divin: Bliss in co.npany with others he organiz:d a Sabha at his place called the Advaitainrita Varshini Sabha, which consisted mostly of sadhus and Mahatmis It was held once every week and whatever conclusions were drawn from an earnest discus. sion on Vedanta thev were worked upon and ·( 21 ) piactised by the members in solitude for a week and the experiences related before Rama in the next meeting for further instructions. Thus Rama became mr.ore and inore absorbed in the real Bliss and nothing could shake him from his concentration of mind and inner peace. Although outwardly he was sometimes very busy but inwardly he enjoyed the 8. First Tract. eternal peace. It was dur ng these very day s, in 1898, that for the benefits of the student community Rama delivered a lecture on Mathematics, which was afterwards published in the form of a pamphlet and called " How to excel in Mathematics "the treatise now published again in the present form. This was his first English speech and written work and it was followed by writings in different languages He had such an intense devotion to study that a whole library of books on reli. 9. Vast Studies. gion and philosophy of the west was mastered in a short time The Rishis of the Upanishads, Patanjali Jaimini, Kanad Kapila Gautama Vyas, Krishna, Shankara were as much at his fingers' ends us Hafiz, Attar, Shams fabrez and Maulana Rum Kant, Schopenhauer Fichte and Hegel, Gouthe" and Carly lo were as familiar authors--as Tulsi Das, ·( 22 ) Sur Das, Kabir. Tuka Ram and Nanak who were undoubtedly his inspirers. He was perfectly at hòme in Persian English, Hindi, Urdu and Sans. krit Literatúres. He studied the four Vedas in 1906, and was a master Pandit of every Mantra, whose every word he analysed with the acute accuracy of' a philologist. Not only had he a mastery over literature bui was a keen student of Science and Mathematics. He loved Science and was an amateur chemist and botanist, His special study in the Philosophy of Science was Evolution. He enjoyed the scientific cand. our and truthfulness of Spinoza, Spencer, Darwin, Haeckal, Tyndal, Huxley, and Professor James 1 hus he made himself quite a prodigy of learning. It seems every minute of his thirty. three years was so well utilised. He was very hard working till his last moments. While in America he went through, in two years, in spite of his strenuous public labours, almost the whole range of American literature taking a particular delight in the free chants of Walt Whitman and 'Thoreau. “ He was in a strange humour. all his own when he judged all the world's 10. Character authors, prophets, poets and mysand Iersonality. tics. There was no pedantry and not the slightest shadow of affected ·( 23 ) ( pride or anything unreal when he acted like an inpartial judge in his own way. He was a scholar, scientist and spiritualist of a very high order in one Simultaneous with his intellectual culture, he had brought his spiritual development to a very high pitch. Crowded Lahore could no more satisfy the amptitudes of his, soul, What. ever time he could get he would spend in the Himalayan hills and jungles, meditating on tlie Upanishads and the secrets of the Ancient Aryan “ Bralı coidyl." " It was in the forests of Brahmapuri, near Rishikesh, in 1899, that Rama 11. Realization. realized his, object, – the Atman, the Self He went there all alone, and without any thing but a few Upanishads, Again and again he went over them and meditated by the Ganges side on bare rocks: day and night, little caring for rain or sunshine but all absorbed in the one thought of self realization. . He had determined to lose his very life in Éhe attempt or to gain it and he did succeed. Fle attained to that fearless, blissful oneness state of mind where there is no more delusion or repentence and knowing or rather realizing which nothing remains to know, ·( 24 ) The inner fountains of Divine Bliss were now incessantly and spontaneously flowing out of him and shedding benediction all around him. Shrutis and I'mritis verses and songs thoughts and things., questions of philosophy and Religion, politics add society, whatever 170w came fron him, were changed by the mysterious effects of his inner soul and came out with refreshing beauty a new form, wearing garment of Rama consciousness, He saw the Universe in Himself and himself in the Universe. He enunciated the great law that the whole Universe serves one as his body, when he feels the Universal soul as his very self. Not only a spiritualist and a veritable prince of all Oriental dreamers and Yogis, 12. Esercise. he was a great champion of physical exercise. He delighted in designing new methods of physical exercise He could never forego his daily exercise Ile was seen even a few minutes before his death, taking as was his wont, his physical exercise, Thus dut of a thin, frail body, he managed to emerge a strong man of staglike nimble activity. He was a great and swift walker He could walk more than 40 miles a day as a Swami in the Himalayan hills. He won in America a 40 miles race, which he ran out of fun in competition with some American soldiers coming two hours ahead ·( 25 ) of the winner. He scaled Gangottari Yamunottari and Badari and Kedarnath peaks cla: in a small siripof a loin cloth a:id a blanket. He crossed from Yarnunottarita Gangottiri through glaciers. He lived in sno s's,slept in cares in thicdrcary jungle: all alone. He would roam about at midnight in dark juigles defying death and ſcar. He was so fearless so bold. so rehement so strong and so roscate and yet he was gentle unaffected, child. lizclpure and noble, sincere, earnest and unissum. ing that all who came in contact with himn with a heart yearning for the truth could not but receive inestiniable bencfit. After cach lecture or class lesson quzsiions were put which were always answered so clearly and concisely, sweetly and lovingly. He was over fillc: with bliss and peace, a constant spring of happiness and ever chanting the sacred syllable Om when not engaged in talking, writing or reading. He saw divinity in cach and all, and every one was addressed by him as " Blessed Divinity." Tree, irce was he like a child and saint. He would remain in God consciousness for days to gether. His unfaltering devotion to India and his desire to raise her benighted people was indeed perfect self-abnegation, His personality may be described as explo- ·(26.) sive. He would remain silent for, 13 Personality. months together as if he had nothing to say. He remained merged in joy All of a sudden he will burst out like a yolcano and give out his thoughts in a wild manner. Whenever he spoke or wrote one could be sure of getting something very refresh. ing and original His highly cultivated emotion, bold independence of thought and his great towering intellect formed an attractive feature of his personality He was deeply sincere and irresistably sweet. Mahomed ins and Aindus loved him alike To see him was to feel inspired with new ideals, new powers, new visions and new emo. tions, Whatever he taught, he hai not oily thought upon. but he had actually 14. Doctrines and Views. seen its working in his own life. He used to say that he believed in experimentul religion. · According to him the art of livirg consists in Luminous belief Just as in science, authority •has little weight in arriving at Truth, so in religion authority should hive little or 110 weight and its truth must be tested by trusting your life to it. Every one must reach the inner nian, the Self, the Atman, through the failures and successes of his own life or through Self-Realization. Life itself is the greatest

·( 29 )
revelation. The great idea which runs as an
undercurrent in all his discourses is the renun.
ciation of body consciousness (Alankara) and
the realization of Self to be the Self of universe,
The false ego is the cause of all limitations. Elimi.
nate it and the spirit of in an is the universal
spirit pervading everywhere and everything
This liigher life is to be realised and Raina
sanctions all means by which it may be attained.
The bed of thorns or the bed of roses whichever
induces the state of realisation. in us is to be
blessed. Total self-abnegation is the essential
prelude to this realisation and it niay be effected
biy different individuals in different ways. Hence
he gives only the getieral outlines of his main
conclusions and sketches the metliods which were
most helpful to him
a
Vedanta is to him by 110 mealis a mere
intellectual assent but mnost
15. Ideal, solemn and sacred offering of body
and mind at the holy altar of Love.
Rama's Vedanta is the beautiful calm of that
super-consciousness which transcends the limits
of body and mind where all sound dies, where .
the sun'and moon get dissolved, where the wliole
cosmos ripples like a dream and is eddied into
the Infinite. It is from here that he throws the

·( 28,) 1 ladder for us to reach him and see the sights of the world below Pererinial peace is dilfused there and the man is entirely lost in God All discussion ceases there And those who are there simply look around and smile and say to every object 'thou art good " thou art pure thou art holy thou art That's · Neither the sun shines there, nor sparkles the moon. Pranas and Sound are bushet into silence, All life reposes in soal s ewee glumber, No gud, jo mdu, no coemos there, n') soul, Naught but golden Calm ard Peace and Splendour. In the summer vacation of 1899 he went to make a pleasure trip in Kashmir. 16 (1) Journeys. He yisited Shrinagar and thence went on a pilgrimage to Amar Nath also. On his return in the end of 1899 he suffered froin fever and colic pain to such an extent that one nigit no liop: remained of his life when he lay senseless during the nizit But nature had so.nething different in store and so he was alıight the next day Thereafter he desired that his thouglits and ideas should reach the public as soon as possible For this an Urdu magazine called "Alif" was started and continued for some time from a new press called Anand Press managed by swami Narayaną and sup. ported chiefly by L Har Lal He took great ·( 29 ) delight in vriting original articles to this magazine, so much so that he now wanted to leave off his two hours service in the college also. In the mean while having a desire to see the sea he went to Karachi and Sukkur where he was honorably received by so.ne kini admirers and fassed a few day there in great pleasure although he did not take with him a single After the issue of the 3rd No of his magazine Alif, he was so saturated with spirituality and overfilled with it that he could no longer remain shut up in his household or the crowded towns. pie, So in July 1900 he resigned his service and went to jungles along with a few (ii) Vanprastha companions including his wife and children. 'All of them reached Hardwar and thence they went to Tehri by way of Devaprayag. There they took up their abode in a calm, quiet and lonely but very charming place in a garden by the side of the Ganges, Here Rama ordered his companions to throw away all the cash if they had any (iri) True Faith and Incident into the Ganges and keeping faith in God to sit all absorbed in Hini Who alone maintains and takes care of all. He said that if any of them suffered from any want it would be only due to his own want of full faith

·( 30 )
in Him and if so it would be far better for such
a one to die than to live a miserable life wanting
in faith in the Creator.
It so happened the same day that Swami
Rama Nath, the manager of the Calcutta Kshetra
of Rishikesh was touring about in connection
with the arrangements of Kshetras of Gangottari
route, He heard about Raina and came to visit
him in the garden.
On seeing him all absorbed in God-conscious,
ness, he, of his own accord, ordered the shop.
keeper, who accompained hi.n, to supply rupees
ten worth of corn every month to these men
engaged in spiritual exercises.
After this strange incident, all of them were
struck with wonder and a firm faith in God took
hold of them for future, more than ever. All of
them began to practise meditation etc, with full
faith and thorough concentration and Rama now
began to contribute to : Alif 'with a greater zeal
and fuller energy.
One night Ramı, all of a sudden, left all
sleeping and went out all alone in the midnight
towards Uttar Kashi. When walking or rather
feeling his way out in the dark Himalayan gorge;
at a time when all was silent, the clouds gathered

·( 31 ) in the lightening flashed forth aiid the rain burst out in a storm over the lovely traveller, 'bare: footed, bare-headed, no umbrella, no clothes, save a single dhoti, But on and on he went until he saw the very path give way before him under the heavy deluge and torrents of water rushing over the stoep rocks And yet Rama was not to be daunted. He scaled and climbed the mountain side catching hold of the grasses and boulders a fcat which cven a mountain goat could not possibly do under t'ic conditions. In a moment he had crossed the gulf-and was shouting on the top of a hill by himself Om! Om !! Om !!! Nothing could harm nothing could dare injure One who had rcalized himself to be one with the Universal Self, Even Death itself had to await his orders. and sa On his susiden absenca, Rama's wife felt th: shock very keenly and fell down in illness from which she could not recover herself cven after Rama had come back a few days after she desired to go back to her home along with her young son Brahmanınd. She was therefore 'ordered to go back in care of Swami Narayana who took her to the plains an / returned back. After a period of 6 months of solitary lifc in the jungles, in the beginning of (iv) Sannyas? 1901, just a few days before the Ashram passing away of Swami Viveka.

·( 32 ) nand, Rama desired to take 'Sannyasa He had the permission of the Shankaracharya of Sharada Matha to 'take Sannyasa by the Ganges side when he might find himself qualified to do so. It was now in the midst of the Ganges that he made over charge of his sacred thread to the rushing current and put on his orange robes with a continuous chant of the sacred syllable, OM! ON!! OM !!! After this he remained wrapt in deep meditation and Anand for 'hours together at the banks of his dear Ganges. Gosain Tirtha Rama was now Swami Rama Tirtha, having come in the order of Tirtha Sannyasa of the Sharada Peetha -Dwarka and hereafter he began to live all along by himself in the same jungle allowing nobody to see him except on very rare occasions After a six months residence here, as many people began to come for his 17. Further travels in visit, he changed his place on 14th Himalayas and June 1901 'to a cave about 4 or 5 pluins. miles away and after a few months more he left this place also on 16th August 1901 with Narayana and L. Tula Ram for Yamunottari. Gan.gottari Triyugi Narayana, Kedar Nath and Badari Narayan. For a month they lived in Yamunottari, near the hot springs in a cave and a

·( 33 )
wooden house and also made an ascent over the
Sumeru Mount, the white snowy peak at the
sources of the river Yamuna After this they crus.
sed over snowy hills by a narrow pith, direct but
dangerous over which no pilgrim cold venture
and reached Gangottari on the 3rd day instead of
10 or 1.2 days usually taken by others by. the
ordinary path, Again after a monili's stay at
Gangottari they went to Kedar Nath and Badari.
Narayan by way of Triyugi Narayan and reached
Badari Narayan a wcek beforc Diwali.
The return was made in December 1901 by way
of Almorah to Mathura where Swami Rama
was invited by Swami Shivagan Acharya who had
elected him as president of a religious society.
Here his lectures were allended by thousands
who were so attracted by his personality and all.
pervading love that they followed himn like Gopis
following Krishna over.shrubs anci rough ground
and sat down on bire ground to listen to huin by
th: Yamuna side till late in the winter night
Thence he was invited by is. Surjan Lal l'andey
tu Fyzabad ir the second annual inceting of
Sadharan Dharma Sabhiz in February 1902.
After that in j'ay 190: he retired into the thick
jungles oi Tehri State in the Himalayas cncc
inore for ineditation in solitude.

·( 34 ) Here once the Maharaja Saheb of Tehrí, while on his way to Dehradun lappened to touch the skirts of the forest where Rama was residing and on hearing of Rama Maharaja Saheb felt very anxious to see him. He had become agnostic through the influence of some · Western philosophy like that ct Herbert Spencer and did not believe in the existence of God On meeting Rama all his doubts were dispelled ons by one during a long continued talk and after that he requested Rama to grace Tehri for his sake which Raina accepted with pleasure. In July 1902 it was published in the news. papers that a Religions Confe- 18. Foreign Travels, rence was going to be held in Japan in which all the religious Leaders were invited to attend Maharaja Sabeb of Tehri requested Rama to go to that Conference and preach Vedan'a Rama accepted the request and Malaraja Saheb inade all the arrangements for kama's voyage through Ihomas Cook & Co. Ramı went to Calcutta alone but when people insisted much on his taking a companion suami Narayana his disciple was taken with him. They left Calcutta for Jap.l} on 28th August 1902 l'uring the voyage they (1) Japan touched Penang Ilongkong Shan. ghai Naga Saki and finally

·( 35 )
Yokohama. They were cordially received by the
Sindl merchants at these parts and hat i week's .
halt at Hongkong for a change of ship and Rama,
lectured there to the all attentive and interested
audience On reaching Japan they learnt that
there was 110 Religious Conference there and
that it was all wrong news, However, they
proceeded to the capital Tokyo to ascertain the
facts for ceriain and met there many indian
Students who had come to learn arts and
sciences in Japan Rama happened to ineet
with alr. Puran, there who had just started an
Indo Japanese Club for the promotion and help
oi Indian Students in Japan and who was appoint,
ed its Secretary Rama also gave a lecture on
Secret of success in Tokyo College which
pro.
duced a deep and lasting effect on the hearts of
the Students and Professors.
Professor Chhatre's Circus happened to be
there at the time who became an ardent admirer
of Rama and on his request Rama accompanied
him to Imerica Here Mr. Puran being decply.
effected by Rama's speeches tookSannyas to serve
all humanity and roamed about in all the Japa:
Diese towns and also issued a magazine "Thunder.
ing Dawn", but on his return to India he again be.
came a-householder and subsequently a sikla.(his.

·( 36 ) family religion) while Swami Narayana who had accompanied Rama upto Japan was advise'l by hiin to travel in a different direction preaching Vedanta, viz. Burma, Ceylon, Africa and Europe. Rama when he reached America gave a number of lectures sometimes for (ii) America. three hours together of which the shorthand notes were taken by the Americalls and typewritten copies presented to Rama. Those copies were afterwards printed in India in the forın of four volumes called "In Woods of God-Realization" In cimerica, where everything is sold and has its value in dollars Rama never allowed his lectures to be attended by l'ickets although it cost a good deal to hire halls for his lectures, This in itself is a testimony of how much the Americans loved Rama and appreciated his lectures. Rama accompanied Prof Chhatre upto Siatle Wash but after that the Americans made him their own guest and one of them Dr. Albert Hiller served him with all heart and inind for about a year and a half at San Francisco Some of the Americanis moved by Rama organized Societies for the help of the poor' Indian Students in America and also to gain daily Spiritual food from the society of Rama.they organized a body called the Hermetic ·( 37 ) Brotherhood Tlie Americans became so much enamoured of Rama that they took his photo like that of Christ and published it in the l'apers under the heading "Living Christ has come to America,'The President of the United States also came to visit Rama and although the Millionaires of America liked to put him up in their palatial buildings Rama liked forests more and always used to take his abode on some mountain side far away from the busy haunts of mankind and roamed about in a single thin cloth even in the icy cold of North America living simply on nuts, fruits, vegetables and milk, He was full of unresistable joy and laughter and nobody could remain sorry in his company. All doubts vanished like vapours before his sunny face. Once an American lady, a resolute atheist came to discuss with him but on seeing Rama all absorbed in Samadhi, she waited in and when Rama came to his normal consciousness she broke the silence with the words "My lord I am not an atheist. My doubts have disappeared on seeing you Mrs, Wellman, another American lady, loved and admired Rama so deeply that she renounced all Western dress and putting on the Sanyasi's Orange Pobes she wandered from town to town ·( 38 ) without any inoney but with full trust in God and coming to India visited with great pleasure, the birth place of Rama, the village Muririwala in the district Gujranwala of Punjab Such was the Universal love of Kama that it not only moved the hearts of a nericans bit when he w.us in Egypt on his return in Cairo he bewitched the hearts of Mohamedans by his lucid lecture in Persian and was called by them the Hindu Philosopher About two and a half years travel in foreign countries Rama returned to India 19. Return to and landed in Bombay in 1904, India, His first lecture on his return was organized in Boinbay, whence he made a tour through Agra, Muttra and Lucknow to Pushkarraj in Ajmer, giving his worldwide experiences to the all expectant audience Arya Samajis, Sanatan Dharmis, Brahmo Samajis, Sikhs even Christians and Mahomedans all alike joined his reception wherever he went, and when asked to start a new society he simply answered that all societies were his own and that he would work through them, He loved mother India So much so that he realized himself as India incarnate and professed that within 10 years ludia would get practical Vedanta and that love would conquer hate to unite man s hearts, ·! 39 ) In the meanwhile Swami Narayana. leaving Japan visited Singapur, Penang. 20. Narayan's Burmah and Ceylon After that Travels, he went to Africa, visited Port Said Cairo (Egypt). Alexandria Gozo, Malta Tunis Algiers, Morocco and Gibralter etc, and lastly reached London in September 1903, whereafter about a 5 months' stay he fell ill owing to the severe winter and was advised to leave London at once He therefore "in January 1904, on receiving orders fro.n Rama returned to India and reached Bombay in July 1904 six months before Rama's return, and in October 1905 when Rami went to Hirdwir after a tour in Bengal and U. P and fell there ill he came to him from his tour Rama was dangerously ill for over a week and when recovered went to Vuzaffar Nagar for a change of climate and sent Narayana to Lucknow. After regaining health Rama desired to seek solitude and called Narayana back. - 21. Himalayas Hence in November 1935 Rama again. and Varayana went by way of Hardwar and Rishikesh to Vyas Ashrama a very fierce and lovely forest on the other side of the Ganges where Rishi Veda Vyas, the author of Mahabharat, is said to have performed his tapas.

·( 40 ) There they passed their winter of 1906 in lovely straw hyts, a couple of milcs distant from cach other and Rama studied and meditated over Nirukta and Sama Veda. . In thic suinmer they moved on further to Devaprayag Tehri, and went to Vasishtha .Ishram, a place about 12 or 13 thousand feet high above the scalcvel and so miles far from Tehri where Rama began to live in the care of Vasishtha Muni in Niarch 1975, and sent Narayana in his place to the plains to lecture in the various mcctings wherever he was invited But Rama's body soon fell ill and Narayana had to como back after two months. On his arrival they shifted their habitats by a few miles more ex. perimentally so that Rama now began to live in a cave at a greater height* while Narayana moved down in the valley. Thie scencry round this cave is described by Rama in his ictters as the " Garden of Fairies,' There was another cave above this whicla was occupied by an enormous snake (Azdaha) while another cave across the valley and just opposite to Rama's was the den of a large tiger who used to look at Rama from his place and sometimes passed by Kaina's cave also which was a large an i open one. This cave was quito ·( 41 ) unprotected either from wild beasts, of which there was no fear for Ramı whom 'beasts and men all obeyed in his universal love or from rain which really proved a nuisance specially when the rains set in and wetted all the clothes, and goods and keeping Rama awake during the nights. He had therefore to quit this place also and came down to the plain in the valley where the hill-men at once constructed for him a Kuti (small hut , . Here Mr. Puran with two coinpz. nions came to see Rama in his Vasishtha Ashrama and lived for about a month. kama was at this time taking for food only milk as the local grains did not suit him and on the arrival of these guests he was pressed by them to take some grain food also. He did so, moved by their love but he as well as the new comers fell down sick with dysen. try and fever They then asked, Rama to move down to plains which he accepted with the limitation not to go beyond Tehri Hence Narayana went to make the necessary arrangements for departure and Mr. Puran accompanied him to return to the plains Rama also walked with them for a mile and in the way told Mr Puran that. 22 Forebodlogs. Rama may soon have his pen at rest and his tongue silent as he ·( 42 ) had become too weak and that he may perhaps no more visit the plains Heace he advised that they should no.y themselves beco ne Rama and read, write and work all absorbed in Him These remarks brought down a stream of tears n. their eyes and it really proved the last meeting with Rama of Vr Puran Now in order that the place may not be shifted too often Raina searched for a suli. 23. L'ist Solitudr, tude fit for every season at the bins of the Ganges somewhere near Teh:i. He did find such place where some Mahatmas had lived for long and which was in a solitude surrounded by the Ganges on three sides. Here Maharaja Saheb of Tehri had at once built for him a Kuti according to Rama's own plan, Narayana was now told by Rama to go to live in Bamrogi cave some miles away where they had 0:10+ previjusly stayed for some time, and was advised by hi o to come to see Raina weekly on Sundays unless specially called When sending off Narayana to the cave Rama accompanied hiin for over a mile even bare fonted and bare-headed and on reaching the road addressed him with the same remark', as to Mr. Puran that it may probably soon happen that Rama's pen.may cease to run and his tongue may stop to speak. That Rama no more ·43) might be felt inclined to tnuch any worldly work and...may never leave the Ganges side to go down to the plains again. That wherever he' invited Narayana will have to go and hence he should dive himself deep in Real Rama while in the solitude care and come out of it all heart; body and soul transformed into Rama or Vedanta incarnate, Narayana had not lived there for five days. shen suddenly a messenger came 24. The grofal there and brought him the most message and end, heart rending news of Rama haring been carried away by the Ganges while bathing in it, Rama, while exercising against the rushing waters of the Ganges as was his wont, this time rather in decp water was suddenly carried away into a whirlpool where he struggled long and though finally came out with a strong dive, but being exhausted was cariied all'ay further to midcurrent where at last he left his body uttering loudly Aum! Aum !! A um !!! Narayana and Mr. Puan afterwards found his last written passage on the 25 Tasi Xote, table which ran as follows: • O Death ! Take away this body if you please ! I care not I have encugh of bodies to use. I can wear those divine silver

·( 44 )
threads, the beams of moon and live.
1 Cart
roam as divine minstrel, putting on the guise
of hilly streams and mountain brooks
I can dance in the waves of sea I am the
breeze that proudly walks and I am the wind
inebriated. My all these shapes are wandering
shapes of change. I came down from yonder
bills raised the dead awalened the sleeping.
unveiled the fair faces of some and wiped the
tears of a few weeping ones. The Bulbul and
the rose both I saw and I comforted them.
touched this I touched that, I doff iny lat and
off I am
Here I go and there I go, none can
I keep nothing with me.”
I
find me
OM I OM !! OM !

·MATHEMATICS
Its Importance
AND
THE WAY TO EXCEL IN IT.

·No text on this page.

·THE IMPORTANCE OF THE STUDY OF MATHEMATICS, I am fully aware of the difficulties which I shall have to encounter in trying to enlist your interest in what is commonly called ' a dry subject.” The usefulness of the study of Mathematics sounds like a paradox to the superficial observer, An ordinary man cannot help putting such questions as:-- (a) Why should we bother our heads about the 47th Proposition of Euclid's First Book ? () Or what use in the world can the Binomial Theorem be ? (c) Why should we spend a considerable portion of our life at a, b, c, and long s (f)? (a) What is the use of dealing with the Greek Mathematical signs? 1. The inability to answer questions like these or the apparent uselessness of Mathematica makes this study very unpopular.

·[ 2 ] 2, Another reason why it is disliked is that .it is a very hard subject which taxes both the memory and the intellect; it is difficult to understand and more difficult to reinember To read it is not like walking on a smooth paved road ; but here the path is, so to speak, both slippery and rough, presents many stumbling blocks and rubs in the way. 3. A third reason why Mathematics is felt so heavy and tedious is that generally it is not administered in proper doses or in an agreeable form ; in other words, teachers do not always try to make it attractive. Carbon dioxide swallowed as in soda-water, in conducive to liealth; but inhaled, it injures the system. Just so, Mathematics does us good only if taken or studied in the proper way. Students as a rule, complain against the University because Mathematics is made a compulsory subject in some examinations, they blame the Syndics and have all sorts of hard names to give to Mathemnatical writers, To begin with, let us, for the sake of argu. ment assume that Mathematics has really no reward to offer, has nuthing to pay. But, dear friends, let us not in whatever we undertake, be led and guided by a desire of reward, This !

·( 3 )
Imercenary spirit ought to be checked. The
event or fruit of any action ought not to influence
us; let us do whatever we engage in, goaded by
a sense of duty and tot drawn by the bright
future :-
If duty calls to brazen talle,
How base the foul who dinches.
Let us work into life the following advice of
the author of Bhagwad Gita:-
.................... Find full retraid
Of doing right in right! Let riglit deeds be
Thy motive, not the fruit thich comes from them,
And live ip action! Labour ! Make thine acte,
Thy piety..............
......"
Learn to acquire knowledge for its own sake;
hunger and thirst after knowledge, Learn a
lesson from tlie life of Old King Ulysses who
with one foot in the grave wooes knowledge and
asks his followers
To follotr knowledge like a sinking flar,
Brygad the ulmoet bound of huinan thought.
The assumption above made is far from
being correct. The advantages of Mathematics
are very many. They do not lie on the surface,
but are hidden and concealed -
(i) Mathematics is like the ocean rough,
boisterous, and fearful on the surface;.

·- [ 4 ] but having precious pearls, and gems of the purest ray serene at the bottom; or (ii) it may be compared to the statues of the old satyrs and sileni of Greece ; repulsive figures to look at but enclos. ing within them the finished and fascina: ting statues of the most beloved gods of the Greeks. (iii) Like the solar light it appears quite colourless to the unthinking multitude, while it is in reality composed of the colours of the rainbow, Mathematics (Gr. Mathe-Matike) in its ginal sense signifies skill, knowledge on 'science." And in all its subsequent developement it has had the idea of "skill, knowledge -or science" always underlying it. It is in no small measure to Mathematics that the world owes its Sciences of Astronomy, Optics Acoustics, Statics, Dynamics, Hydrostatics, Hydrodynamics Thermodynamics, Magnetism, etc; and the Arts of Navigation, Ingineering, Architecture, and the like. - Mathematics is well called an exact science and a sure and certain branch of knowledge (cf. the phrase " Mathematical certainty)," ·[ 5 ] Geometry," Pascal observes, " is almost the only subject in which we find truths wherein all men agree ; and one cause of this is that geometricians alone regard the true laws of demonstration." So Geometry or Mathematics, we may say, has been like that solid and substantial food to science which goes for the most part to form bone or the supporting element. According to Roger Bacon, Mathematics is the "gateway and the key to other sciences.” Professor Ball says "It is interesting to note that advance in our knowledge of Physics is largely due to the application to it of Mathematics, and every year it becomes more difficult for an experimenter to make any mark in the subject unless he is also a Mathematician." What generally happens is that the Mathe. matician takes the results of some every day observations and raises on them splendid superstructures which attract the attention of the Experimentalist, who steps forward and verifies by experiment the results thought out by the Mathematician. Then the labours of the two com. bined ențich the world with inventions and discoveries ; give to it its railways, telegraphs; balloons and what not. Happy the man who is a Mathematician and Experimentalist in one.

·[ 6 ] 1) - 8 " The most general division of Mathematics," says Herbert Spencer, "dealing with number guides all industrial activities, be they those by which processes are adjusted, or estimates framed or commodities bought and sold or accounts kept. No one needs to inave the value of this division of Abstract Science insisted upon," "For the higher arts of construction," the same writer continues to say some acquaintance with the more special division of Mathematics is indispensable. The village carpenter who lays out his work by empirical rules, equally with the builder of a Britanica-Bridge, makes hourly reference to the laws of spice.relations. The surveyor who measures the land purchased ; the architect in designing a minsion to be built on it; the builder when laying out the foundations; the masons in cutting the stones ; and the various artizans who put up the fittings : are all guided by geometrical truths. Railway making is regu. lated from beginning to end by geometry ; alike in the preparation of plans and sections ; in staking out the line ; in the measuration of cuttings and embankments ; in the design'ng and building of bridges, culverts viaducts, tunnels, stations. Similarly with the harbours, docks, piers and various engineering and archi. tectural works that fringe the coasts and

·[ 7 ]
overspread the country as well as the mines that
run lin icrneath it And now a days even the
farmer, for the correct laying out of his drains,
has recourse to the level-that is, to geometrical
principles.
"On the application of Jechanics ( a branch
of Applied Mathematics ) depends the success of
modern manufactures The properties of the
lever, the whiccl.an:1-axlc, etc, arc rccognised in
every machine, and to machinery in these times
we owe all production." The following is the case
in England and will in no long time be the case
here too :
"Trace thic history of the breakfast roll The
soil out of which it cam: was drained with
machine.mide tiles; the surface was turned over
by a machinc ; the wheat was reaped, thrashed
and winnowed by machines; by machinery it was
ground and bolted ; and had the four bcen sent
to Gosport, it might have been made into
biscuits by a machine. Look round the rooin in
which
you sit. If modern, probably the bricks
in its walls arc machinc.inare and by inachinery
the flooring was sawn and player, the mantel.
shell sawn and polished, the paper-hangings made
and painted. The vencer on the table, the turned
legs of the chairs, the carpet, the curtains are all
product of machinery,

·[ 8 ] " Your clothing-plain, figured or printedis it not wholly woven, nay, perhaps even sewn by machinery? And the volume you are reading, are not its leaves fabricated by 009 machinc and covered with these words by another ? Add to this that for the means of distribution over land and sea, we are similarly indebted. And then observe that according as knowledge of mechanics is well or ill applied to these ends comes success or failure. The engineer who miscalculates the strength of materials, builds a bridge that brca's do:vn. The iminuíacturer who uses a bad machine cannot compete with another whose machine wastes less in friction and inertia, The shipbuilder adhering to the old model is outsailed by one who builds on the mechanically justified wave-line principle. And as the ability of a nation to hold its own against other nations depends on the skilled activity of its units, we see that on mechanical knowledge may turn the national fate,' Let us now see to whom most of the modern inventions and discoveries of which the world is so proud owe their origin ? By whom was the first Stean-engine made ? James Watt, a Mathematical Instrument maker, By whom was the clock invented ?

·[ 9 ] Galileo a Mathematician. By whom was the first telescope made? Galileo a Mathematician. By whoin, the Barometer ? Pascal a Mathematician, Who found out the amount of alloy in the golden Crown of King Hicro of Syracuse ? Archimedes, a Mathematician Who was it that discovered thc Law of of Gravitation ? Newton, the prince of Mathematicians. In a word, directly or indirectly almost all our conveniences and articles of comfort are due to this branch of Philosophy or Science which we call Mathematics, Professor Adams, the Mathematician forc. told the cxistence in thc hcarcns of satcllite not known to the world before, and then the practical astronomer actually discovered the samc. Mathematics enables us to calculate accurately distances, billions upon billions of milcs in length, as the distanccs of stars, cic; and it also enables us to measure magnitudes about onc billionth part of a cubic inch in volume, like the size of a molecule or atom. From finitc quanti. ties it leads us on to the region of the infinite, ·[ 10 ] By Mathematics we discover some of the Universal Laws of Nature written with incrasible ink on the faces of sukstances by the unering finger of the Almighty. In the lines and figures of Geometry welcarn those characters to use an expression of Galileo' in which the great book of the universe is written" ) In Statics and Dynamics the Mathematician deals with forces varying according to different laws and in case a new kind of energy should come to light and give rise to forces obeying laws different from those which the forces of ordinary nature obey, the Mathematician will be found fully equipped to receive it; whereas the mere experimentalist if not calling Mathematics to his aid, will be at a loss how to deal with it at the first sight. Let a 11cw fluid bc discovered and its fundamental property lncun; it will find itself alrcady registered in the works on Higher Hydrostatics as an old servant with specified duties to discharge 'There is a variety among individuals of all specics : again the different species of the same genus are in no instance exactly alikc; and the different gcncra differ widely. So, ' persume that different plancts of the same Solar System have 110 fronotony and the different Solar Sys- ·[ ] tems are not alike in every respect They are, in all probability governed by now laws and are blessed with new materials, nel: liquids and new kinds of Energy. Mathematics cinbraces the properties of these new things as well as those of the old familiar ones This is knowledge of intrinsic worth. Its rules and laws govern the phenomena and facts that can ever takc pla:c on the background of Eternity. 'l'he old order ceaseth, yielding place to new but thc Mathematical dogmas remain still controlling all these vicissitudes and undergoing no change in themselves. Says Herbert Spencer --" of course as thosc facts which concern all mankind throughout all timcs must be held of greater moment than thosc which concern only a portion of them during the continuance of a fashion, it follows that in a ralionul cs:imate, kuowledge of such facts, being knowledge of intrinsic worth, must, other things being cquul take precedencc of knowledge that is of quasi-intrinsic or conventional worth." 1 Hence you can ju lyc of the importance of Mathematics which, beyond doubt, imparts knowledge of the kind of facts here alluded to.

·[ 12 ] If most people pride themselves on posses. sing a knowledge of Law, ( Law dealing with inatters of this transient world ), why should a knowledge of the eternal laws dealing with all worlds and possibly with the world to come be disdained, " That very law thich moulds a lear, And bids it trickle from its source, Tlint law preserves the earth a sphere, And guides the planets in thoir course. This law and many similar laws are treated in the works on Mathematics, To show that the sphere of Mathematics is not confined to the płysical objects alone, but extends over the mental and the psychic phenomena as well, I may refer to the distinguished writers on the Calculus of Probabilities who have applied it to Belief and also to Edgeworth and Jevons who have shown it to be capable of application to Feelings. Milton holds that a part of the happiness of the pious will consist in the consciousness of the knowledge which they acquired in this world. If this be true, Mathe.natics is sure to make you happier in the world to come, as it embodies knowledge of the widest application, ·[ 13 ] 1 I have been discussing so far the value of Mathematics as knowledge. Now, let us discuss its value in the way of discipline. And here, without question, it holds a supreme place. The Vernacular word for Mathematics is Riyazi” and this very name signifies "pertaining to " Riyázat” or discipline The study of Mathematics involves a mental exercise best fitted for strengthening the faculties. The advantages of Physical exercise are not apparent to an ordinary Indian boy ; and Physical exercise is not so pleasant to him as eatables being ignorant of the fact that in proportion as he takes more physical exercise, he will enjoy and digest the eatables better. Similarly the advantages of mental exercise involved in the study of Mathematics are not apparent to an ordinary Indian student, and so, he reads Mathematics with great ieluctance, not knowing that in proportion as he studies more of Mathematics, he will relish and master other subjects better. "I have mentioned Mathematics," says Lock, 'as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all inen should be deep Mathema. ticians, but that having got the reasoning which that study necessarily brings the mind to, they

·[ 14 ]
might be able to transfer il to o‘her parts of know.
\edge as they shall have occasion "
There are men who are already playsically
strong, yet physical exercise will inake them
still stronger Similarly there are men already
intellectually very strong yet a study of Mathe.
matics will most certainly adil to their intellec
tual powers.
Rev. Dr. Chalmers has stated : -"I am not
aware that as an expounder to the people of the
lessons of the Gospel, lam much the better for
knowing that the tirree angles of a triangle are
together equal to tivo right angles ; or, that the
square on the hypotenuse is equal to the squares
of the two containing sides in a right-angled
triangle. But I have a strong persuution that
both the power to apprehend and the power to
convince may be migátily strengthened that
the habit of clear and consecutive reasoning may
be firmly established by the successive journeys
which the mind is called on to perform along the
pathway of Geometrical Demonstration, "he
truth is that as a preparative whether for the bar
or for the pulpits I have more value in Mathemną
t'cs for the exercise which the mind takes as it
travels along the road, than for all the spoil which
it gathers at the landing place.''

·[ 15 ] The author of " The History and l'ilusopisy of the Inductive Sciences" has shown in his "Thoughts on the study of Mathematics so that Mathematical studics judiciously puisued from one of the most cffective means of developing and cultivating the reason : and lhat "the object of a liberul education is to devel: pe the whole mental system of a man;- to make speculative inferences coincide with his practical convictions ; to enable tim to give a reason for the belief that is in him, and not to Icave him in the couldition of Soloman's sluggard, who is wiscr in his own conceit than seven men who can render a reason." To this may be subjoined the judgment of Jolin Stuart Jill, siļich he has recorded in his invaluable system of Logic , Vol 11. 1 in the following terms :-". The value of Mathematical instruction as a preparation for the more difficult investigations / pliysiclcgy, sccicly governinent, etc.) consists in the application of its method, Mathematics will user remain the frost perfect 1) pc of the Deductive Method in gercral; and the applications of Mathematics to the branches of l'hysics ſur pislı the cnly school in which philosopliers can Icarn the most difficult and important luiticavi their art, 11.c cmployer.cat of the laws of flic in pler i licacir.coa ici ca plaining and

·[ 16 ]
.
predicting those of the more complex. These
grounds are quite sufficient for decming Mathe.
matical training and indispensable basis of real
scientific education and regarding., with Plato,
one who is a ye tot er þros, as wanting in
one of tlie inost essential qualifications for the
successful cultivation of the higher branches of
philosophy"
'The Study of Mathematics strengthens both
the intellect and memory and tends to impart to
us an assimilative memory rather than a sensu.
ous one inasmuch as it teaches us to remember
things by the aid of the intellect or thinking
faculties; and discourages us from memorising
a demonstration and the like by endless repeti.
tion It gives us a Memory which has brought
jinmense wealth to , Professor Loisctte, The
nature of the subject admits of no such thing as
crainining. We cannot cram Mathematics, what.
ever we learn of it inust be got up intelligently.
It is true that Mathematics at first appears
to be a very dry subject and inost distateful, but
for that very reason we ought to study it with
zest and zea). In so doing, we shall be the
stronger in will-power " Perhaps says Huxley
"th: most valuable result of all education is the
ability to inake yourself to the thing you have to

·[ 17 ] do when it ought to be done whether you like it or not, It is the first lesson that ought to be learned, and however early a man's training begins, it is probably the last lesson that he learns thoroughly " The abstruse nature of the subject compels a student to concentrate his attention Mathe matics is the best cure for mind-wandering. Bacon says —"If a mali's wits wander, let him study Mathematics, for in demonstration it his wits be called away ever so little, he must begin again." Now, if on no other account, on account of this grand virtue which it inculcates, viz., concentration of attention, we ought to value Mathematics, No one who is stricken with absentmindedness can make his mark in any department of human activity. The path to proficiency in Mathematics is so rough, and so hard an application is necessary that on the way we lose all our roughness and become perfectly smooth and frictionless, as it were, just as the wooden harrow used in this country becomes smooth by passing over the rough and uneven ground turned into clods by the plough Now a smooth ball or the like if put in rolling or sliding motion on the College floor will ·[ 18 ] come to rest very long after a rough ball that was put in motion simultaniously with it So, brains that have lost a considerable amount of their friction by working in the rugged field of Mathe. matics and have now been smoothed down, so to speak, when once put in motion or set to some hard task will, other things being equil, stop or be tired out long after the brains that have not been similarly trained Not only does the study of Mathematics thy; habituzte us to stealfastness anl perse. verence, but it engenders in us a strong inclina. tion to work. It tends to make us bitter opp). nents to inaction, it stores in us immense energy. The student of Mathematics being compelled to work very hard and long for the sake of success in his subject, goes on working hard even after this impressed force is withdrawn, being then impelled by the energy accu nulated in him just as a railway train continues travelling for a long tim: even after th: steam is 'shut off But alas! for the rash youth, who set free from the great motive power - Mathematics or other branch of learning -and enter life, than they come to a dead stop on account of the brake of sensual indulgence; or at least get their mɔtion consider. ably retarded by that brake. no sooner are soma ·[ 19 ] US Matliematics, startling as it may sound, aids Religion in a most remarkable manner and strengthens the foundation of moral character, Every now and then it puts us in a most humi. liating mood, it makes realize our own incapability, it repeatedly brings us face to face with something which we think we calinot surmount. It makes us humble and meek It tends to do away with our vanity and self-conceit. It breaks us down and consequently exercises the will of God on us "Do you," says. Theodore, Monod a French divine "know what is God's chief difficulty with us? It is not the making us, it is the breaking us It is not the edifying us it is the putting us down, And therefore it is that God's chief instrument for edification is the picks-axe He must break us down, down, down, and whatever he gives us to do for His service He will first of all show us that we are not able to do it O Gad, ta'e ine, break me, and make me." The value of Mathematics in this respect is well pointed out in the following remark by Loc' :- A man in the study of Mathematics will see that however good he may think his understanding yet in many things and thɔs. very visible, it inay fail him This would take off that presumption that most men have of themselves in this put and they would not be ·[ 20. ] apt to think their minds wanted no helps to enlarge them, but there could be nothing added to the acuteness and penetration of their understandings.' All this shows that the sharp discipline to which it subjects a man has a wonderful influence in smoothing down his asperities in accustoming him, as a rule, to the habits of patience, perseverance, self-denial and humi. lity. * True science," says Huxley, (including Mathematics undoubtedly), and true religion are twín sísters, and the separation of either from the other is sure to prove the death of both. Science prospers exactly in proportion as it is religious; an i religion furishes in eract proportion to the scientific depth and fitness of its basis. The great deeds of philosophers have been less the fruit of their intellect than of the direction of that intellect ........ by an eminently religious tone of mind. Truth has yielded rather to their þrtience, their love their single hearle.l. ness and their self duni il than to their logical acumen. Isaac Todhunter in his Essays on Education says that of all the subjects required for passing University Examinations, Mathematics furnishes the most reliable test of a man's working pɔ.vers.

·[ 21 w may have A student may do remarkably well in the, Ixamination in a language; and yet this been owing to his keeping constant compairy with a man who always speaks that language and is a thorough master of it. A student may distinguish himself in History in some Examination, and yet this inay largely be due to his passitely hcaring other students while they were preparing that subject for their Examination. A man may obtain very high marks in Practical Science Examination; and yet this may bo on account of his having familiarized himself with the Science-rlpparatus and its use for amusement s sahe. And so with the other subjects. But a man who excels in Mathematics could not have done so, except by dint of hard labour, He proves himself capable of facing difficulties and doing his duty well, however disagrceable that duly may be. a Nothing particular has as yet been said about ' problems” as against "book.work" in iviathematics,. They are hard puts to crack for the student But once cracked they yield an ambrosial kernel; and the student thus derives an exquisite pleasure from the sweets of intellec. tual conquest, No other branch of knowledge can present a lilc phenomenon. After a hard ·[ 2 22 ] problem has been solved you will often observe the dlathematician's eye brighten and at length. with a pleasure (of which the ecstacy of Archime. des was but a simple expansion ) hear him explain, "I have got it I have got ito It inay not be out of place to say something as to how charming and fascinating this subject has been to some persons or to what extent people of yore have been impressed by its importance. Plato loved it to such a degree that the inscription over the entrance to his school ran- "Let none ignorant of Geometry enter my door", and on one occasion an applicant who knew no Geometry is said to have been refused admission, It is related of a Mathematician. that while he absorbed in in solving some problem the besieged city in which his house lay was taken by the chemy, and to the spot where he sat musing, came up with a drawn sword in hand a soldier who was about to break the slate of his life. The Mathematician who had been quite ignorant of the capture of the city, did not even now, lift up his head and look at the soldier. 'l he astonished soldier slicuted at the top of his voice to make the poor victim prepare for death At this the Mathematician iaised his eyes and said: · Wait a moment; I am ałout to solve it" (the problem). The city was captured by the (vas ·[ 23 ] enemy, but his heart had been captivated by Mathematics Sir Isaac Newton oftentimes, when busy at some Vathematical theorem used to forget taking his meals I may add two amusing anecdotes:-(1) Newton invited a friend to dinner and forgot it The friend arrived and found the philosopher in a fit of abstraction Dinner was brought up for one. The friend, without distur. bing Newton, sat down and depatched it Newton recovering from his reverie looked at the empty dishes and said : Really if it wasn't for the proof of the contrary before my eyes, I could have sworn i had not yet dined" (2) Once when riding home from Grantham he dismounted to lead his horse up a steep hill, when he turned at the top to remount he found that he had the bridle in his hand, while his horse had slipped it and gone away, Galileo had very long been purposely kept in ignorance of Mathematics, but one day, by chance hearing a lecture on Geometry, he was fascinated by the Science that he thenceforward devoted all his spare time to this study, and final. ly he got leave to discontinue his former studies. He preserved his enthusiasm for the subject in tpite of poverty public ridicule, and persecu- 8011.

·[ 24 ] And so did Kepler notwithstanding domes. tic troubles, poverty and other inconveniences, Archimedes could not disengage himself from Mathematical dreams even when walking or when bathing as is evidenced by the well-known story which says that archime.les one day while taking his bath was so much elated at the discovery he then made that unable to contain himself he immediately ran almost naked into the street crying Eureka, Eureka I have found it, I have found it." It is related of Euler that even in the perusal of Virgil's poetry he met with images that would recall the associations of his more fainiliar studies, and lead him back from the faity scenes of fiction to the element, more congenial to his nature, of Mathematical abstraction. Amongst the ancient Hindus, Mathematics was so extensively loved that evea their females were well versed in the subject. Amongst the rich, Mathematics has exercised its sway over Boyle, Cavendish, Napier, Lord Kelvin, and others. Amongst men of letters Milton, Bacon, Locke, Carlyle, Helps, Froude ... and many others may be counted among its fervent admirers, if not votaries, ·[ 25 ] Perhaps some of you can still see no connection between abstract and practical science, and hold the former in little esteem, despising mental discipline unless you perceive its direct reference to the actual business of life, and so reject Mathematics as of little practical interest, calling it with Alexander Pope as - " Tricks to show the stretch of homan brain, Mere curious pleasure or iogenious pain." Remember, Gentlemen, immediate usefulness alone is a fallacious recommendation for a branch of learning. Don't shun Pure Mathematics on the ground of its purely: speculative charicter. "That sound judgment." says Professor De Morgan in his remarkable introduction to the London Edition of Ram Chandra's Vaxima and Minima "that sound judgment which gives men well to know what is best for them as well as that faculty of invention which leads to development of resources and to the increase of wealth and comfort, are both materially advanced, perhaps cannot rapidly be advanced, without a great taste for pure specul ition among the general mass of the people, down to the lowest of those who can read and write .... ......." After giving a most satisfactory proof of the above statement the above-mentioned writer puts the conclusion in the following words :- ·[ 26 ] "The History of England as well as of other countries has impressed me with a strong con. viction that pure speculation is a powerful instrument in the progress of a nation." Plato advised the Athenians to betake themselves to the study of Dlathematics, in order to evade the pestilence incident to the international war which was raging in Grecce Mathematics is knowledge and consequently it is power. It is a weapon, though a very heavy one, If we cannot wield that weapon, the fault is all our own; because we could wield it if we would, by dint of patience and perseverance : and once wielded; that weapon is something awful in our hands, Knowledge of Mathematics is like an estate which should be watered and cultivated laboriously before it yields abun. dant crops. Many men have reaped rich harvests out of this apparently barren land. The processes of the Differentia Calculus seem far remote from the Propositions of Physical Science, yet Newton was led by their aid to found a system of Mechanics cqually suited to determine the motion of the stane falling to the ground, or the revolutions of the Planetary bodies. Conics is a branch of pure Mathematics dealing with the sections of a cone, It could hardly be ·[ 27 ] imagined as susceptible of any usefill or interest: Ing application whatever, But Kepler came and he applied it to the motions of heavenly bodies, thus clearing up most intricate difficulties in Astronomy. Jſoreover the same Conic Sections was found to apply to the motion of anything whatever projected here on our own planet; be it a cricket ball, an arrow or a bullet, or even our own bodies in the act of jumping. The process of finding the H. C. F of any two numbers in Algebra has been made use of by Sturm in solving with great ease Equations of any degree whatever. The Theory of Quadratic Equations was made use of by our own countryınan, Master Ram Chandra of Delhi, in working out problems of great practical interest in Maxima and Minima, In Trigonometry and Algebra we meet with what are called Exponential Functions and Imaginary or 1111 possible Quantities. When you first study them, I suppose you will be inclined to say "Of what use in the real world are Imaginary quanti. ties, why should we waste our time on Impossibilities p's My friends, let me inform you that what you will thus cast off with disdain, has lately been made the corner stone of a new mansion in the world of Science, being developed in to Hyperbolic Functions 'l he symbols e and Ti (ineaningless to the unthinking student,) repre- ·[ 28 ] sent numbers which enter into analysis : from whatever side Science and Art are approached. An anécdote might be quoted for illustration De Jorgan Was explaining to an actuary what was the chance that at the end of a given time a certain proportion of some group of people would be alive; and quoted the actuarial formula involying TT which he explained stood for the ratio of the circumference of a circle to its diameter His acquaintance, who had so far listened with interest, interrupted him and exclaimed, My dear friend, that must be a delusion; what can a circle have to do with the number of people alive at the end of a given time ?" Don't be surprised to know that Ball writes of a distinguished Professor remarking that" it is impossible to conceive of a universe in which e and it should dot exist." I sympathise with those of you to whom the abstract principles involved in Mathematics appear to have scarcely any use or aim ; but if you continue your inquiries, your malured judgment will rectify your first opinion and at length you will find yourselves possessed of, to use the words of Professor Hall," an instrument of matchless power and of universal application ; a language which nature must hear, and to which she shall always reply."

·[ 29 ] Even if the study of Mathematics bear 110 fruit at all, do not regard your labour spent ou it as wastci Nothing is wasicd or lost in naiure, matter is indestructible and cannot be lost, energy is indestructible and cannot be lost; and so I maintain labour is indestructible and cannot be lost. Rivers take away with them a great deal of carth and other substances froin the plains, and so far as we can see the carth carricd away is lost, but the same carth collects ir: the sca, and in course öl timc forms islands there. The Sundries up in the summer tanks, pools and lakes, and we think the water is lost; but bcforc autumn is ushered in, this samc water COMICS dren again in the form of rains. Similarly kinetic energy is converted into potential cnergy, thermal energy, clectric or any other form of Cheres, but it is nesc: lost, although it may so appear to 15, just ir: the same way, rest assured, lab.sur is never lost; it is sometimes changed july experience, at other times it becomes, as it were, storci up for future use; but it is never lost. The labour of Columbus. although it dici not bring forth the desired result, was far froin being lost; the attempts of Englishmen at finde ing the North-West passage to India although apparently fruitless, caused the Arctic Occan to be explored. Similarly attempls at finding thc philosopher's slonc lcd to thic discovery of the ·] a [ 30 Science of Chemistry. Again attempts at unreal Astrology led to real Astronomy. So, the ap parently bootless endeavours of geometricians at the duplication of a cube, the trisection of an angle, and the squaring of a circle, were the cause of Conic, Sections being discovered. The vain struggles and efforts to construct a perpetualmotion machine advanced most considerably the Science of Dynamics, The celebrated John Hunter occupied a great deal of his time in studying inust carefully the growth of deer's horn (a sheer waste of time and ener. gy in the opinion of most of usi; but this appa. rently useless knowledge well applied in the case of a dyins pitient was one of the causes which rendered his name immortal, dis labour was not inst an} sy will not your labour be lost which you devote to the study of Mathematics, but will reproduce itself in other forms of fruitful energy. It is rather sacrilegious to think of lost labour in connection with a subject of which in the words of no less an authority than Helmholtz we may say, "Of all branches of human knowledge, there is none wbich, like it, has 'sprung as a completely armed Minerva from the head of Jupiter; none before whose death-dealing Aegis doubt and inconsistency have so little dared to raise their eyes." .

·[ 31 ] The vibrations of a lamp suspended from thc ceiling taught Galileo liony to construct the first pendulum.clock; a falling apple gave Newton a lesson on the mysteries of the solar systein; a boiling kcttle instructed George Stephenson hus to make the steam enginc; a frog's log twitching when placed in contact with different metals directed Galvani to come to the important results wherein lay the germ of the Electric Telegrap!). If apparently insignificant objects could cach such important lessons, will not Mathematics (which mcans Knowledge and Sciclicc itself be able to teach you a great deal? Only a third cyc is wanted (an cye in tlic head or brain, Vabadler's third cye) to discover the Purculi of joy and glory on the inountains of Mathematics. Oh ! for the kcen penctrating cyc to which "Thrpe oro longting in trene, books in the running brooks, formoni in rloney and good in everything." Il care reaping abundantly the fruits of the labours of others, WVc travel by rail, the most desirablc kind of convcyancc; wc get our crrands run by clcctricity harnessed for our sakc, wc live in comfortable houses, wear the clothes cut and sewn to suit our convenience, get our food cooked and prepared in such a way as to keep

·[ 32 ]
Let us try
us in good health and many other things we
enjoy which have been thought out and worked
out for us by others. Let us not forget that we
also ought to do something for others in return
We owe a heavy debt to humanity.
to leave the world better than we found it. Let us
try to leave somne foot-prints on the sands of timne,
Let us try to dive deep into the Ocean of Science
and Mathematics and bring out, if possible,
some pearls which may adorn the world.
Then work, work; work with all your heart,
with all your might, remembering that werk is.
worship and reinembering also that work is
life. -
1 Pe live in decde, nnt days;
in thoughts, not breatlıs;
in feelings, not in tigures
on a dial,
He lives most who thinks most,
feels the noblest, acts the best."
Genuine work will be found to be its own
reward. Work is the normal state of man.

·How To Excel
IN
MATHEMATICS.
There is no royal road to Mathematics.
Mathematicians, like poets, cannot be made
but they are born, Still I have firm conviction
that the following guiding principles and cau.
tions, if strictly observed, shall convert Jathe.
matics from a cold. unsociable stranger with
knit brows and frowning countenance into a
warm-hearted, cheerful and loving friend,
1(a) Never approach Mathematics just after
taking heavy meals. Let the food be well digested,
and then apply yourself to this subject. Otherwise
you will find it a very dry and rather repulsive
study and most uninteresting.
(b) In days of hard Mathematical work you
ought to take light simple food that
you
can
digest very easily; and be temperate. Don't take
ghee in ex cess, High thinking and plain living
should go side by side.
2 (a) Don't attack Mathematical problems or
hard pieces of book-work when you are sleepy or
when about to go to bed. You will in that state
find them quite invincible and impregnable,

·[ 34 ]
Not only will they offer passive resistance, but
will then lay you Nat down on your bed. I'lainly
pealing you will in IWO Or three minutes,
altcr taking a difficult problctn in hand, fall fast
asleep. But you may, with adtantasc, at such
a timc, revise that part of Mathematics which
you arc alrcady thoroughly conversant with, or
work casy sums and simpic riders that require
very little mcnlal cxcrtion.
(b) In order to cxccl in Mathematics you
should always give to sleep what is its duc
Il'c caminot have a clcar brain iſ wc do not have
cnough of slccp. It is said of
a great
Mathematician, Des Cartes, that on account
of his delicate health, he was permitted to lic
in bed till late in the inornings; this was a
custom which lic always followed. and when he
visited l'ascal in 1647 he told him that the only
way to do good work in Mathematics and to pro.
serve his hcalth was never to allow any one to
make him get up in the morning before he felt
inclined to do so.
3 (a), 17, hon cier circumstances obligc you to
study difficult portions of Mathematics or solve
hard problcms just after taking mcals or just
before retiring to bed, you ought to keep standing
as you work, or be walking up and down while you

·[ 35 ]
think. Otherwise your efficiency of labour will
be very small, and -laziness will get the upper
hand of
you
(6) Never neglect to take bodily exercise.
This is a neglect which proves ruinous to most
students.
Irregular students waste the greater part
of their time in idleness but overwork themselves
just before the examination, taking no.exercise
and setting at nought the laws of health, Thus
they succeed very easily in breaking their health
though not in passing the exainination. Then,
is imputed to labour what is brought about in
reality by laziness; the charge is laid at the
door of hard work, whercas it was indolence
thąt impaired their health. Remember it is not
labour that kills a student, but it is laziness or
neglect of exercise that does so,
Workers are
sadly wanted in India, but not lazy - workers,
4
When you begin a new book, it is ad.
visable first, to go through the book-work of
the whole, at the same time doing the easy
sums which come out on the first or, at most at
the second trial. After thus once passing through
the book begin it anew, and omit no example,
By adopting this system, you will save a great

·[ 36 ] deal of your time and labour and your work will be most efficient, 5 As far as possible try to do cverything with your own enaided efforts. Yot only should you try to solve the examples by your own exertions, but try to do the book work also without the aid of the author. Try, as it were to rediscover everything. This will do you immense good. Read the heading in the case of each Article or the cnunciation in thic case of cach Proposition and then shut your book, and try if you can give your own demonstration, Think over the subject for a tiine, if your cxertions seem to be fruitless, read one or two sentences froin the top in that sirticle or Proposi. tion and then closing the book try to complete tlie proof; if even then your attempts avail nothing, read one or two 'sentences from the bottom of the same Article or Proposition, and do your best to supply the parts of thic proof not seen by you. If, then also you fail, read a little more of the book and try to fill up the gap yourself. Tbus a part at least of each Article or Proposition must by all means, bc drawn out from your own brain, if you want to acquire a sound knowledge of Mathematics, You may, at first read very little by this method, but whatever is mer ·[ 37 ] * not learnt in this way forms but a very poor part of cducation. By and by your power will incrcase and this process will no longer be slow, Your progress will, after try.ng this inethod for a time, be both rapid and thorough, and you will find yourself quick to perceive and slow.to forget It is to such readers that the Roman proverb applics : " Beware of the man of few books," "The great danger." says a Mathematician, " which all inathematical students have to guard against is that of leirning off book york without fully mastering the essential points of the methods Mathematics cannot be crammed To baible to write out book work faultlessly is not sufficient. The vly and whe efore of each step must be fully grasped, and students must not rest content ujless they fully understand in every case what is the property to be proved what known results are assumed, and what methods are to be applied Otherwise their memory will be unfairly taxed, the work will degenerate into mere drud. gery, and all this will be of little avail if the book work so assiduously committed to memory should be set with so:ne triffling alteratiin -a frequent artifice among examiners for Suding out whether candidate; really knw their work.

·[ 38 ] The solution of easy probleins and riders, which is also practically indispensable. also depends almost entirely on a thorough knowledge of fundamental principles and methods, and those who do not clearly realize this are too often apt to rush on to results in their answers in the exa nination, and to use the words it is obvious" or "evident" to conceal their ignorance of the intermediate steps, which, however, deceives no one but the candidates theinselves. On the other hand those who will take the trouble to realize fully the methods of the book-work and the framework of facts on which each Proposition is built 'up, will possess sufficiently powerful machinery to solve any reasonable problems that may be set. All that will then be required is readiness in applying their knowledge, and this can only be brought about by frequent practice in work. ing examples. 6. Don't disdain or pass over sums containing easy applications of the formulæ and never be satisfied with knowing merely the way, how to work out a rider; work it out actually carry your theory. into practice Never forget the precious • maxim ** The way to more light is the faithful use of what we have." By so doing you will * acquire practice which alone makes us perfect ·t - 39 ] You know the greater part of your University - Examination-papers will consist of such easy riders; and even those questions in which brainwork is most prominent, depend not a little for their full and ready solution on practical appli. cations of the form ulæ If you are already practised in that works, you will finish in a very short time the whole of the paper, except those portions which require thinking, and ont of the total amount of time alloted having got a great deal at your disposal for thinking only, you will most probably succeed in ycur efforts in this direction too, and thus.do the whole of the paper. As it is not enough for a man to know the theory of swimming but he ought to have practice in that art if he wants to swim across a river; so is practice necessary for you if you want to swim across the troublous sea of University Examinations. Simple riders and easy sums are a great recrca. tion to the student of Mathematics Most students when asked to work out a sum, sometimes after making a few fecble efforts but frequently before making any give up in despair ejaculating the words “It is very difficult, it will not come out '' I ut the self-same students after the problem has been explained to them, cannot help ultering, Oh, it was so easy!" I say, yes, it was so easy, but you could not get it out :

·[:40.3 because you did not enter into it. into it. You got frightened by the very appearance of the excer. cise You had no courage, no strong will, no patience or no Mathematical virtue, 7 Frequently revise the portions which you have already read; otherwise your further progress will be very very slow, and you will find yourself no match for the examiners. “Every Vethematical book that is worth any. thing," says Professor Chrystal, must be read backwards and forwards Go on but often return to strengthen your faith. When you come on a hard or dreary passage pass it over ; and come back to it after you have seen its import. ance or found the need for it further on. 8 In order to attain dexterity in analysis and calculation and becom; expert in giving ready solutions to probleins it is desirable to acquire the habit of performing mathematical investigations mentally No other discipline is so effectual in strengthening the faculty of attention, it gives a facility of apprehension an accuracy and steadiness to the conceptions; and what is a still more valuablu acquisition, it habituates the mind o arrangements in its reasonings and reflections To give an illustra. tion of how much it improves the intellectual powers I may cite the case of Euler, who had ·[ 41 ] always accustomed hiinself to that exercise ; and having practised t with assiduity he is an instance to what an astonishing. degree it may be acquired "Two of Euler's Pupils had calculated a converging series as far as the seventeenth term, but fonnd on coinparing, the written results, that they differed one unit at the fiftieth figure; they co.n.nunicuted this difference to their master, who went over the whole calcula. tion by head, and his decision was found to be the true one, For, the purpose of exercising his little grandson in the extraction of roots, he has been known to form to himself the table of the first six powers of all numbers from 1 to 100, and to have preserved it actually in his memory,', 9. Mathematics requires of us a great deal of time and energy ; we should be continually working at it. But though it requires our body to be always in motion, ever working, and sub: ject to the laws of Dynamics; it demands our mind to be always at rest, in equilibrium and in a state subject, as it were, to the laws of Statics. А wanting to excel - in Mathematics, should banish and anxiety from his mind, think of nothing else but his work should have a serene and tranquil heart, should allow man care ·[ 42 ] [ nothing to disturb his peace and calm of mind. His labour will bear little fruit unless he is able to keep his mind in perfect solitude; which in most cases, will require his body also to be in lone. liness. One lesson, Nature, let me learn of thee, One lesson phich in every wind ia bloin, One lesson of two duties kept at one Thouglı the loud world proclaim their eninityof toil uisever'd from tranquillity? Of labour, that in lasting fruit outgrows Far noisier schemes, accomplislı'd in repose, Top great for heste, too high for rivalry! Yes, while on earth a thousand discords ring, Man's seuseless uproar mingling with his toil, Still do thy qaret ministers move on, Their glorious ta-ks in silence perfecting; Still working, blaming still our vain turmoil; Laborarers that shall not fail, wlien min is gone. (Murthelo Arnold.) 10. A student of Mathematics should al." ways llave a humble heart and a docile spirit. Carefully store in every piece of knowledge, gather every bit of Mathematical truth, what, if you can make no immediate use of them and what, if no pleasing result seems likely to spring from them, because right is right, to follow right Were spisdon in the score of coasegueace.”

·[ 43 ] What a noble spirit of research was betray. ed by the great Mathe nitici in when be spoke of himself as having been all his life but "sa child gathering pabbles on th: sea-shore" similitude expressing not only his humility, but alluding likewise to th: spirit' in which, he had pursued his investig itions, as having been that not of selectioa and system-building but of childlike alacrity in seizing upon whatever contributions of knowledge Nature threw at his feet." .8 These directions may be summed up in a single one: -Love the subject. (Love, conquers all,) and try, by every means possible, to keep yourself fn a state in which you may be able to concentrate your mind and pay close and undivided attention to the subject. This is a facul. ty, which if we consider the testimony of Newton sufficient evidence, is the great constituent of inventive power It is that complete retirement of the mind within itself, during which the senses are locked up; that intense me. ditation on which no idea can intrude ; that firm, straightforward progress of thought, deviating into no irregular sally; tnat perfect yoga, where the mind becomes one with the subject; which can alone plice Vuthern itical subjects in a light suficiently strong to illuminate them fully, and

·[ 44 ]
preserve the perceptions of the mind's eye in
the right order.
In the end I shall lay before you the secret
of success in the study of Mathematics as well
as in that of any other undertaking. It is seeking
not our own aggran lisement, but the glory of
it is like the Red Cross Knight to labour
and struggle for the Faerie Queen Gloriana or
the Glory of God. It is thus to make our whole
life a co itinurus prayer by our acts It is to
carry into practice the noble advice of Lord Shri
Krishna
God;
"
, . In thy thoughts
Do all thiou dost for Me! Renounce for Me!
Sacrifice heart and mind and will to Me!
Live in the faith of Mel"
Let me close with the following strictly true
lines of Shakespeire:
" Heaven'doth with us as we vith torches do,
Not light them for oura rez ; for if our virtues
Did not go forth of us, 'tivare all alike
As if we had them not. Spirits are not finely touch'd
But to fine issues ; nor Nature never lends
The smallest scruple of her excellence,
But like a thrifty goddess she determines
Herself the glory of a creator,
Both thanks and use."

·In Woods of God-Realization, THE COMPLETE WORKS OF Swami Rama Tirtha (in English) VOLUMEI. 3rd Elution. Thoroughly Revised. With a preface by Mr. Puran Singh, F.C S., an introduction by Mr. C. F. Andrews, M. A. and two portraits of the Swamiji. CONTENTS. PART I.--1.-Happiness Within 2-Expan. sion of Sell. 3,- The Infinite in the Finite, 4.-The Sun of Life on the wall of Mind, 5 The Real Self. 6-Sin ; Its relation to the Atman or Real Self. 7.--Prognosis and Diagnosis of Sin. PART II -1.-The Secret of Success (deliver. ed in rokio Japan ) 2 -Secret of Success (delivered in San Francisco America) 3 The Nature of lospiration. 4. - The Way to the Fulfilment of All Desires. 5.- The Spiritual Power that wius. G-The Rod of Moses. PART II1,-1,-Law of Life Eternal. 2. Balanced Mind of Misery to God Within 4.-Informal Talks 5 - How to make your Homes Happy, 6 - dlarried Life and Realization, 7,- Vedantic Idea of Eating Meat Demy Svo, 500 pages; Cloth Bound Rs 2. Exclusive of transit charges. The Raina Tirtha Publication Leagire : Lucknow. 3-Out ·VOLUME II. Second Edition. Thoroughly Revised. Containing Parts IV & V with two Portraits, and a Liſe-sketch of Swami Rama 'Tirtha sent to ịhe 'Press by Mr. Furan Singh F C.S., 'just after the Swamiji left the world, CONTENTS. PART IV -1.-The Path of Truth 2.-The Goal of Religion. 3 – True Spirituality and the Psychic Powers. 4,- The piritual Law of Char: acter, 5.-The Kingdom of Heaven. 6.--The Eacred Syllable OM' 7.- God Within. 8.,- Rep. ljes to Class Questions 9 – The Way to Realization of Self 10-lufirmal Talks on self. Realization 11. Informal Talks (continued.. 2.- Questions and Answers. 13. - Is a particular Society necded? 14.. lhe Brotherhood of Man. PALT V.- 1. - Religion 2 -Criticism and Universal Love. 3 – Ilie Spirit of Yajna 4 Forest Talks Nos, I-XII. 5 - Letters from the Himalayas. Demy Svo. 512 pp Cloth Hound Rs 2. < Transit charges extra. The Pama Tirtha Publication League : Lucknow, ·VOLUME III. Second Edition Thoroughly Revised. Containing Parts VI & VII and 2 Portraits CONTENTS, PART VI. I -Idealisin and Realism Recon. ciled 2 Replies to some questions on Vedanta. 3 – Maya or the When and the Why of the World. 4 -Hypnotism and Vedanta, 5.- Man, the Master of His own Destiny. 6 - After Death or All Religions reconciled. 7.-Replies to Class Quastions 8. - Informal Talks. 9. --Re-incarnation and Family Ties. 10,- Realism and Idealism 11. -Vedanta. 12 I am all Light. 13 - Be not centre out. 1-Aids to Realization or Pranayam 15 - Saham 16, ~ Vedanta and Socialism. 17.-Hints to Realization. No 11 18.-Hints to Realization No III, 19.-Frag, ments 20.-The Problem of Sin. PART VII 1- The Present Needs of India, -2 -National Dharma 3.-The Problem of India. 4.- The Future of India. 5 - The Ancient Spiritualism of Indią 6 - The Civilized World's Spiritual Debt to India, 7 can Appeal to Americans on behalf of India. 8.-Facts and figures about India. 9.-Indian Womanhnod. 10.- About Wifehood 11 - Letters (00 pages). Demy 8vo. 542 pp Cloth Bound Rs. 2 only. Transit charges extra, The Rama l'irtha Publication League ; Lucknow,

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