( 413 ) 



fact that the tlieoretical forDiiilao ^vliicli I had used for the same 

 comparison were incomplete. For 1 had not noticed tiiat Radau in 

 his valuable " Recherc/ws concernant h's inci/alih's plaiu'taires da 

 mouvement de la Itine" ^), had found that besides the "Jovian Evection" 

 there exist some other ine(iualities of a nearly' inonthly period with 

 appreciable coeflicients. Nor had I paid attention to tlie fact that 

 according to Hill's researches on the inequalities resulting from 

 the figure of the earth '), made following Delaunay's method, an 

 apprecial)le term of inojithly period must be added to those inserted 

 into the tables of Hansen. 



It is this gap of my preceding investigation which I shall here 

 try to till u[). lUit I shall go no farther, for from the beginning 

 the aim of my work was limited and there would be still less 

 reason to continue it, now that Mr. Coavell intends to continue his 

 work and to extend it also to other periods. 



15. The principal terms of a nearly monthly period which, according 

 to Radau and Hill, are still to be added to the true longitude from 

 Hansen's tables are : 



— 0".68 sin ((/ + 2 JT + 3 F— 5 ^) (I) 



— 0.S8 sin {(J ^2 Jt —2 J) (II) 



-4- 0.32 sm (<7 + 2 -r — 3 J -^ 7°) (Ill) 



+ 0.45 sin 8 cos g (IV) 



where V, E and J represent the mean longitude of Venus, the 

 Earth and Jupiter. The first three are terms found by Radau as 

 arising from the planets, while the fourth expresses the difference 

 between the inequalities arising from the figure of the earth after 

 Hill and after Hansen"). 



^) Annales de VObservatoire cle Paris. Mémoires T. XXL 



~) G. W. Hill Determination of the inequahlies of the moon's motion which are 

 produced by the figure of the eartli. A^tron. papers American Epliemeris and 

 Naiit. Ahn. Vol III. Part. II. 



■') Comp. also Gowell I.e. Gowell introduces still two other terms, numbered 

 by him 2 and 6 (Observ. p. 350). It seems doubtful to me whether their intro- 

 duction is sufficiently justified. 



As to 2, we must, if wo consider Newco.mb's empirical term of long period as 

 an inequality of the mean longitude, like the first Venus-inequality of Hansen, and 

 this seems the most plausible, also accept the inequality of short period in the 

 true longitude connected with if. 



Gowell's correction 6 results from the rejection of Hansen's constant term in 

 the latitude — I ".00. It seems however that the correction of the tabular latitude 

 or declination with 4-l"-00 is a posteriori not justified. From a comparison of 

 the declinations determined at Greenwich in the years 1895—1902 I found as the 

 mean difference Obs.— Gomp. — 0".17, and after ihe reduction to Newcomb's 



