Remarks on the Theory of the Figure of the Earth. 339 



refraction, chiefly by observation of Capella ? If this turn out 

 to be the case, it would become exceedingly curious, as by 

 numerous experiments the refractions of Capella appear to me 

 to equal the mean refraction, and that of Lyra and Aldebaran 

 the two extremes. 

 Hartwell, April 16, 1824. 



LVI. Remarks on the Theory of the Figure of the Earth. 

 By J. Ivory, Esq. M.A. F.R.S. 



¥T is not my intention to trace minutely the various labours 

 -*• of philosophers on the Figure of the Earth, but to state 

 concisely the present mathematical theory on that subject, and 

 to add some observations upon it* 



1. To whatever branch of the philosophical system of the 

 universe we turn our attention, we are immediately led to the 

 immortal author of the true theory founded on the law of uni- 

 versal gravitation. Newton not only laid down the principles : 

 he, in a great measure, reared the superstructure ; or, at 

 least, he sketched out so accurately the proper view to be 

 taken of every part of the subject, that his followers have done 

 little else but fill up his original outlines. The modern theory 

 of the figure of the planets, still imperfect in some respects, 

 coincides in the main with the physical ideas of Newton, 

 which the progress of the mathematical sciences has enabled 

 the philosophers of the present day to develop and extend. 



It is supposed in the Principia, that the earth is a mass of 

 homogeneous fluid, the particles of which attract one another 

 in the inverse proportion of the square of the distance. If 

 there were no rotatory motion, the only figure consistent with 

 the equilibrium of the attractive forces, woidd be a perfect 

 sphere. But as the earth revolves upon an axis, a centrifugal 

 force is communicated to the particles of the fluid, causing 

 them to recede from the axis, and changing the sphere into 

 a figure oblate at the poles and protuberant at the equator. 



The proportion of the centrifugal force to gravity is easily 

 found. Every point of the equator describes, in a second of 

 time, a circular arc having its versed-sine equal to 0*67 of an 

 inch ; which is very nearly ^ of 16 T \ feet, the space through 

 which a heavy body falls in the same time. Hence the cen- 

 trifugal force is „}r Ti of the observed gravitation ; or v fo of the 

 attractive force that would prevail if the earth preserved its 

 figure and were at rest. 



In the question of the figure of the earth we may therefore 



suppose (l sphere consisting of a homogeneous fluid, at rest 



U U 2 and 



