11. 



THEORY OF THE FIGURE OF THE EARTH. 



[LECTURES on the Theory of the Figure of the Earth were delivered by Adams 

 in the Lent Term of 1871 and were repeated once or twice with little alteration. 

 They were prefaced by a historical sketch of the problem, translated from Laplace 

 (Mecanique Celeste, livre XL ch. 1), continued by Chasles (Recueil des Savans Strangers, 

 t. IX.). It does not seem proper to reprint this matter here, and it has been omitted. 

 The concluding lectures have also been omitted ; these dealt with attractions of ellipsoids 

 and ellipsoidal shells; the greater part has since become familiar in current text-books, 

 and what was most interesting and original in it was published by Adams himself 

 (Camb. Phil. Soc. Proc., II. p. 213), and has been reprinted in the first volume of 

 his papers, No. 53, p. 414. The form of lectures, never very marked, has not been 

 preserved in the remainder. It divides roughly into three portions. 1 5 make an 

 informal commentary upon certain propositions in Newton's Principia, lib. I. sect. xii. xiii. 

 It should be remarked that these propositions by no means represent all that Newton 

 contributed to the theory of the Figure of the Earth. 6 -10 give a characteristic 

 discussion of the potential and attraction of a spheroid of small ellipticity on any 

 point. 11 15 demonstrate Clairaut's theorem, deducing it from hypotheses as to the 

 internal strata of equal density, and these hypotheses are further considered in a theory 

 of the internal state of a fluid earth of heterogeneous structure, supposed to rotate as if 

 solid.] 



ATTRACTION OF SPHERES AND SPHEROIDS BY METHODS ANALOGOUS 



TO NEWTON'S. 



1. Attraction of a uniform spherical shell. 



Let be the centre of a spherical shell, a its radius ; M an attracted 

 point, MO = r. 



A. II. 



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