SECT. 4.] TAKING INTO ACCOUNT THE PERTURBATIONS. 277 



of time is embraced, this method can also be made to answer in several cases for 

 the more precise determination of the masses of the disturbing planets, at least 

 of the larger planets. Indeed, if the mass of any disturbing planet assumed in 

 the calculation of the perturbations does not seem sufficiently determined, besides 

 the six unknown quantities depending on the corrections of the elements, yet 

 another, p, will be introduced, putting the ratio of the correct mass to the assumed 

 one as 1 -f- p to 1 ; it will then be admissible to suppose the perturbations them 

 selves to be changed in the same ratio, whence, evidently, in each one of the com 

 puted places a new linear term, containing /*, will be produced, the development 

 of which will be subject to no difficulty. The comparison of the computed places 

 with the observed according to the principles above explained, will furnish, at the 

 same time with the corrections of the elements, also the correction p. The 

 masses of several planets even, which exert very considerable perturbations, can 

 be more exactly determined in this manner. There is no doubt but that the mo 

 tions of the new planets, especially Pallas and Juno, which suffer such great per 

 turbations from Jupiter, may furnish in this manner after some decades of years, 

 a most accurate determination of the mass of Jupiter ; it may even be possible 

 perhaps, hereafter, to ascertain, from the perturbations which it exerts upon the 

 others, the mass of some one of these new planets. 



