403 
of Edinburgh , Session 1881-82. 
L=p2-5^F.0'32 cm .sin 30° cos 30° 
5 1) 
= -F. 0*21 cm . 
Now if S denote the number of grammes in the sun’s mass, we 
have 
F — ^-pS.980 dynes , 
since the earth’s attraction on a gramme of matter at its surface is 
about 980 dynes ; and so we find 
L = — S. 980.0 '21 - ^ S.207 
L ) 6 ±j 6 
• (5), 
Now if <b denote the acceleration of the earth’s angular velocity 
produced by this couple, we have 
where I denotes the earth’s moment of inertia ; and, allowing for 
the increase of the earth’s density from the surface inwards, accord- 
ing to Laplace’s probable law, we have, approximately, 
•* Zi 
(instead of I — — r 2 E , as it would be if the mass were homogeneous), 
5 
E denoting the earth’s mass. Hence 
r 3 S207 
D 3 I7 ' 
Now D 3 /r 3 = 12‘3.10 12 , S/E — 3L9.10 4 , r — 6 - 370. 10 s centimetres 
which gives r 2 = 40 '6. 1 0 16 . Hence 
. 31-9.10 4 207 
"~hl-3.10 12 40-6.10 16 
4-0-10-®. 
This is the rate per second of gain of angular velocity, The earth’s 
2 w 
angular velocity at present is , or approximately ^ . 
Calling this to, we have 
-= 5-5, 10“ 2 
to 
3 F 
VOL. XX. 
