ART. III.-1. Traité de Géodésie, ou exposition des Méthodes trigonométriques et astronomiques, applicable soit à la mesure de la terre, soit à la confection des canevas des cartes et des plans topographiques; par L. Puissant, Chevalier de l'ordre Royal et Militaire de St. Louis, &c.-Paris 1819.

2. Méthodes Analytiques pour la determination d'un arc du Meridien; par J. B. J. Delambre, Membre de l' Institut National et du bureau des Longitudes, &c. &c., précédées d' un Mémoire sur le même sujet, par A. M. Legendre, membre de la Commission des poids et mesures de l' Institut National.-Paris, An. VII. 3. An account of the measurement of an arc of the Meridian between the parallels of 18° 3' and 24° 7', being a continuation of the grand meridional Arc of India, as detailed by the late Lieutenant-Colonel Lambton, in the volumes of the Asiatic Society of Calcutta; by Captain George Everest, of the Bengal Artillery, F. R. S., &c.-London 1830.

4. Geometrical Theorems and Analytical formula, with their application to the solution of certain geodetical problems, by William Wallace, L. L. D. Emeritus Professor of Mathematics in the University of Edinburgh, &c. &c.-Edinburgh 1839. THERE is much of truth in a common proverbial saying, that one half of mankind is unacquainted with the other half. This is not more true regarding those portions of the human family that are farthest separated from each other in local habitation, than in respect of those who, though dwelling side by side, are separated and disjoined from each other by differences of rank and station, differences of opinion and motive, or differences of intellectual habits. We have heard of a Princess of the blood royal, who, on being told that many people, during a period of scarcity, were dying of starvation, declared that she thought them very foolish to permit themselves to die from such a cause; for her own part, rather than die of hunger, she would even live on bread and cheese! We have heard too of a man, who being asked how he thought Astronomers could predict eclipses, declared that nothing could be more simple-they had only to look in the Almanac! These are extreme cases, and may, perhaps, be referred to extreme thoughtlessness, rather than to extreme ignorance; but it cannot possibly be questioned that there does exist, in every class of every community, a great amount of ignorance regarding the habits and pursuits of all the other classes. To break down the barriers that thus dissever the different sections of the human family, and to excite in the breast of each a kindly and generous sympathy with the hopes

and fears, the joys and sorrows, the successes and disappointments of all, is one of the blessed effects that may be expected from that general diffusion of sound knowledge by which the present age is so distinguished. Unquestionably it is the will of Him who has made of one blood all generations of men to dwell in all places on the earth," and who has linked the various classes of Society together by mutual interests and obligations and dependencies,-that such a generous and intelligent sympathy should exist among those whom he has thus made brothers in the same family, and fellow-workers in the same service.

Perhaps there are no two classes of men who are less acquainted with each other, who know less of each other's ends and objects, difficulties and perplexities, hopes, fears and feelings, than the mathematical and the non-mathematical portion of the community. Speak to the generality of men about a mathematician, and immediately there rises up before them the image of a wretched parchment-skinned old man, in the world but not of it, dissociated from all the concerns that interest his fellowmortals, and spending his days and nights in vain attempts to trisect an angle and to square the circle, to do that in one particular way which every carpenter does a hundred times in a day without any difficulty in another, looking with an eye of scorn on all the pursuits of the working world, and despising the finest productions of human intellect and taste, because he does not see what they are meant to demonstrate! It is ever thus, that men will ply the pencil of the caricaturist in sketching those whom they do not know. Thus the merchant will be described as a man whose whole soul is in his ledger, whose affections are all concentred in "another and another lakh;" the lawyer is pictured as a compound of precedents, and rules nisi, and certiorari; and every class is conceived of by every other with reference only to those singular exceptions in whom the peculiarities of the class are ridiculously prominent. There have undoubtedly been triflers in mathematics, as well as in other pursuits; but it is a grievous mistake to suppose that mathematical studies, even of the most abstract kind, are necessarily destitute of a direct bearing upon the ordinary interests and concerns of man. Lord Bacon, who did more than any other man to render the sciences practical, seems fully to have understood the important connexion that subsists between the cultivation of abstract mathematical science and the progress of mankind in practical science. Not to mention the multitudes of passages in his philosophical writings, we may quote a letter to the Marquess of Buckingham, in which he

states his conviction that the foundation of the Savilian and Sandisian Professorships of Geometry was of more importance than the foundation of Dulwich Hospital. The letter is as follows:

"To the Marquess of Buckingham.

"My very good Lord. I thank your Lordship for your last loving letter. I now write to give the king an account of a patent I have stayed at the office. It is of license to give in mortmain eight hundred pound land, though it be tenure in chief, to Allen, that was the player, for an hospital. I like well that Allen playeth the last act of his life so well; but if his majesty give way thus to amortize his tenures, his courts of wards will decay which I had well hoped should improve.

"But that which moved me chiefly is, that his majesty now lately did absolutely deny Sir Henry Savile for 2007., and Sir Edward Sandys for 100l. to the perpetuation of two lectures, the one in Oxford, the other in Cambridge; foundations of singular honour to his majesty, the best learned of kings, and of which there is great want; whereas hospitals abound and beggars abound never a whit the less.

"If his majesty do like to pass the book at all; yet if he would be pleased to abridge the 8007. to 500l. and then give way to the other two books for the university, it were a princely work. And I would make an humble suit to the king and desire your Lordship to join in it that it might be so. God ever preserve and prosper you.

"Your Lordship's most obliged friend and faithful servant, "FR. VERULAM, Canc.

York House, August 18, 1618. "I have written to my Lord Chamberlain, being Chancellor of Oxford, to help in the business."

We find also in his will that Lord Bacon designed the endowment of two professorships on the model of the Savilian Professorship. The following is an extract from his will:

"And because I conceive there will be upon the moneys, raised by sale of my lands, leases, goods and chattels, a good round surplusage, over and above that which may serve to satisfy my debts and legacies and perform my will; I do desire and declare that my executors shall employ the said surplusage in manner and form following; that is to say that they purchase therewith so much land of inheritance as may create and endow two lectures in either the Universities, one of which lectures shall be of natural philosophy and the sciences in general thereunto belonging; hoping that the stipend or salaries of the lecturers may amount to two hundred pounds a year for either of them; and for the ordering of the said lectures, and the

election of lecturers from time to time, I leave it to the care of my Executors to be established by the advice of the Lords Bishops of Lincoln, and Coventry and Litchfield.

Nevertheless thus much I do direct, that none shall be lecturer, if he be English, except he be master of Arts of seven years' standing, and that he be not professed in divinity, law or physic, as long as he remains lecturer; and that it be without difference, whether he be a stranger or English; and I wish my Executors to consider of the precedent of Sir Henry Savil's lectures for their better instruction."

We regard these extracts, (especially the former) from the incidental writings of the great father of practical utilitarian philosophy, as most valuable testimonies to the importance of the study of pure demonstrative science, and as furnishing a rebuke to those multitudes who believe that they are treading in the footsteps of Bacon when they decry the study of pure mathematics as a remnant of scholastic trifling.

To the enlightened advocates of practical philosophy it is not difficult to shew that a science which brings man into contact with the eternal relations of things, which brings us back to the principles on which the universe is constructed, and which must ever be the director of observation in regard to the actually existing universe, cannot be a useless study if judiciously cultivated. Neither should it be difficult to convince the man who is accustomed to observe and analyse the workings of the mind, that so far from dissociating their devotee from the rest of the world, mathematical studies are best of all fitted for cultivating those talents and accomplishments which enable a man to attract and please and instruct his fellows. It may seem a somewhat startling affirmation, but we are persuaded it is true, that the imagination is the faculty which the mathematician is called chiefly to exercise. We speak not of course of the mere learner of mathematics, who can merely make himself master, by an effort, of a proposition of which the demonstration is put before him. We do not regard him as a mathematician at all. At the best he stands in the same relation towards the true mathematician in which the brick-layer stands towards the architect. He may doubtless discharge all his functions without a particle of imagination. But mathematical invention is effected by forming in the mind new combinations, by so tracing relations and connexions as to be able intuitively to detect the bearings of a demonstrated truth upon other subjects than those regarding which it is demonstrated; and this we suppose is just as much an exercise of the imagination as is that put forth by the poet or the painter.

But we despair of being able to convince the generality

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of readers, by taking them into the study of the mathematician, that he is or can be any thing but a being poring over diagrams and tables, and puzzling his brains over imaginary difficulties. We therefore propose not to enter into the study of the recluse, but rather to bring him out into the wide world, and shew him engaged in one of those works which he only is able to accomplish, in order that our readers may see that he is capable of entering with effect into the business which men regard as useful and important to them. Of all the practical works that are accomplished by the direct application of mathematical studies, the two greatest are astronomical and geographical. The latter, or rather one great department of the latter work, is that which is now to occupy our attention; and it is our purpose to give a very rapid view of the object to be accomplished in a trigonometrical survey, and then to make some remarks on the great trigonometrical survey that has for a long time been going on in British India.

The idea of a great Trigonometrical Survey of a country, to be undertaken by the Government of that country, was first conceived by General Watson, at the suppression of the "rising" in Scotland in 1745. The execution of it was committed to General Roy, and was originally intended to extend no farther than the disaffected districts of the Highlands. The design however was subsequently enlarged, and the grand Trigonometrical Survey of Great Britain and Ireland was projected a Survey that has cost the country an enormous sum of money, which, albeit it has not been paid ungrudgingly, it is yet very creditable to the country to have paid. This Survey, begun just a hundred years ago, has been frequently suspended, but never wholly abandoned; and it is now, we believe, brought within a little of its termination.

This survey has effected much for science in various ways. It was in the course of conducting it, that the real difficulties of the accomplishment were evolved, and the most scientific men in Europe were set to work to overcome them. The extreme accuracy that was required, gave an impulse to the efforts of our instrument-makers, and may be regarded as having given a beginning to the process of improvement in this department, which has advanced so stedfastly ever since, that now we have probably attained almost as near perfection as it is permitted to man to reach. It was in this Survey too, that the great accuracy of the instruments first brought into notice an element that had never been taken account of before, and whose treatment gave occasion to the discovery of some of the most elegant propositions in spherical trigonometry. As this element is a