1231 
motion of the argument of libration and of the order of mm! ; thus 
the divisor, which appears at the integration, is of the order of 1’. In 
this divisor neglecting A2*, which is only of the order of m'?, the 
solution of the differential equation, taking account only of the term 
OR 
in aal from the right member, becomes : 
1 OR, 
OR, 06" 
00? 
Substituting the numerical values of the various quantities, we get : 
00 = + 7.89 e' sin 2 
and, for e' taking the value 0.0272 (Struve, le. pg. 172) and 
expressing the result in degrees: 
06 = + 12°3 sin &., 
The value from observation is (Struve, |. e. pg. 290): dé = + 14.°0 
sin ©; thus the agreement is very satisfactory, considering the sim- 
plifications admitted for the deduction of the theoretical value. 
The value of OI is to be determined by a quadrature from the 
equation : 
06= 
dor OR, 
eS a ees 
dt 02 
| ddO 
while 4 results from the equation for roa without any integration. 
Considering the fact that R, as well as the mean motion of @ are 
of the order of m', the values of dr’ and OA are seen at once to 
be of the order zero with respect to m'. 
The value of d® results from the equation: 
dd® 0°(R 07(R 
ORR), 
+R,) J OR, 
dt =—sSs OWA : 
or 
r+ 
or 
ddO 
Subtracting the equation for ae from four times this equation, 
we get: 
dób dd6 0?R 0?R òR 0?R 
Pica a Ap ER 0 ah 4 0 han Pee 
dt dt emt ae 24+] or: | end dp 
0°R 0’R ò°R o*R OR OR 
1 ï 1 i 1 1 )T : As 2 > 
+|4 arOA | =| OA E orm? sa NITRA PE 
Taking into account the relations: 
n vi ay 3 _42R | 
drdA | da om dAor ’ 
O® is seen to be of the order zero with respect to im’. 
