402 
Proceedings of the Royal Society 
centrated in a point, and a portion of matter m, concentrated in a 
very distant point — 
L = 3 m 
(B-C )yz ^ 
(x 2 + y 2 + z 2 Y 
(i), 
where x , y , z denote coordinates of m relatively to rectangular 
lines OX, OY, OZ coincident with the principal axes of inertia of 
M through its centre of inertia ; B and C the moments of inertia of 
M round OY and OZ ; and L the component round OX, of the 
couple obtained by transposing, after the manner of Poinsot, the 
resultant attraction of m, from its actual line through x, y , z, to a 
parallel line through o , the centre of inertia of M. Suppose now 
M to be a homogeneous ellipsoid of revolution, having for semi-axes 
a, by c , we have 
B - C = g M (c 2 - 6 2 ) 
= \w(c + b)(c-b). 
Hence for a prolate spheroid of the dimensions stated above, we 
have 
B - C = g M> 0’32 (2), 
where r denotes the earth’s radius in centimetres. To fit the 
formula (1) to the case represented by the diagram in fig. 2, we 
have 
yz = D 2 sin 30° cos 30° ...... (3), 
where D denotes the sun’s distance from the earth. With this and 
(2), (1) becomes 
_ 3 mMr 0*32 cm sin 30° cos 30° 
“5 IP 
( 4 ), 
where M denotes the mass of a quantity of mercury equal in bulk 
to the earth, so that if E denotes the earth’s mass M = 2*5 E. How 
is the attraction of the earth on the sun : hence if we call 
J > 
this force F, 
