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We leave Gholam Hossein's pages with a feeling of respect for the man. As was said of Jean Thevenot, the French traveller in India, “an honester man ne'er lived in the world." He hits hard when occasion demands it, but he never allows bitterness or rancour to weaken the force of his criticism. When he is unfair, it is not deliberate speciousness, but the result of the limitations of his own knowledge. He accepts British rule as a fact not to be disguised, questioned or resented, any more than he would disguise, question or resent one of the phenomena of nature ; but, in order to transmit such useful hints to Government as might conduce to the welfare of the distressed inhabitants of this land,” he points out to the English certain places where the shoe pinches, , and contrasts, naturally but not very fairly, the painful attempts of the English to bring order out of anarchy with the ordered tranquillity and excellence, by this time idealised, of the time of Akbar and Shah Jehan. And all this he does, as he himself tells us in other words, in the hope that he may do his country, and incidentally himself, good. “In compliance, therefore, with the sentence of the Holy Writ, that whosoever induces others to good promotes his own welfare, we shall endeavour to point out the right way; and may God grant that we may all see it. Amen."

PHI OMEGA. intervals, had scarcely any communication with each other, and so great was the increase of beasts of prey, that the little communication that remained was often cut off by a single tiger known to haunt the road.' .

"When we look at the India of to-day, North and South alike, we find a difficulty in believing that it is peopled by the near descendants of the beings thus described. The population is dense, almost too much so, but it is free from crime and orderly to an unusual degree. Roads, canals, railways and busy manufacturing and commercial communities are everywhere to be seen. Five Universities and nearly one hundred thousand public schools provide all grades of instruction : a large revenue is raised with a very low rate of incidence. The Country has passed, in a few generations, from anarchy to the reign of law.”-H. G. Keene's History of India, Vol. I, pp. 363-4.

We are, it is true, far enough from the millennium in India to-day. But it is a pity that Gholam Hossein cannot come to life again, and see modern India. He would admit that in spite of their alleged defects these unsociable foreigners had done something for India. As the progress of the next hundred years, given ordered peace, will vastly overshadow that of the last hundred, our descendants of 2016 may find the writings of our modern Gholams an equally interesting study. Some of the stock grievances will then be admitted, perhaps by all, to have been quite true in fact, but an absolutely inevitable accompaniment of the constructive process through which India had to pass, or perish!

THE THEORY OF FUNCTIONS OF

A REAL VARIABLE.

An Inaugural Lecture delivered before the University of

Calcutta, December 1915.
BY W. H. YOUNG, Sc.D., F.R.S.,

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Hardinge Professor of Mathematics, etc., etc.

IT seems fitting, as I have recently returned from a some

what extended tour through America, China and Japan, that I should begin my lecture to-day by a few reflections which, if not directly suggested by that tour, are in close connection with it. Briefly I may say that I have returned to India even more convinced than I was when I went away, that the future is to the thinker and that action is bound to become more and more a simple corollary to thought.

Even up to the end of the nineteenth century the position was tenable that it was better even for the leaders to err on the side of practical knowledge than on that of theoretical equipment. But everything I have seen and heard has borne in on me that the contrary is now the case, that now though both are necessary, it is better to have rather too little practical knowledge than too little power of dealing with the concepts which alone render practical knowledge vivifying and fruitful.

It is neither the time nor the place to elaborate the grounds which I have for taking up this position. It is sufficient to allege one fact known to all the world. The time element has in this sense come to be a permanent constituent in our conception of the universe, that we cannot think of it except as a changing one, as an assemblage of events and not of stationary parts. The speed with which one can move from country to country has its analogue

in the rapidity with which each separate portion—if any portion can be said now to be separate-of the earth's surface is itself undergoing modifications in the mental and moral characteristics of its inhabitants and of the system under which they are living. Indeed, I am credibly informed that serious efforts are being made to solve the problem as to how the physical and intellectual characteristics of a certain prominent Asiatic people may be suitably influenced-even to the extent of trying to modify the shape of their skulls.

In this changing universe law and order still have their place. Codified knowledge is still required and still desirable, and most of us must stop there. But the highest place is reserved for him who can consciously or unconsciously adapt himself to changing conditions, who can remain in touch with growing knowledge, who can shape that knowledge to the ends of an ever higher civilization, can himself rise to creative acts. The coolie can, if he is properly taught, learn to embody in concrete form after the approved fashion what the highest intellectual resources of the race may have been needed to conceive. But there is no longer any finality: what the aeroplane is to-day it will not be tomorrow, and the people which rests on the achievements of to-day, will be overtaken and passed before the night is over.

The heritage of the future is for the thinking races.

How does this bear on India ? And how is it connec. ted with the subject on which I have elected to speak to you this session ? The best people in India have always been thinkers; the Indian then starts with a handicap in his favour in the race which the nations of the world have

We are then justified here in looking forward to the future with great hopefulness. On the other hand his thinking has for the most part related to a stationary universe: in India then even far more than in Europe it is essential that the changing character of the modern world should be brought home to its best minds, otherwise the Indian will have to set against the balance to his credit, to which I have just referred, serious disabilities. He is like a man who has money in the bank and does not know how to use it, because he does not understand the conditions which are governing the commercial world round him.

to run.

We see then the need for earnest and intense effort, if we are to bring home to the thoughtful Indian the necessity for doing everything in his power to encourage what is understood by the word research in its highest form. By this we do not mean that laboratories must be created and equipped ; at least we do not mean this exclusively nor even primarily. Laboratories suggest to some chemical experiments; to others nothing more than bottle-washing. But even those who understand and appreciate to the highest degree the function of laboratories in the modern world, even these often fail to realize the fact that laboratories only represent a part of what is characteristically modern in intellectual activity. It would be a misfortune for any people if with it research were understood to mean laboratories and nothing more. In every department of human effort and mental activity attention must be concentrated on the time elements, on the formulation and solution of new problems, and on the attacking of old problems by new methods. Otherwise only a small section of the leaders of the nation will be qualified to take part in the new developments which every rising sun may now be said to bring with it. I would go further and would say that the highest intellectual work of the kind I have in view cannot be done in the laboratories, though some of it may be done outside by men who actually or virtually direct the labours of those whose chief interest lies in the actual carrying out of experimental researches.

I am, I may say, convinced in my own mind that India needs, for example, a mathematical institute properly equipped and staffed, far more than it needs a new laboratory. It is true that in such a laboratory successful experiments may result in the temporary material amelioration

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of a section of the population. What is needed far more even than this, is that Indian leaders of thought should be produced in sufficient quantity and of the right quality. You will then ask for and obtain what India needs most. The right experiments can only be made when the right kind of thinking has determined the subjects with which the experiments are to deal. For this not mere technical knowledge but broad and independent thinking, leading as it must do to proper preliminary enquiries, is the most essential requisite. Where so much needs doing, where so

, many new possibilities present themselves, the need above all things is for the thinker who has all his thinking life been in contact with change and growth, to whom progress, the solution of difficulties as they arise, and creative acts of the intelligence become almost matters of routine.' The man who has spent his time in developing the experiments of others or in painfully acquiring a knowledge of the results at which others perhaps long since have arrived, is not a thinker. Even in England our specialists have too often been men of this type, with the result that it is a common proverb in Government circles that specialists are always prejudiced, that they cannot take a wide view, that they were born to be servants. The explanation is a simple one : England's success in the nineteenth century was so great that she finds it difficult to abandon nineteenth century methods; and in her Universities real research in the best sense of the word has a secondary place, and in some is all but stifled by the examination system. A country is apt to have the experts it deserves. I do not need to tell you of the new spirit which is abroad all over the British Empire, and which is now transforming old ideas into new, and which makes us confident that this reproach against our experts will soon have no justification in fact,

I cannot in these few words hope to have convinced the sceptic ; I should be satisfied indeed if I have made my point clear even to a portion of my most sympathetic hearers.

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