that the direction of their inclination was towards the mountain. He deduced his results from those among his observations which he considered as the best, being about one out of ten of the whole; but it is much to his credit as an observer, that Baron Zach afterwards found that all his observations, good and bad, gave the same average result as those he had selected. Zach also established the same fact by his observations in the neigbourhood of Marseilles, namely, that the vicinity of a mountain affects the level, which was the instrument he used, and not the plumb-line.

The labour of deducing an approximation to the earth's mean density was undertaken by Dr. Hutton. By getting the best possible estimate of the materials of which Schehallien is composed, and comparing what we must call the weight of the plumb-line towards the mountain with its weight towards the earth, it appeared that the mean density of the latter is about five times that of water. This, considered as a numerical approximation, alone and unsupported, would have been worth little, owing to the doubt which must have existed as to the correctness of the estimation of the mountain's density. It would prove that there was attraction in the mountain, but would give no very great probability to the value of the earth's density, as deduced. But a few years afterwards Cavendish made an experiment, with the same object, and by an entirely different method. By producing oscillations in leaden balls by means of other leaden balls, and by a process of reasoning wholly free from astronomical data, he inferred that the mean density of the earth was five and a-half times that of water. The experiment of Cavendish was published in 1798. This experiment is now being repeated under the direction of the Council of th Astronomical Society.-(See Comp. to Alm., 1838.)

The Schehallien experiment was carried on under many difficulties and privations; and its successful result places its author in the list of those who first opened the road to the determination of a fundamental element of the solar system. But brilliant as it must appear, it is by no means the most useful of Maskelyne's labours. Excepting Bradley, he may almost be called the first who systematically directed his efforts to the attainment of the minutest accuracy in astronomical observation. His celebrated Catalogue, A.D. 1790, consisted only of thirty-six of the principal stars, but the places of these, especially in right ascension, were determined with a degree of precision which was then believed to be hardly attainable. The means by which he accomplished his objects, such as taking the nearest tenth of a second instead of the nearest second, or half second, of time in his transit observations, the practice of uniformly observing all the wires of the instrument, instead of one; the introduction of the movable eye-piece, by which the several wires could all be viewed directly, instead of obliquely, and many little things of the kind, are the indications of a man who was familiar above his contemporaries with the sources of error, and who had formed at once a bold estimate of the extent to which they might be avoided, and a correct view of the means of doing it. It is difficult to say what portion of the present improved spirit of observation in these points may be attributed to Maskelyne, but it certainly was not small. Delambre, who knew at least as well as any man of his time what had been done and was doing, and who was never profuse of praise, as his History of Astronomy' amply demonstrates, pays him the following compliment in the memoir which he contributed to the Biographie Universelle "Maskelyne était en correspondance avec tous les astronomes de l'Europe, qu'il considér

rait comme ses frères, et qui, de leur côté, le respectaient comme un doyen, dont les travaux leur avaient été éminemment utiles."

We have spoken, in the life of Harrison, of the controversy about the merits of the time-piece of the latter. As Astronomer Royal, Maskelyne was the official investigator of the rates of those instruments, and both in the case of Harrison, and in that of Mudge, his decisions underwent printed attacks, which he answered. Without entering into the merits of these questions, since all the grave accusations which were brought against him have fallen harmless, we shall only state, that Maskelyne's answers are full of documents, and free from passion; both very favourable symptoms.

Dr. Maskelyne held church preferment from his college, and was besides in possession of an easy fortune. He died February 9, 1811, leaving behind him an unblemished personal reputation, and a character for scientific utility of the first order. He left behind him much evidence of his utility in the labours and character of the assistants whom he formed; all of whom, says Lalande, were useful astronomers. The late Dr. Brinkley, Bishop of Cloyne, who added the reputation of a distinguished mathematician to that of an eminent observer, was for some time one of his pupils in the practical part of the science.

JOSEPH LOUIS LAGRANGE was born at Turin, January 25th, 1736. His great-grandfather was a Frenchman, who entered into the service of the then Duke of Savoy; and from this circumstance, as well as his subsequent settlement in France, and his always writing in their language, the French claim him as their countryman; an honour which the Italians are far from conceding to them.

The father of Lagrange, luckily perhaps for the fame of his son, was ruined by some unfortunate speculation. The latter used to say, that had he possessed fortune, he should probably never have turned his attention to the science in which he excelled. He was placed at the College of Turin, and applied himself diligently and with enthusiasm to classical lite

rature, showing no taste at first for mathematics. In about a year he began to attend to the geometry of the ancients. A memoir of Halley in the Philosophical Transactions, on the superiority of modern analysis, produced consequences of which the author little dreamed. Lagrange met with it, before his views upon the subject had settled; and immediately, being then only seventeen years old, applied himself to the study of the modern mathematics. Before this change in his studies, according to Delambre*, after it, according to others, but certainly while very young, he was elected professor at the Royal School of Artillery at Turin. We may best convey some notion of his early proficiency, by stating without detail, that at the age of twenty-three we find him-the founder of an Academy of Sciences at Turin, whose volumes yield in interest to none, and owe that interest principally to his productions,―a member of the Academy of Sciences at Berlin, an honour obtained through the medium of Euler, who shortly after announced him to Frederic of Prussia as the fittest man in Europe to succeed himself,-and settling, finally, a most intricate question† of mathematics, which had given rise to long discussions between Euier and D'Alembert, then perhaps the two first mathematicians in Europe. He had previously extended the method of Euler for the solution of what are called isoperimetrical problems, and laid the foundation for the Calculus of Variations, the most decided advance, in our opinion, which any one has made since the death of Newton.

In 1764 he gained the prize proposed by the Academy of Sciences for an Essay on the Libration of the

Eloge de Lagrange, Mémoires de l'Institut. 1812.

The admissibility of discontinuous functions into the integrals of partial differential equations.