( 423 ) 



small, that although not absolutely impossible, it is hardly probable 

 that the correction obtained for the mean anomaly should have been 

 caused totally or for the greater part by an error in n. Taking the 

 obtained AM for the 25^1' of Sept. we get : 



44" 6955 



A a = H = 4- 0" 016787 



^ ^ 2662.50 ^ 



and thus the real error of ft should be 67 times the mean one. 

 Adopting this correction of fi, the mean anomalies for the 28''i of 

 August and the 10^^ Qf October would be only 0" 469 smaller and 

 0" 249 greater than the adopted ones. 



It is more probable that the correction of AI arises from neglected 

 perturbations of tiiat element by Saturn. This perturbation is given 

 by the formula 



t t 



^^'^ =ƒ!?'''+ƒƒ- 



de 



dt 



to fo 



Even if instead of the sum of the values each term was known 

 separately it would be equally impossible to conclude from the value 



J^dii 

 — — dt, or the correction 

 (It 



of II for 1906. Observations during a much longer period can only 



decide in this case. 



Something like this holds for :it and <f. During the short period of 



the observations, we may even substitute for a part of the correction 



hM corresponding variations of jr and (p. If we keep to the plane 



of the oi'bit, the apparent place, except for small variations in the 



radius-vector (of little influence near the opposition), depends wholly 



on the longitude in the orbit, or on 



I =: Jt -\- V. 



So we can apply small variations to the elements without varying 

 perceptibly the computed positions, if only 



A l=z Ajr-|- A Ü = 

 or 



A jr =: — A y. 



This relation provides us with the means to throw a pai't of the 

 correction found foi- M on rr or on cp or on both together. In the 

 first case we have to satisfy the equation 



dv 

 A .T = — — - A M. 

 dM 



