44 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
The quantities ay, 4, a, etc., may be computed by Hansen’s for- 
mule given in his work, Auseinandersetzung, etc., 1 Abth., § 61, 
and wes found R, S, and T are found from the Seale 
R= 2a7; S = 2a,, sin Q; T= 2a,, cos Q. 
It would be interesting to know what influence the supposed 
intra-Mercurial planet would have on the other bodies of the 
system, especially on Venus. 
The differential equation of the motion of the ascending node is 
do 365.25 k dV 
dt ~ Ya+m)sini di’ 
The quantity & is the well known Gaussian constant, expressed in 
seconds of arc, and its logarithm is log k = 3.5500065746. 
The value of p’ is expressed by 
ep? =a? -+ a? — 2ad’ cos (a’, a) 
from which we have 
d(p*) ap , a[cos (a, a’)] 
Bis ae ain the di 
But cos (a, a’) = cos cose’ + sine sin <’ cos J, 
cos I = cosi cos?’ -++ sinisin? cos (0 — 0’), 
cot P sin (0 — 0’) — cot sini = — cos (0 — ) cost. 
Differentiating we get 
d® sin’? 
di sn (0—0) (cot i’ cos it + cos (0 — #) sin t) = ¢, 
We also have 
d any noe 
a = — cos?’/sini + cos isin? cos (0 — ”) = t,. 
From these expressions we obtain 
_d(cosa, a’) 
di 
and therefore d(p”) becomes 
= (— cos ¢’ sine + sin ¢’ cose cos I)t, + sin & sin ¢ t,, 
cial = p,cose’ + q, sin &’ 
in which 
p= 2aa’ sin « t,, 
and 
=— 2aa’ (cose cos I t, + sine ¢,). 
