164 



Prof. G. H. Darwin. 



[Dec. 13, 



The case of fe=0 gives the planet infinite mass at the centre, and 

 the values are only inserted in order to complete the series. 



fe. 



Length mod. 

 at surrace 

 m terms or 

 a as unity. 



e = ta x 

 where 

 x = 



CB 



T 



Laplace 



CB 



t 



C — A 



Laplace 

 C-A 



| where 





G{t-^m) 



1 *o 



00 



.... . . 



0*000 



1 .AAA 



. . . 



1 '00 



1 oo7 



1 '67 



1 



j — OO 



•9 



3 '333 



'132 



1 Uoo 



1 '04 



1 .ft A 1 



1 71 



— 4*667 



•8 



1 *667 



"293 



1 14/ 



1 '09 



1 "833 



1 '77 



— 1*333 



•7 



1-111 



0-488 



1-244 



1'15 



1 -952 



1'83 



-0-067 



•6 



1-1 -2 



0-722 



1-361 



1'21 



2-111 



1'90 



! 0*333 



. K 

 



1 — 1 5 



1 "000 



T . K AA 

 1 OUU 



1 '27 



2 '333 



1 '98 



-667 



•4 



1-1-8 



1 -322 



] -661 



1-34 



2-667 



2'07 



*889 



•3 



l-r-2-1 



1 -688 



1 -844 



1 'Al 



3 '222 



2' 17 



] 1 -048 



•2 



1-2 4 



2-093 



2-047 



1 '48 



4'333 



2'28 



j 1 *167 



•1 



1-2-7 



2-532 



2-266 



1-56 



7*667 



2 '40 



1 -259 



•0 



1-3-0 



3-000 



2-500 



1'65 



00 



2'55 



! 1 -333 



•667 



1-000 



0-562 



1-281 



I'll 



2-000 



1-85 



J 



1 jpoc log w 



•333 



1-2-0 



1-562 



1-781 



1 '39 



3-000 



2'13 



1 -ooo 



Note. — The values in the two columns applicable to Laplace's theory were found 

 by graphical interpolation from a series of values given in " Month. Not.," R.A.S., 

 Dec, 1876, or Thomson and Tait, "Nat. Phil." (1883), § 824'. 



In Laplace's theory ^>oc (to 2 — 1), and the modulus of compressibility <x w 2 . In 

 the present theory the modulus oc w y . 



The value fe = *667 corresponds to constant compressibility, and It = '333 to 

 gaseous compressibility. 



One of the grounds on which Laplace's solution is held to be satis- 

 factory is that if we take the value of a?, as determined by the known 

 angular velocity and mean density of the earth, and the value of z as 

 determined by geodesy, and find the value of fe, the ratio of surface to 

 mean density, which corresponds with the ratio ce/e, this same value 

 of is found to give a proper value to the coefficient of z — -Jm, so as 

 to obtain the observed precessional constant. To be more precise, m 

 is found to be 1/289*66, which gives ce=l/231'7, and z has been found 

 to be approximately 1/295. These give cb/jc = 1*273, and this corre- 

 sponds with fe=l/2*06=-49. This value of fe, with the same values 

 of z and m, gives the precessional constant as '0033, and Leverrier 

 and Serret give its value as '00327. 



Now it appears remarkable that almost as good a correspondence 

 is obtainable from my solution. The value cejz= 1"273 corresponds 

 with fe='675, and when fe=*675 the coefficient of z—\m in the pre- 

 cessional constant is 1*99, which gives the same precessional constant 

 •0033. 



This value of & corresponds very nearly with constant modulus of 

 compressibility, and with pressure determined by p = 2tt log w. 



