( J07 ) 



values of the long-periodic inequalities are computed. Let these 

 be dl,', and let dl," he the values used in computing Ihe tabular 

 places which were compared with the observations. Then evidently 



the correction to the mean longitude corresponding to the assumed 

 masses (and equations of the centre is 



Lk'= LI, —(()/,' — 6k'). 



From these LI,' we then determine the amplitude, the phase and 

 the period of the libration. If' this period co-incides with the one 

 computed from the assumed masses, then the approximation is suffi- 

 cient, if not, then the whole process i.s repeated with different masses. 



The communication of' the different approximations and of the 

 residuals remaining after the substitution of the finally adopted values, 

 woidd exceed the limits set to this paper. The formula finally derived 

 for the libration is 



t — 1895-09 

 »=z .158 sin — . 



7-0 



The adopted masses are 



/«J = 0.0000 256 



m 3 = 0.0000 231 



m, = 0.0000 820 



and the corresponding ratio of the distribution of the libration over 

 the longitudes of the three satellites is given by 



#, »">, ». 



— ^ = + 0-175 — = — 0-260 — = + 0-022 s 



,*> .'> & 



The mean longitudes (excluding libration on 1900 January 0, 

 Greenwich mean noon, are (counted from the point Aries) 

 /, = 142°-604 

 I, = 99 -534 

 I, = 107 -999 

 /, = 234 -372, 



By a comparison of these with the values at the epoch 1750.0 

 the following sidereal mean daily motions 1 ) were derived 

 n\ — 203°-4889 5652 

 » s = 101 -3747 2411 

 n, = 50 -3176 0790 s 

 n é — 21 .5710 7132. 



I have added no probable errors, which in the absence of the 

 details of the observational material can only have a subjective value. 



') i.e. sidereal menu motions in a mean sola 

 Proceedings Royal Acad. Amsterdam. Vol. X. 



