MR. LUBBOCK’S RESEARCHES IN PHYSICAL ASTRONOMY. 
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e q z' (qx’ — py') 
nearly. 
r \Zx ,a - + y'°- Vx' q + y'- + 2 '' 
The resistance acting in the direction of the normal, and since the velocity 
= Joe' 2 -f y' 2 J ( p 2 + q 1 + r 2 ) nearly; 
C d r = 0 
Bda I (A + + 
y J r { £c' a + y hi +■ s' 2 } 
.4dt I (C B)crdt-dt ft y ' Z ' { ' + e °-)- z 'y'} e ^ , ( qx '- p u') V^+7 q ds{p q + g q A-r q ) 
1 V 7 J r{x' q + y' q + 2 2 } 
sin — — (n t + y) d c + c ^ cos ^ (n t + y) d y 
A A 
72 die 4 Px'z' q (qx' — p?/') \Ar ' 2 + 2/' a ds 
_ -___y 
{^2 + y* 2 + s'2-J. 
C — A / , . x, (C- A) . C-A, t , 
cos (« t + y) d c — c- — - — -sin — - — (n £ + y) dy 
^ A A 
_ n d i e 4 /"V/' s' 2 (9^ — py') V' x' 2 + t/' 2 d s 
J ~ {z' 2 + y'* + s' 2 } 
since J' x H z'~ d s =y y'- z' q d s 
"* x ' y' z ' q V a?' 9 + y " 2 d s 
, n d t e* c Tx'- z ' 2 x " 2 + y'- d s , n d t e* ■ n (C — A) , N f*x' y' z 1 
dC= -^T-y + / ~ + a«} ■■ 4 TJ lm2 ~ ‘ + y 2/ {?+V + ^} 
neglecting the term which is periodic, 
H r _ ^ e 4 d £ Px ' 2 z' q */ x’° + y'~ d s 
nC ~A~J {x' q + y' q + s' 2 } ' 
T p x^z^Wx'- + t/ l2 ds _ n 
{x'* + y'* + z'*} 
D being a positive quantity. 
J. 
dc = — 11 n d 1 e c = nD J*- , e being the base of Naperian logarithms. 
When t is infinite c = 0 ; hence the latitude of the axis of instantaneous rota- 
tion increases until it reaches 90°, which is its limit. 
Having determined the variations of c, y and n by means of the above equa- 
tions, the variations of the other constants u, ^p 0 and <p 0 may be determined 
from the equations 
p d t = sin <p sin 9 d — cos <p d 9 
qdt = cos <p sin 0 d \j/ + sin <p d 9 
r d t = d <p — cos 6 d \p 
