( 712 ) 



(CooKSON, heliometer) and 1904 (Cape, plates). The reduction has 

 been carried out in Gron. Publ. 17. Tiie masses (A) an; the result of 

 this discussion. The period of the lihi-ation being independent of 

 y! , it is the same for the masses (B) as for (A). Also the transition 

 from (B) to (C) does not affect this period. It is thus only necessary 

 to investigate in how far the change from (A) to (C) affects the 

 inequalities of group II, and what is the effect of this on the 

 libration. This effect was found to be so small that a new determin- 

 ation of the libration appeared superfluous. The finally adopted 

 libration is thus the same as in Gron. Publ. 17, viz : 



T- 1895.09 



^ = 0°'158 sin — , 



7.00 



where the time T is expressed in years. 



The probable error of the period corresponding to the adopted 

 probable errors of the masses (C) is ± 0.13. 



The corrections to the mean longitudes on 1900 Jan. 0.0 also have 

 been adopted unaltered from Gron. Publ. 17. 



Table IV contains the observed corrections to the mean longitudes, 

 with their probable errors as derived directly from the observations, 

 and the residuals remaining after subtitution of the final values of 

 the inequalities of group II and the libration. The last two columns 

 contain the p.e. of the quantity td^ — 3 A/^ -j- 2 A/„ and the residuals 

 for this same quantity. 



In determining the libration from extra-eclipse observations we 

 find the mean longitudes for epochs, which approximately co-incide 

 with the epoch of opposition, and which therefore are on the 

 average separated by intervals of 400 days. This interval differs but 

 little from the periods of the inequalities of group II. These latter 

 thus present themselves as inequalities with apparent periods between 

 6 and 8 years, and are therefore not well separable from the 

 libration. In the eclipses this difficulty does not exist. 



The method of successive approximations, which has been used 

 iji Gron. Publ. 17, to derive from the observations the most probable 

 values of the libration and of the inequalities of group II, need not 

 be explained here. It must suffice to refer the reader to that publi- 

 cation (see also these Proceedings, June 1907). The residuals of 

 Table IV are practically the same as those found in Gron. Publ. 

 17, and they also need not be considered in detail here. Those 

 of the satellites I and III are not very satisfactory, as has been 

 pointed out there. On this point also the results derived from extra- 



