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with the powerful influence of general custom, were stated to be, an aversion to the trouble of rearing and disposing of the children, and a mixture of pride that would not affiance a daughter without giving her such a portion as would shew from what an illustrious tribe she came, with the avarice that refuses to charge itself with such an expense. In some few instances this pride may has overborne this avarice, and a daughter has been spared. Affection, or humanity, or a sense of duty, were found by the Colonel 'not to have been the inducements to the saving of those extremely few females that had been permitted to escape the common fate. He met with only two instances that could be imputed to such principles, and one of them was afforded by a professed robber.' The present work is such a display of human character, that this lawless barbarian appears like a tender enthusiast, fit for the most sentimental province of the country of romance; and there is hardly a more interesting paragraph in the book than that which relates to him.

• Hutaji is a professed robber, with whom sentiment and feeling might be supposed to be strangers. The profession which he followed did not prevent me conversing with Hutaji, nor to avoid a pretty frequent intercourse with him. This man, with the aspect and manners of a barbarian, possessed all the feelings of natural affection, which led him to cherish his daughters, in opposition to the usage and prejudices of his tribe. They are between six and eight years old ; and he brought them both to my camp, where they were vaccinated. I observed their father caressing them with pleasure, and exulting in thens with true pareetal satisfaction ; and their persons and manners were very interesting. It deserves remark, as exhibiting a strong feature in the character of the Jarejahs, and of their feel. ings with respect to their daughters, that these girls wore turbans, and were dressed and habited like boys. As if ashamed or afraid of acknowledging their sex, they assured me they were not girls, and with infantile simplicity appealed to their father to corroborate the assertion. p. 67.

It should be observed, that the law of destruction takes effect much less generally on the illegitimate female offspring; whose mothers are held by the Jarejahs in a capacity between wives and slaves, and are taken, with little care of selection, from any of the neighbouring tribes, whereas they shew the utmost nicety of pride in selecting their wives from the most honourable Raj-put families; even the poorest and lowest Jarejah feeling the utmost solicitude not to taint his blood by an improper alliance. It is not, as may easily be supposed, from humanity, that these infants of meaner quality are frequently spared, but rather,' says Col. W., from a contemptuous opinion of their inferiority. These children are not considered to belong to the caste, and their future situation in life is of little consequence, though the pride and prejudices of a Jarejah nake him occasionally also destroy his spurious offspring. These daughters are bestowed on Mussulmans, or on Hindus of an inferior caste ; and their settlement is attended with little expense or publicity; the motives therefore which lead the Jarejuhs to destroy their legitimate daughters do not exist with equal force with respect to those by the rack las, or mistresses.

We must suppose that the pride of this depraved race has such an ascendency over all betrer feelings, as to preclude any affection for these daughters of reputed inferior blood, even when they are growing up, as, else, the fathers, being thus made sensible how interesting their other daughters also would become if spared, could not with such perfect indifference doom them all to perish.

Colonel Walker acknowledges' his want of any good data for a calculation of the number of female infants that annually thus perish by violence, though he has made many inquiries, and received several loose estimates on the subject, from perisons considerably acquainted with the country. A number between fifteen and twenty thousand would probably be the mean of these calculations of the yearly destruction in Guzecrat and Kutch.

It would be gratifying to abridge the narrative of Colonel Walker's indefatigable and most meritorious exertions for the suppression of this unequalled enormity, if our limits now allowed room for any thing more than an animated congratulation to bim and to the very cause of virtue itself,--among the most memorable of whose agents he has taken bis rank,-on the complete success of those exertions, throughout one wide portion of the country in which they were so judiciously and soʻresolutely 'prosecuted. In the remoter part of it, the terri

tory of Kutch, the fear of the English had not yet grown to a sufficient strength to second effectually the force of persuasion: and the Colonel's repeated and earnest appeals to their humanity, and what they call their religion, had thus far failed, though the time is very likely not far distant, when they also will begin to feel the illuminations of that logic which has so mighty a power over Asiatic understandings and indeed those of all other nations. But in Guzerat the great object of Col. W's exertions is accomplished. He persevered in spite of all the obstructions which would have reduced a less determined spirit to despondency and inaction; and finally persuaded almost all the Jarejuhs of any consequence in the country to subscribe such an engagement to renounce the abominable custom, as expressly subjects theni, by their own consent, to a punishment trom the British and Gaikawar governments in every subsequent instance of intanticide. At the date of the latest, notices here inserted, the Colonel had remained long enough at Barodu to ascertain that the measure was proving effectual, and to receive the most , gratifying demonstrations of gratitude and joy from both the mothers and fathers whose offspring he had thus reduced them to a kind of necessity of preserving. He is one of that privileged and enviable class of men whom Providence las employed, each, to accomplish some one grand distinct operation in the great process of reforming the world.

It is in a train of happy moral revolutions, corresponding to this, that we earnestly hope we see the intention of Provi. dence in facilitating what appears so strange an irregularity in the economy of the world, as the acquisition of a vast empire in Asia by the people of this island. We do not know in what way those

persons among us who do not care for such revolucions, or who deprecate and hate the projects for effecting them, maintain their complacency on the subject of India, amidst the evidence, growing every year more glaring, that in any

other view our Indian successes are a great and almost unmixed calamity. We know not in what way,----unless they are expecting the state of the case to be reversed in consequence of a miracle of moral transformation, speedily to be wrought upon the managers of power in this ill-fated world. Unless this shall come to pass, we must expect that India, which used to be dreamed and ranted about as an exhaustless source of wealth to the nation,--will continue to be, no one can conjecture how long, a most destructive drain on our domestic resources, absolutely a pit to throw the hard earnings of the English people into, and at the same time a pernicious vent for an influence that is poisoning our morals. But the period must sometime arrive when either wisdom or necessity will change this condition of things; and in the mean while, it will be a consolation, and partly even a compensation, to the benevolent and religious part of the community, that the English power in India is operating as the cause of most important innovations among the people, in some particular instances by a direct authoritative interference, and more generally by that indirect and even involuntary sanction and weight, which the supreme power in the country necessarily gives to whatever benevolent and pious undertakings it protects. For how many wasted millions (no apology, however, for the men and the system that have wasted them) will it be a moral compensation, that, twenty years hence, there will be very many thousands of human beings of an age to reflect with gratitude, that it has been owing to English interference that they were not all murdered in their natal hour; and who will therefore have

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a most powerful motive to receive with favour, and to consent to promote, the measures by which the English may at that time be solicitous to diffuse among them civilization and Christianity. And if at length a general civilization and Christianity in Iudia shall be the result of such measures as could not have been prosecuted so effectually but under advantage of the ascendency of the English power, what a triumphant balance of good will this be (still no thanks to corrupt and ambitious men) against that grievous pecuniary burden which the posses. sion of India imposes on us, and will impose for a long time yet to come.

Mr. Moor's disorderly miscellany of contributions to this volume are of all kinds, mythological, philological, and historical ; and though some of them are unimportant, and many of them out of place, they may afford to a patient and combining reader some considerable instruction in Indian matters. There is a large and elegant map of Guzerat, for the accuracy of which he has given the most respectable pledges.

Art. II. An Elementary Investigation of the Theory of Numbers, with

its application to the Indeterminate and Diophantine Analysis, the analytical and geometrical division of the circle, and several other curious algebraical and arithmetical problems. By Peter Barlow, of the Royal Military Academy. 8vo. pp. xvi. 507. Price 14s.

in boards. Johnson and Co. 1811. ALTHOUGH Mr. Barlow, in undertaking the work before

us, has not opened any new channels of thought, the subjects to which our attention is invited, have, each of them, until within the last ten years, been almost entirely neglected for nearly a century. On the theory of numbers, there is very little extant, between the times of Euclid and Archimedes, and that of Malcolm: and from Malcolni's time to the present, scarcely a new property was added to the stock, before the recent publications of Legendre and Gauss. The Diophantine analysis, indeed, has met with a rather more respectful attention : but still has but seldom been treated with the perspicuity of which it is susceptible, or been made to furnish any practical applications. We are persuaded, however, that the Diophantine method may be employed with great success in the finding of fluents; and we should have been gratified to meet with a few examples to this effect, in Mr. Barlow's work. That he has developed many of its uses in other scientific enquiries, our readers may perceive from the following analysis of his work.

It is divided into two parts, of which the first is subdivided into ten, the second into seven chapters. In the first part the author treats of the sums, differences, and

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products of numbers in general,-divisors, and the theory of perfect, amicable, and polygonal numbers,—the lineal forms of prime numbers, and their most simple properties, the possible and impossible forms of square numbers, and their application to numerical propositions,-the possible and impossible forms of cubes, and higher powers,-the properties of powers in general,--the products and transformations of certain algebraical formulæ,--the quadratic divisors of certain formulée,--the quadratic' forms of prime numbers, with rules for determining them in certain cases,the different scales of notation, and their application to the solution of arithmetical problems. This part is terminated by a dissertation on the notation of the Greeks (avowedly taken from Delambre), and some miscellaneous proposi- . tions.

In the second part we find the subject of continued fractions, and their applications to various problems,-the solution of indeterminate equations of the first, second, third, and higher degrees respectively,--the solution of indeterminate equations of the form 7—1=M(a), with a table of indeterminate formulæ,--the solution of Diophantine problems, with miscellaneous examples,--the analytical and geometrical division of the circle, including the solution of Gauss's celebrated problem relative to the inscription of polygons in a circle. The volume concludes with two tables; namely, one of prime numbers to 4000; the other, containing the least values of p and q; in the equation pemNqo=1, for every value of n, from 2 to 202.

Such of our readers as are acquainted with Legendre's work, entitled “ Essai sur la Théorie des Nombres,” and Gauss's “ Disquisitiones Arithmeticæ,” will observe, from the preceding analysis, that much of the ground over which Mr. Barlow conducts us, has been already explored by those able mathematicians. But it inust not thenice be inferred that he pursues the same route, and strikes into no new paths. While he wisely facilitates his own progress by the experience of his predecessors, he sometimes cuts through a hill which they had ascended and descended, and now and then, by main strength, removes an obstacle which they had 'slily evaded. In general, his manner of proceeding is, strictly speaking, his own. Diophantus, Bachet, Fermat, Kersey, Euler, Waring, Legendre, and others, frequently furnish him with materials; but he work them up in his own

casts the whole into a shape which is at once neat, interesting, and useful.

We have already given some proofs of his talents, in our account of the new edition of Euler's Algebra, which it now appears, was Vol. VIII.

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