46] ROYAL ASTRONOMICAL SOCIETY TO M. LE VERRIER. 



with the utmost accuracy the mutual disturbances of all the primary planets 

 which appear to have any sensible influence on each other's motions, might 

 well have appeared incredible if we had not seen it actually accomplished. 



I will now proceed to give a brief outline of the investigations relating 

 to the motions of the four larger planets, with which we are now more 

 particularly concerned. The most important parts of these investigations are 

 printed in full detail in the volumes of Memoirs which form part of the 

 Annals of the Observatory of Paris. 



As in his former researches, M. Le Verrier here also exclusively employs 

 the method of variation of elements, and the investigations are based on 

 the development of the disturbing function given by him, in the first volume 

 of the Annals of the Paris Observatory, with greater accuracy and to a far 

 greater extent than had ever been done before. 



The 18th Chapter of M. Le Verrier's researches, which forms nearly the 

 whole of the 10th Volume of the Memoirs, is devoted to the determination 

 of the mutual action of Jupiter and Saturn, which forms the foundation of 

 the theories of these two planets. 



These theories are extremely complicated, and I shall endeavour briefly 

 to point out, and to explain as far as I can without the introduction of 

 algebraical symbols, the nature of the peculiar difficulties which M. Le Verrier 

 has had to encounter in their treatment, and which he has so successfully 

 overcome. These difficulties either do not present themselves at all, or do 

 so in a very minor degree in the theories of the smaller planets. 



First, then, the masses of Jupiter and Saturn are far larger than those 

 of the interior planets, the mass of Jupiter being more than 300 times and 

 that of Saturn being nearly 100 times greater than the mass of the Earth. 

 For this reason it is necessary to develop the infinite series in which the 

 perturbations are expressed to a much greater extent when we are dealing 

 with Jupiter and Saturn, than when we are concerned with the mutual 

 disturbances of the interior planets. Also Jupiter and Saturn are so far 

 removed from these latter planets that the disturbances which they produce 

 in the motion of these planets are extremely small, in spite of the large 

 masses of the disturbing bodies. 



But the great magnitude of the disturbing masses is far from being the 

 only reason why the theory of the mutual disturbances of Jupiter and 

 Saturn is so complicated. 



