( <77) 



The solution was not actually made in tliis nay, but all equa- 

 tions were treated simnltaneously. This consideration is only given 

 here to point out that the position of the equator is ultimately 

 determined liy die condition that it shall be the same for the four 

 satellites, i. e. that the inclinations shall be constant, and the motions 

 of the nodes shall be consistent with the theoretical ratios. Since a 

 small displacement of (he equator has a large intluence on the 

 motions of the nodes, in consequence of the small inclinations, it 

 can be expected that the unknown x and the quantities which 

 determine the iX)sition of the equator will mutually diminish each 

 others weights. (That this decrease of weight is actually much more 

 marked in the case of //„ than for x„, is accidental and depends on 

 the choice of the zero of longitudes). 



By these considerations I have Iieoii led to (ly whether the value 

 of X could not be determined from a c(im|)arisoii with other obser- 

 vations. I have used the values of &i for 1750 given by Delambrk. 

 A value of x was adopted, such that the value of &^ carried back 

 to 1750 from the modern observations would be nearly equal to 

 the value given by Dela.mbke. The unknowns .(,■„, y„, dy; and öF,-^ 

 were then determined from the modern observations alone. 



This gives solution VII. In solution VI on the other hand all 

 unknowns (inclusive of x) were determined from the modern obser- 

 vations. I give below the results from these two solutions, which I 

 consider as the best that can be derived with our present knowledge 

 of the masses. I do not venture to choose between the two solutions. 

 Probably an eventual correction of the coeflicienfs <Ty will tend to 

 reconcile the two solutions. 



Instead of r, I give at once &i = il% — F,-. The values are given 

 for lyOO ,Iaii. Greenwich Mean Noon. 



