( 06 ) 



ployed. The notations used by different writers on the theory ol the 

 satellites are discordant in a most regrettable manner. The tallies, 

 both those of Damoiseau and of Delambre, distinguish the four 

 satellites by the numbers 1, '2, 3, 4. This example is followed by 

 Marth, and 1 have also in all my previous work on the satellites 

 used this notation, as is also done by Mr. Cookson in the discussion 

 of his observations. The theoretical writers, on the oilier hand, Laplace, 

 Tisserand, Souillart use the suffixes (l, 1, 2, 3 or a corresponding 

 number of accents. Another fundamental difference is in the designation 

 of the perijoves. The letter w in the writings of Damoisf.au, Marth, 

 Cookson and myself represents die "own" perijove; Souillart and 

 Tisserand use it for the osculating perijove. There are many more 

 differences of this kind, which need not be enumerated here. Though 

 thoroughly convinced of the great importance of a consistent notation, 

 I am, reluctantly, compelled in this communication lo deparl from 

 the notations employed by me elsewhere. In the first article of the 

 present communication, which treats of a theoretical point, I have, to 

 avoid the writing out at length of many well known formulas and 

 results, closely followed Tissp.rand's very clear argument in the 

 fourth volume of his Traite de Mécanique Celeste. Accordingly in 

 tins first article, I will adopt Tisserand's notation, with one exception. 

 In the further articles 1 will return to the notation employed in my 

 previous work. 



1. Theory of /In- libration. As has been explained, Ihe notations 

 employed are Tisskkand's excepting the mean longitudes, which 1 

 denote by /,, /. 2 , / : , instead ol' by /, /', /". In addition to the quantities 

 /•', F' <!. G' defined by (li>) page 11 ') 1 wish to introduce 



Tisserand assumes 6r, = G and G x ' = G' , which is only approxi- 

 mately true. If it is not desired to introduce this approximation, 

 then on page 11, formula (20) we must in /., replace G by G 1 and 

 similarly in A',' G' l>,\ G x ' . 



The only further difference from Tisskkand's notation is in the 

 definition of the libration. I pul 



') The references of pages and formulas are to those of Tisserand, volume IV. 



