304 Transactions of the Boyal Society of So^ith Africa. 
Argument. 
Action of— 
Primary. 
Secondary. 
Tertiary. 
Mercury 
+ 0-130 
- 0-003 
Nil 
Venus 
+ 3-813 
- 0-002 
Nil 
131' - 8X 
Venus 
-1-253 
- 0-003 
Nil 
m'-s\ 
Venus 
+ 2-091 
-0-012 
Nil 
r-x 
Mars 
+ 0-102 
+ 0-006 
Nil 
151' - 8X 
Mars 
+ 0-161 
- 0-009 
Nil 
2/' - 2\ 
Jupiter 
+ 1-901 
-0-012 
Nil 
(See for further examples Le Verrier's "Theory of the Sun " (Les Annales, 
iv., pp. (9)-(18) ). The secondary terms given appear to be the largest 
in this theory.) 
In the action of Saturn on Jupiter we find — 
Argument. 
Primary. 
Secondary. 
Tertiary. 
sr-2x~co' 
+ 26-79 
- 0-10 
+ 0-02 
Largest individual term of 
the Great Inequality 
-1522-78 
+ 11-18 
+ 0-41 
(See Les Annales, xi., p. 121, &c.) 
In the last case the next term may be estimated at about 0"-04. For 
such a quantity to have any real significance we must know the mass of 
Saturn correctly within its 300W0 P^-^^' ^^^^ ^^le annual motion of Jupiter 
within 0"-00008. Both of these requirements are beyond our power of 
attainment ; in short, terms of the tertiary order are of very little import- 
ance, whilst those of the next order are quite negligible in the theories to 
which an algebraical development can be applied. 
It may, however, be necessary to include such terms in the considera- 
tion of the secular perturbations, but in this case it is possible to give 
general expressions of great simplicity, extending to any powers of the 
eccentricities and mutual inclinations, and these will be found in the last 
table of the present paper. 
Chessin has shown {Ast, Journal, No. 442, 1898) that it is possible to 
simplify the expressions for the computation of the values of the Newcomb 
operators ; he gives the following example : — 
Newcomb — 
7680n^ = D6 + (8^ - 25)D5 + (20^^ - 130^ 185)D4 + ( - 80t^ + 340* - 255)D3 
+ ( _ 80i4 + 640*3 - 1765*^ + 2280* - 1466)0^ 
-f- ( - 128*5 + 1360*4 - 5280*3 + 9535*- - 8454* + 3096)D 
+ ( - 64*6 + 800*5 - 3740*4 + 8200*3 - 8588*^ -f 3608*). 
