56 A NEW METHOD OF DETERMINING 
CHAPTER III. 
Development of the Perturbing Function and the Disturbing Forces. 
By means of the formule given in the preceding chapter, the functions pals), 
acre (4)"; etc., can be put in the desired form. The next step is to determine the com- 
plete expression for the perturbing function, and also the expressions for the disturb- 
ing forces. 
If # is taken as the measure of the mass of the Sun, and m the relation between 
the mass of the Sun and that of a planet, the mass of the planet is represented 
by mk’. 
If x, y, 2, be the rectangular codrdinate of a body, those of the disturbing body 
being expressed by the same letters with accents, the perturbing function is given in 
the form 
a=.) 2a] 
Now 
IS = (Wa) =e (=) a (C= 2) 
=p tr? Dr’. A; 
hence 
oO= [bas 2] 
ItmtL4 rl? 
If a © is regarded as expressed in seconds of are, and if we put 
SST nes oa CG). (eo 
1m 
we have 
GQ = Me Gi— @): 
