( 669 ) 



ting inclinations and nodes can confidently be regarded as a correct 

 measnre of the accuracy. How nincli better the observations are 

 represented by these values than by those adopted in Souili.akt's 

 theory is evident at once by comparing the residuals with the 

 observed corrections. 



For 1750.0 I now find : 



The agreement with the values found by Delambre and Damoiseau 

 is now satisfactory. If the probable errors of 6^ and 6^ in 1750 are 

 estimated at ± 5° (see Cape XII. 3 page 111), the diiference in 

 both cases hardly exceeds the sum of the probable errors. As has 

 been already said, I consider the probable errors of Solution IX as 

 a true measure of the accuracy. This however they only remain 

 for 1750 on the assumption that the theory, by means of which the 

 elements have been carried back from 1900 to 1750, be correct. 

 This, however, cannot be assumed without some qualitication. It is 

 well known that Souillart has integrated the equations of motion 

 by two ditferent methods. The difference between the motion of the 

 node of II in 150 years according to tiie two methods is nearly 

 1°.4. It is thus quite possible tliat the terms of higher order in the 

 masses, which are neglected in both methods, may also amount to a 

 very appreciable qnantity. In the inter\al of 150 yeai'S 6^ has completed 

 nearly five revolutions, while its motion is practically derived from the 

 interval 1891—190-4:, during which the node has moved about 155° 

 degrees. Remembering this, the agreement between the values carried 

 back fi-om 1900 to 1750, and those directly determined, is as good 

 as could reasonably be expected. 



In Cape XII. 3. I pointed out that the solutions VI (modern 

 observations alone) and VII (motion of 6^ from comparison with 

 Delambre) wei-e in perfect agreement except for the motions of 

 the nodes and for //,,. I then stated as my opinion, that the 

 substitution of better masses for those of Souillart could l)e 

 expected to reconcile the two solutions. This expectation has been 

 entirely fulfilled. With regard to the motions of the nodes, (which 

 are practically the same in Sol. VIII and Sol. IX) we have just 

 seen that tiie agreement with 1750 is satisfactory. With regard to 

 y^ the following comparison of the different solutions shows that 



