# The Calcutta Review of Ramchundra's 1859 reprint

A review of the London reprint of Ramchundra's book A treatise on problems of maxima and minima solved by algebra which contains August De Morgan's Editor's Preface appeared in The Calcutta Review 33 (July-December 1859), xxiv-xxxii. This review contains much material which is taken from August De Morgan's Editor's Preface but we choose to give the full review here.

For Ramchundra's autobiographical notes see THIS LINK.

For De Morgan's Preface to Ramchundra's book see THIS LINK.

For Ramchundra's Preface to his 1850 edition, see THIS LINK.

For The Calcutta Review of the 1850 book, see THIS LINK.

Review of Ramchundra's 1859 book

This is one of those books which provoke rather than deserve remark. It is a reprint heralded into the world by a preface of about twenty octavo pages by the Professor of Mathematics in University College, and published by order of the Court of Directors "in acknowledgment of the merit of the author" and "to promote native effort towards the restoration of the native mind in India."

The original work was published in Calcutta in 1850, and noticed in the pages of this Review in a way which Ramchundra is pleased to style "very unfavourable," and like many others with even less grounds of complaint, he rushed to his own defence through the columns of the Englishman. We are not aware that newspaper complaints and defences, so notoriously common in certain of the Calcutta Newspapers and so disgraceful to the press, ever bring any amends to the writers of them, or that the Editors find that in so satisfying a depraved appetite for gossip they increase the sale of their papers in certain quarters, - but we presume that if Ramchundra had taken the hint offered in our pages with a sincere desire for his good, and shown that we were correct in expressing our conviction, 'that he was capable of far better things than are achieved in the work before us,' he would have gained much in the opinions both of "Calcutta Reviewers" and of Mr De Morgan.

We make no apology for giving these details of the life of the author in noticing a mathematical book. To the mind of any one but the merest tyro in science they form the most interesting part of the work before us. We have quoted the author's own words from the feeling that they contain the most unvarnished piece of native biography we have met with. The most Sceptical must believe it. It is the manifestation of a spirit which it would rejoice every true well-wisher of India to see pervading its masses. After reading it, we turned with real interest in the author to the work it precedes, but must confess to disappointment. In his preface the author 'flatters him self that his labours will be of some use to those mathematical students who are not advanced in their study of the differential calculus. This at once led us to expect a preliminary dissertation however brief, on the nature of Maxima and Minima. But not a word of it. The young student is not even told that the terms are not used absolutely, but only in reference to the values of the functions immediately adjacent to those to which the names are applied. If the work is intended for students who require to be instructed in the reduction of equations, in finding the area of a triangle, the circumference, and area of a circle, the summation of the squares of the first n digits, &c., which Ramchundra has carefully treated of, we are certainly of opinion that definitions, with some illustration of the terms maximum and minimum at least, were also required. And as the work is styled a "treatise," we had a right to expect some criteria by which to judge when a function does or does not admit of such maximum or minimum values, and a general analysis of the method he proposes to follow. Had the author proceeded on such a plan, and followed up an outline of the principles by a few illustrative examples and as copious a collection of exercises as he pleased, his object would at least have been comprehensible, and to some extent his book might have deserved the attention of the teacher and the student.

Mr De Morgan himself, though evidently bent upon making matters look the best, glosses over the fact that it is merely a collection of solutions, as well as he is able, by saying, - "It was Ramchundra's object to found an elementary work upon his theorem, for the use of beginners, with a large store of examples. As to the method which he has adopted, Europeans must remember that his purpose is to teach Hindus, and that probably he knows better how to do this than they could tell him." We have always held a very high opinion of Professor De Morgan both as a logician, and as a writer on mathematical subjects, but we are forced to differ from him here. Whatever may be the aptitudes of the Hindu, we never have been struck by his skill in the pedagogic art. It is a thing too alien to his traditions and experience to expect. Education has not, for centuries past at least, if ever, appeared to him in the light a Pestalozzi or a Stow would view it. To the Hindu, if we keep out of sight the passing of a creditable examination and the obtaining a lucrative situation, knowledge is the first and last object; mental power is what he has perhaps never dreamt of obtaining. It would be strange indeed if he attempted to present his knowledge in such a form as tended to train the mind of his pupils or readers. We do not mean by these remarks to reflect on Ramchundra. He may be a very able teacher for ought we know, but we presume, as Professor De Morgan has done on another matter, to point out to young Hindus what we consider one of their weak points, and which can only be strengthened by the exercise of self-denial and self-reliance, - seeking, as students, to master their difficulties by independent thought, without having recourse to the vicious sys tem of consulting keys, and such mental soporifics, and, as teachers, to inculcate principles, rather than destroy the minds of their pupils by allowing them to burthen their memories by ever so much committed by rote.

Without even a definition, Ramchundra commences his first chapter consisting of 55 examples selected from well known English works on the calculus, involving equations of the first and second degrees only. Nearly every one of these is solved twice. The first method is that given in some of our ordinary school books, the second, which the author is pleased to term a new method, is neither more nor less than the solution of a quadratic by first taking away the second term, and then solving the equation thus rendered a pure quadratic. So far as the solution of an equation is concerned then, the process is as old as the time of Cardan; and Ramchundra himself confesses that he had found it employed in English works on Algebra. It was no discovery then to employ it for the determination of maximum and minimum values of functions, since, if these are found by one, they will also be found by any solution of a quadratic. But had he compared a few of his solutions, he might have seen that when the function is written in the form
$F(x) = x^{2} - 2 ax + r = 0,$

$F(x)$ has always a critical value (is a maximum or minimum) when $x = + a$, that is, when the root is equal to half the co-efficient of the second term with its sign changed. Having proved this general proposition, all that was necessary in order to solve the problems in the first chapter, was to reduce the proposed question to the type form of the function, and halve the co efficient of the second term changing its sign. As it stands, every problem is first reduced to an adfected quadratic and solved at length, the quadratic is then deprived of its second term and again solved.

So much is made of this second solution that Professor De Morgan remarks - "The constant occurrence of the same solved without impossible roots," and the transformation by which it is effected, will remind the English mathematician who has his half century over his head, of the old 'pure quadratic,' and the victory which was supposed to be gained when the 'adfected quadratic' was evaded by attention to the structure of the given equation. Ramchundra and Dr Miles Bland, &c, &c., are here precisely on the same scent, both making much of the same little." Ramchundra does not seem to have been ignorant of the general solution of the equation, for in a supplement, (p. 178) he deduces it from the ordinary adfected quadratic. And though he does not put the statement in words, he shows that the quadratic is a maximum when its roots are equal.

In the second and third chapters he applies this principle to the determination of the roots of functions of the third and fourth degrees. Here he deserves credit for an ingenious and original application of the familiar principle in the theory of equations that if a be one of the roots of the equation $F(x) = 0, F(x)$ is divisible without remainder by $x - a$. Making a negative and indeterminate, Ramchundra divides the cubic $F(x) - r$ by $x + a$. Making the remainder vanish, he obtains an equation between $r$ and $a$, and the quotient is a quadratic which, in order that the function may have a critical value, must have equal roots. The same principle is applied to equations of the higher degrees, the problem in its most general form being to determine the value of $r$ so as to render a pair of the roots of $F(x) - r$ equal. But the execution of the solutions is clumsy, and the constant repetition of the same processes in their minutest details is schoolboy-like, if not pedantic. Professor De Morgan evidently allows this to be a defect, and he begs the reader to excuse Ramchundra, by remarking that, "the excessive reiteration of details, and the extreme minuteness of the Algebraical manipulations, are excellent examples of that patience of routine which is held to be a part of the Hindu character." A person may take a fancy for fencing by observing the expertness of a good swordsman, but he will never become a fencer from merely watching the skilful play of another, - he must do something himself. Ramchundra's minute manipulations are all very necessary practice for the learner, but he has left nothing for his reader to trace, - every step, however self-evident, is carefully indicated. We see how he deals with the problem, but we are not left to find out or supply a single process. Our thinking powers find nothing to call them into action. To solve the last problems we are not even required to remember what has been repeated in a hundred be fore.

The work has been reprinted in England under the following circumstances. In 1850 Ramchundra visited Calcutta and was introduced to the Hon'ble J E Drinkwater Bethune, whom he presented with 36 copies of the first edition, and from whom he received Rs. 200 as a donation. These copies were forwarded to England for distribution among Mr Drinkwater Bethune's friends, and among others a copy was sent to Professor De Morgan. He saw, or thought he saw, merit in it, worthy of encouragement both for its own sake and for the promotion of native independent speculation as an instrument of national mental-progress, and accordingly in 1856 brought the matter to the notice of the Court of Directors through Colonel Sykes, the Chairman. The Court made inquiry, and reported back to Professor De Morgan, requesting him to point out how Ramchundra might be brought under the notice of scientific men in Europe. The author himself was at the same time presented with a Khillut and Rs. 2,000 by order of the Court, and Mr De Morgan recommended the circulation of a reprint of the work in Europe and India. The reprint is a very careful one by that most able mathematician, in which the errata of the first edition are corrected, and the inaccuracies and failures of the author generally indicated. The statement of the Professor's views as to how the circulation of Ramchundra's work in Europe is to be the "most effective method of developing Hindu talent, is however very indistinct, and so far as we can judge, most inconclusive. It does not help us in groping for a solution to the great problem of the philosophy of Hindu mind - a problem to which we fear statesmen, no less than missionaries, have given but too little attention, - but solved to some extent it must be, in its contrasts and analogies to that of the Anglo-Saxon, if ever we are to know either how to govern well and attach the natives to us, or to Christianise and raise them in the scale of thought and civilization.

We cannot see how this publication will awaken from the sleep of ages that mind which we long to see aroused to energetic action, and impelled as by a Divine energy in the race of civilization, thought, and true virtue. Professor De Morgan states that he has no sympathy with those who forget "that there exists among the higher castes of this country" "a body of literature and science which might well be the nucleus of a new civilization, though every trace of Christian and Mahomedan civilization were blotted out of existence," - who forget that there exists in India the Sanscrit language with its systems of logic, metaphysics, astronomy, and mathematics, its poetry and drama. And then, as if it were all that was necessary to prove every thing he desires and convince the most sceptical, he goes on to tell us that there were able Hindu mathematicians before the seventh century. We have no patience with the thread-bare arguments of Young Bengal, that because his ancestors (if they really were so) who in the Punjab wrote the Vedas nearly three thousand years ago and in Malwa, the Brahma Sidd'hanta and Vija Ganita at a later period, were to some extent civilized and had acquired literary tastes when western Europe was, so far as she herself now knows, shrouded in mental darkness, therefore, irrespective of what has been done since, or is done now, he ought to be revered and flattered to his face, even by those who, having once got the torch of knowledge in their hands, have never let it drop nor languish as all heathen nations in the world's history have. "In India". says Mr De Morgan "speculation died a natural death." "The Hindu be came the teacher of results which he could not explain, the retailer of propositions on which he could not found thought." In other words, "he fed himself and his pupils upon the chaff of obsolete civilization, out of which Europeans had thrashed the grain for their own use." Greece did not present such a lamentable spectacle of routine and indifference to thought. Her power of speculation only ceased when she ceased to be a nation. Her latest speculations before the taking of Constantinople, as Professor De Morgan affirms, were like her earliest, inquisitive, seeking after the unknown, the undiscovered.

We must now conclude. We have acknowledged what merit the work seems to possess. Its inaccuracies of expression have been passed over. The publication of such a book, and in an expensive form, we do not consider likely to have much, if any effect, in re-creating native mind in India. It may flatter an individual to his hurt, but little more. No scientific man will be greatly delighted with it. The publication is not a method that will ever succeed in exciting native thought. And we believe that if there is a God who rules above, no unreal or sham mode of action will ever succeed in renovating India to any extent intellectually or morally. We verily believe that a conscience, as well as an intellect, needs to be awakened; and we do trust that native Christians, like Ramchundra, with some mental power, will redouble their efforts in one form or another, whether in science or morality, to bring about such a re-creation of mind and soul in this country.

Last Updated April 2016