168 A NEW METHOD OF DETERMINING 
To find the values of the angles (2g + 7'g) at the Epoch we have 
g = 332° 48’ 53.2 
g = 63 5 48 6 
The long period inequality, 5 Saturn — 2 Jupiter, is included in the value of g’. 
From these values of g and g’ we find the various arguments of the perturbations. 
Then forming the sine and cosine for each argument, we multiply the sine and cosine 
coefficients of the perturbations by their appropriate sines and cosines. 
In forming aan (ndz), ete., we can make use of the integrating factors, multiply- 
ing by the numbers in the column (« a < )e Having their differential coefficients we 
proceed as in the case of (ndz), ete. 
We thus find 
(néz)) = + 401”.7, (v)) = + 180”.6, (“) = —22”.6 
Sy (te) = 89026, 2G) 7075) (——) = are. 
“ndt ndt \eost 
And from these we have 
SLOOP i OD SOP, ih = OO 
= — 45.2, iL =-+ 0".4, NG 28.3. 
C= Be Wy 1a", 
The new mean motion is found from (1 — 32’.7162 — 26”.21) nt, which gives 
n = 855’.5196. With this value of n we find the only change is in the coefficients 
of the argument (1— 3), having + 405’.29 instead of 410.16, and — 86”.30 instead 
of — 87.44. 
The constant C now has the value 
C’ = 332° 44’ 16”.3. 
