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Nor were his mathematical discipline and habits of thought of less value in the masterly plans of philanthropic and religious enterprise which filled his life, and which he bequeathed as a rich legacy to Scotland and to the Christian world.

In the contemplation of God, in the computations of eternity, in the solemn estimate of the great concerns of our immortality, mathematical science presumes not to apply her demonstrations, for they cannot reach infinity. But if we have been faithful and docile pupils, we shall find that she has led us to most advantageous positions, and formed us to a valuable capacity for such high contemplations, and such solemn estimates.

In whatever aspect we view the effect of mathematical studies in the training of the mind, we see that their claim to an eminent place in our educational system is amply vindicated.

There is doubtless a possibility of injuring the mind by too exclusive devotion to this class of studies. The demonstrations of mathematics cannot be carried through the spheres of ethical and political reasoning, nor can they always be applied to questions of practical business. We need not overlook the distinction between mathematical demonstration and moral evidence. If one should exercise himself only in the former, he might be feeble in the latter. You cannot always carry a compass and theodolite with you and regulate all your steps by them along all the crowded and hurried paths of real life. But in this practical America there is not much danger of this. There is not much danger of our over-estimating the power which a character derives from that punctuality, accuracy, reliableness—that habit of insisting on being right-scrupulously and reliably right—which the faithful study of mathematics so finely cultivates.

Fain would we cheer on the young in the manly toil of climbing these rugged heights by the assurance that on their summits one breathes the most bracing air, and looks abroad on the most magnificent scenery, and up through the clearest atmosphere, into the most glorious skies. Neither is there any sphere of practical labor in which one may not thankfully use the vigor of limb and valor of spirit which the mountain air and mountain scenery and manly exercise will have imparted.

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ARTICLE II.- EUROPEAN WRITERS ON INDIA.

THERE is an evident increase in the number of scholars who are interested in studies on India; not only of those who acquire a little knowledge of Sanskrit as preliminary to general studies in language, but of those who are drawn into more extensive researches by the great and rapidly disclosed problems suggested by a survey of this ancient and singular civilization. Such students are often, at the outset, perplexed to know where to look for the most trustworthy authorities, especially if they have not the good fortune to reside near large libraries, or to have the advice of those scholars—few in this country-who have traversed the ground before them. It has occurred to the writer that a brief mention of the standard authorities, in European languages, on Indian topics, might be of service to such special students, as well as to that larger class of cultivated men and women who desire to be well informed in regard to subjects which are coming more and more into the thought of the western world.

The literature which has accumulated in this field during the last thirty years is voluminous and diversified. The necessarily tedious but cumulative labors of explorers in such a vast territory are beginning to bear abundant fruit, and the student of to-day is provided with helps which would have gladdened the heart of pioneers like Jones and Rosen and Colebrooke. No pretense will be made of a complete survey, and only such authorities will be named as are of standard value, and may profitably form the foundation of an Indian library. The list will be most profitably arranged under topics, though it may involve repeated reference to some books.

1. Physical and Political Geography.There is no lack of brief general descriptions of India, or of more minute examinations of limited areas, but we have as yet no work which traverses the whole field with the thoroughness which the subject deserves. The best general survey of the configuration and productions of the land, one sufficiently complete for the general student, is by Professor Lassen, in the first volume of his Indische Alterthumskunde, 2d edition.

The Geography of India, with notes on commercial, civil, and social conditions, by George Duncan, Madras, 1870, is a little book of 171 pages, which contains in a nut-shell a great amount of information corrected up to date. The Ancient Geography of India, illustrated by thirteen maps, by the eminent archæologist Alexander Cunningham, is a valuable representation of India as it was seen by Alexander, and later by the Chinese pilgrims. The topographical and other surveys now in progress will in time furnish the materials for a more exhaustive treatment of this subject.

Such special works as Hardwicke and Gray's Indian Zoology, two vols., Donovan's Insects of India, Jerdon's Mammals, and Day's Fishes of India, are beyond the needs, as they are beyond the reach, of most students. The most complete map of ancient India is that which accompanies Prof. Lassen's work, size 23 x 284 inches. As this map was drawn in 1853, and was the first serious attempt to definitely fix the localities mentioned in the ancient literature of India as well as by Greek and Roman writers, some of the identifications were tentative, and have not in all cases been confirmed by later researches. A smaller and less ambitious map, by Col. Yule, is found in Dr. Smith's Histor. ical Atlas. An excellent map of modern India is that in Stieler's Hand-Atlas. 2. Ethnology.The proper ethnic classification of the

popu. lation of India, and the degree of relationship in which the different constituents stand to one another and to foreign nations, are the great puzzles of our inquiries. Even now many of the aboriginal tribes are so little known as to make conjectures concerning their affiliations exceedingly hazardous.

The best general discussion of this subject is found in the first volume of Lassen's work mentioned above. The second volume of Dr. Muir's Original Sanskrit Texts is devoted to an investigation of the ethnic affinities of the Aryans of Northern India, and shows convincingly their relationship to the great civilized nations of Europe. We may here say that Dr. Muir's work is a model for such investigations. The author is exhaustive in his collection of facts, clear in his arrangement of them, and judicial in his decisions. Five volumes have been published, four of which have passed into a second, revised and enlarged edition.

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As we bave already intimated, the inaccessible jungles of Central India and the excessive shyness of their primitive inhabitants have hitherto made it difficult to obtain exact information regarding this part of the Indian people. Much has been learned from missionaries, and something from adventurous travelers, though the hasty observations of the latter are not always to be trusted. Col. E. T. Dalton's elaborate and costly book, Descriptive Ethnology of Bengal, concerns not only the population of that province but of all India, since Bengal has been the common camping ground” of the various races which have successively found a home in the land. What is known of the Santals, one of the most interesting of these primitive tribes, may be found in Dr. Hunter's Annals of Rural Bengal. The Dravidian population of the southern peninsula, usually classed with these tribes as aboriginal, is discussed at length in the Introduction and Appendix of Dr. Caldwell's Dravidian Grammar. Hodgson's Aborigines of Nepal is also valuable.

3. Languages.—Of the two chief divisions of Indian speech, Aryan and Dravidian, an excellent survey of the different periods of the former will be found in the second volume of Muir's Texts. It is not our intention to speak of text-books for studying Sanskrit, as that has been done already, a year or two since, by Prof. W. D. Whitney, in communications to the College Courant. We may mention, however, Delbrück's Das altindische Verbum, a valuable work in which are found an enumeration and brief discussion of the forms of the verb occurring in the Rig Veda. The same author has published a Vedic Chrestomathy, but the accompanying notes are so brief as to afford little help to the learner. Within a few months the St. Petersburg lexicon and Grassmann's special glossary to the Rig Veda have been completed, which will greatly facilitate the reading of that ancient text. Ernst W. A. Kuhn has recently published our best grammar of Pali, the sacred language of Buddhism and the oldest recorded popular dialect which grew out of the Vedic Sanskrit. Prof. Cowell's Short Introduction to Prakrit, a later descendant in the same line, is a sufficient guide to the understanding of the vulgar dialect of the plays. Coming down to the present time, Mr. John Beames has attempted, with excellent success, to collect and reduce to

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system the facts of the popular speech in his Comparative Grammar of the Modern Aryan Languages of India. The two volumes already published treat of phonetics, and the noun and pronoun, and are to be succeeded by a third, devoted to the verb, &c.

The speech of Southern India has been discussed with great ability and learning by Dr. Caldwell in bis Grammar of the Dravidian Languages. A second edition of this great work, revised and enlarged, has been published within a year. A brief survey of all the languages of India, with a map showing their geographical relations, may be found in Mr. Beames' Indian Philology, a little book of ninety-six pages.

4. Literature.We may roughly divide Indian literature into three periods, ancient, medieval, and modern. The modern Aryan literature, beginning about the 12th century, is described in the introduction to Mr. Beames' Comparative Gram

The literary productions of the Dravidians are considered in Dr. Caldwell's book. We may here notice an entertaining book by Mr. Gover, the Folk Songs of Southern India. In the same book an attempt is made to prove the Sanskrit origin of the Dravidian tongues, but with poor success.

An extended notice of the first two periods of Aryan literature by competent writers may be found in Lassen's great work, Weber's Indische Literaturgeschichte, Mrs. Manning's Ancient and Medieval India, and Monier Williams's Indian Wisdom. The best description of the Vedas and the literature inspired by them is the Ancient Sanskrit Literature, by Max Müller. The student may also profitably consult Colebrooke's Essay on the Vedas, annotated by Prof. Whitney, as also the latter's account of the same in his Oriental and Linguistic Studies, vol. 1.. We may say here that Colebrooke's Essays, in two volumes, edited by Prof. Cowell, and his Life, written by his son, are by no means out of date, though that illustrious scholar has been dead nearly forty years. While much has been added to our knowledge of India since his time, no later scholars bave surpassed and few have equalled him in thoroughness of investigation and candor of judgment.

The third volume of Muir's Texts is devoted to Hindu accounts of the origin and authority of the Vedas. An excellent survey of the dramatic and Puranic literature, together with

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