580 Proceedings of the Royal Irish Academy. 



XXXIII. — On the Fltjid State of Bodies composing om Planetaet 

 System. By Heney Heknessy, F.R.S., Professor of Applied 

 Mathematics in the Royal College of Science, Dublin. 



[Eead, February 22, 1886.] 



DuEiKG the past two centuries the constitution of the earth and other 

 bodies composing our planetary system has been a frequent subject of 

 physical and mathematical inquiry. The outswelling of the earth at 

 the equator and its flattening at the poles were accoi;nted for by 

 !Newton and Clairaut on the hypothesis of its original fluidity ; and 

 the shapes of some of the greater planets were similarly explained. 

 Laplace proposed a theory of the formation of the whole planetary 

 system, including the satellites, in which the condition of fluidity 

 formed an essential part. But the former fluidity of the earth, as 

 well as the nebular theory of Laplace, seems not to have been univer- 

 sally admitted. Playfair, in the illustration of the Huttonian theory, 

 attempted to prove that a solid nearly-spherical body, coated with 

 water, would acquire, by abrasion, the observed spheroidal figure of 

 the earth. Sir John Herschel afterwards followed in the same path ; 

 and an eminent geologist of recent times. Sir Charles Lyell, employed 

 the ai'guments of these mathematicians in support of his theories. A 

 member of this Academy, the Pev. Dr. Samuel Haughton, has pub- 

 lished, in our Tramactions for 1852, a Paper, in which he proposed to 

 examine, among others, this question — " Whether the evidence of the 

 original fluidity of the earth and planets, afforded by their observed 

 figures, is satisfactory with respect to all the planets ; whether we 

 possess, from the data afforded by astronomy, sufficient knowledge of 

 the structure of the interior of the earth to enable us to draw conclu- 

 sions respecting it which are of geological value." His answer to 

 these questions was in the negative ; and as it now seems that they 

 should, on the contrary, be answered in the affirmative, it appears de- 

 sirable that the Academy should be placed in possession of the evidence 

 for coming to a correct judgment on the question. 



Most of my recent researches on the figures of the planets have 

 been communicated to the French Academy of Sciences ; and they 

 have appeared in its Comptes rendus. In 1874, a French mathema- 

 tician, M. Amigues, reproduced a result I had long before discovered ; 

 and after establishing my priority to the discovery in the Comptes 

 rendus for October, 1878, I applied this resiilt to the inquiry as to 

 whether the theory of superficial abrasion or that of entire fluidity of 

 the planets would be best adapted for explaining the results of obser- 

 vations made in recent times on the figures of the planets. 



I had long since proved, in a Paper printed in the Proceedings of 

 tliis Academy, vol. iv., that Playfair's method of accounting for the 



