comet, from the name of a German officer, who first saw it but the proof of its revolution round the sun is a step so much more important, that we cannot but assent to the justice of what is urged by M. Arago, that this ought to be established as the ground of nomenclature in such cases, and that the comet ought to bear the name of the French astronomer, Gambart.

Sect. 6.-Application of the Newtonian Theory to the Figure of the Earth.

THE heavens had thus been consulted respecting the Newtonian doctrine, and the answer given, over and over again, in a thousand different forms, had been, that it was true; nor had the most persevering crossexamination been able to establish anything of contradiction or prevarication. The same question was also to be put to the earth and the ocean, and we must briefly notice the result.

According to the Newtonian principles, the form of the earth must be a globe somewhat flattened at the poles. This conclusion, or at least the amount of the flattening, depends not only upon the existence and law of attraction, but upon its belonging to each particle of the mass separately; and thus the experimental confirmation of the form asserted from calculation, would be a verification of the theory in

its widest sense. The application of such a test was the more necessary to the interests of science, inasmuch as the French astronomers had collected from their measures, and had connected with their Cartesian system, the opinion that the earth was not oblate but oblong. Dominic Cassini had measured seven degrees of latitude from Amiens to Perpignan, in 1701, and found them to decrease in going from south to north. The prolongation of this measure to Dunkirk confirmed the same result. But if the Newtonian doctrine was true, the contrary ought to be the case, and the degrees ought to increase in proceeding towards the pole.

The only answer which the Newtonians could at this time make to the difficulty thus presented, was, that an arc so short as that thus measured, was not to be depended upon for the determination of such a question; inasmuch as the inevitable errors of observation might exceed the differences which were the object of research. It would, undoubtedly, have become the English to have given a more complete answer, by executing measurements under circumstances not liable to this uncertainty. The glory of doing this, however, they, for a long time, abandoned to other nations. The French undertook the task with great spirit". In 1733, in one of the meetings of the French Academy, when this question was discussed, De la Condamine, an ardent and eager

VOL. II.

39 Bailly, iii. 11.

R

man, proposed to settle this question by sending members of the academy to measure a degree of the meridian at the equator, in order to compare it with the French degrees, and offered himself for the expedition. Maupertuis, in like manner, urged the necessity of another expedition to measure a degree in the neighbourhood of the pole. The government received the applications favourably, and these remarkable scientific missions were sent out at the national expense.

From this time there was no longer any doubt as to the fact of the earth's oblateness, and the question only turned upon its quantity. Even before the return of the academicians, the Cassinis and La Caille had remeasured the French arc, and found errors which subverted the former result, making the earth oblate to the amount of 1-168th of its diameter. The expeditions to Peru and to Lapland had to struggle with difficulties in the execution of their design, which make their narratives resemble some romantic history of irregular warfare, rather than the monotonous records of mere measurements. The equatorial degree employed the observers not less than eight years. When they did return, and their results were compared, their discrepancy, as to quantity, was considerable. The comparison of the Peruvian and French arcs gave an ellipticity of nearly 1-314th, that of the Peruvian and Swedish arcs gave 1-213th for its value.

Newton had deduced from his theory, by reason

ings of singular ingenuity, an ellipticity of 1-230th; but this result had been obtained by supposing the earth homogeneous. If the earth be, as we should most readily conjecture it to be, more dense in its interior than at its exterior, the ellipticity will be less than that of a homogeneous spheroid revolving in the same time. It does not appear that Newton was aware of this; but Clairaut, in 1743, in his "Figure of the Earth," proved this and many other important results of the attraction of the particles. Especially he established that, in proportion as the fraction expressing the ellipticity becomes smaller, that expressing the excess of the polar over the equatorial gravity becomes larger; and he thus connected the measures of the ellipticity obtained by means of degrees, with those obtained by means of pendulums in different latitudes.

The altered rate of a pendulum, when carried towards the equator, had been long ago observed by Richer and Halley, and had been quoted by Newton as confirmatory of his theory. Pendulums were swung by the academicians who measured the degrees, and confirmed the general character of the results.

But having reached this point of the verification of the Newtonian theory, any additional step becomes more difficult. Many excellent measures, both of degrees and of pendulums, have been made since those just mentioned. The results of the arcs" is 40 Airy. Fig. Earth, p. 230.

an ellipticity of 1-298th ;—of the pendulums, an ellipticity of about 1-285th. This difference is considerable, if compared with the quantities themselves; but does not throw a shadow of doubt on the truth of the theory. Indeed, the observations of each kind exhibit irregularities which we may easily account for, by ascribing them to the unknown distribution of the denser portions of the earth, but which preclude the extreme of accuracy and certainty in our result.

But the near agreement of the determination, from degrees and from pendulums, is not the only coincidence by which the doctrine is confirmed. We can trace the effect of the earth's oblateness in certain minute apparent motions of the stars; for the attraction of the sun and moon on the protuberant matter of the spheroid produces the precession of the equinoxes, and a nutation of the earth's axis. The precession had been known from the time of Hipparchus, and the existence of nutation was foreseen by Newton; but the quantity is so small, that it required consummate skill and great labour in Bradley to detect it by astronomical observation. Being, however, so detected, its amount, as well as that of the precession, gives us the means of determining the amount of terrestrial ellipticity, by which the effect is produced. But it is found, upon calculation, that we cannot obtain this determination without assuming some law of density in the homogeneous strata of which we suppose the earth