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be, the importance and singularity of the subjects, or the advantageous manner of treating them, without pretending to answer for the certainty of the facts, or propriety of the reasonings, contained in the several papers so published, which must still rest on the credit or judgment of their respective authors.
It is likewise necessary on this occasion to remark, that it is an established rule of the Society, to which they will always adhere, never to give their opinion, as a Body, upon any subject, either of Nature or Art, that comes before them. And therefore the thanks which are frequently proposed from the Chair, to be given to the authors of such papers as are read at their accustomed meetings, or to the persons through whose hands they receive them, are to be considered in no other light than as a matter of civility, in return for the respect shewn to the Society by those communications. The like also is to be said with regard to the several projects, inventions, and curiosities of various kinds, which are often exhibited to the Society; the authors whereof, or those who exhibit them, frequently take the liberty to report, and even to certify in the public newspapers, that they have met with the highest applause and approbation. And therefore it is hoped, that no regard will hereafter be paid to such reports and public notices; which in some instances have been too lightly credited, to the dishonour of the Society.
I. On the Grounds of the Method which Laplace has given in the second Chapter of the third Book of his Mécanique Céleste for computing the Attractions of Spheroids of every Description. By James Ivory, A. M. Communicated by Henry Brougham, Esq. F. R.S. M.P.
Read July 4, 1811.
N every physical inquiry the fundamental conditions should be such as are supplied by observation. Were it possible to observe this rule in every case, theory would always comprehend in its determinations a true account of the phenomena of nature. Applying the maxim we have just mentioned to the question concerning the figure of the planets, the mathematician would have to investigate the figure which a fluid, covering a solid body of any given shape, and composed of parts that vary in their densities according to a given law, would assume by the joint effect of the attraction on every particle and a centrifugal force produced by a rotatory motion about an axis. The circumstances here enumerated are all that observation fully warrants us to adopt as the foundation of
this inquiry: for, with regard to the earth we know little more than that it consists of a solid nucleus, or central part, covered with the sea; and with regard to the other planets, all our knowledge is derived from analogy which leads us to think that they are bodies resembling the earth. There is one consideration, however, by which the general research may be modified without hurting the strictest rules of philosophizing; and that is, the near approach to the spherical figure which is observed in all the celestial bodies: and it is fortunate that this circumstance contributes much to lessen the great difficulties that occur in the investigation. But, even with the advantage derived from this limitation, the inquiry is extremely difficult, and leads to calculations of the most abstruse and complicated nature; and, when viewed in the general manner we have mentioned, it far surpassed the power of the mathematical and mechanical sciences as they were known in the days of Sir ISAAC NEWTON, who first considered the physical causes of the figure of the planets. That great man was therefore forced to take a more confined view of the subject, and to admit such suppositions as seemed best adapted to simplify the investigation. He supposed in effect that the earth and planets at their creation were entirely fluid, and that they now preserve the same figures which they assumed in their primitive condition; a hypothesis by which the inquiry was reduced to determine the figure necessary for the equilibrium of a fluid mass. The mathematicians, who have followed in the same tract of inquiry, have seldom ventured to go beyond the limited supposition proposed by NEWTON. They have succeeded in shewing that a mass revolving about an axis, and composed of one fluid of a uniform density, or