136 



By this formula — lie and — kc were then calculated for each 

 year and with these values those for — h^ and — k^ were deduced. 



We thus have two sets of values for — ho and — k^.. 



Before submitting these results to a nearer investigation, I tried 

 to show that the introduction of Brown's terms is justified by the 

 observations, at least as far as the five are concerned, which have 

 perceptible coefficients, and were marked above in roman figures. 



For this purpose tables were drawn up of — Ay and — ko, 

 according to the first calculation, in which all Brown's terms were 

 introduced except the term to be investigated. The yearly results 

 were then so combined, that groups were formed with values of 

 the argument of the investigated term between 0° and 10°, 10° and 20° 

 etc., in such a manner that the results for the different quadrants, 

 when necessary, were reduced by a change of sign to those for the 

 first quadrant. The h and k, when we represent Brown's terms by 

 a sin [g -\- /), then give nine equations each of the form — h^ = « cos x 

 and — ko = « sin x- 



Now X = Xo ~l~ f* (^ — 1900.0) and, as we take the period or ft as 

 known, we can deduce from the observations the value for « and 

 Xo for each term by the formulae 



tg (Xo + f^ {« - 1900.0)) ^ ^' «=" =: ho^ + V ') 



In this solution weights are given to the various equations propor- 

 tional to the number of years that they are based upon. 



The results found, compared with those according to the theory, 

 follow below : 



This agreement may be considered as satisfactory, it certainly 

 completely justifies t!ie introduction of Brown's inequalities. 



Finally I endeavoured to deduce from the observed h and k for 

 the largest term Br. II, the Jovian evection, also the length of the 

 period. The — h and — k, corrected for all other terms, being 

 represented for each year by 



1) For Br. V we have only a coefficieul k, so thai the deduclion for this term 

 becomes somewhat different. 



