142 



calculation was made again, when h,. and k^ were neither corrected 

 for my empirical term nor for the inequality Brown I (the period 

 of which differs little from that of the empirical term). In making 

 the three calculations weight V2 was given to the h and k of 

 Newcomb's first series, and the mean discordances given below refer 

 to an h and k with weight unity. "We found : 



1848 — 1875 

 1890 — 1910 

 Together 



We see in the first place that the mean residual discordances in 

 h and k agree in the three cases very well with each other, and it 

 is shown clearly that in the period 1848 — 74 the term Brown I 

 and my empirical term counteract each other to such an extent that 

 they could both be omitted without the mean discordance being 

 perceptibly increased, and that therefore apparently the non-existence 

 of Brown I had to be inferred from the observations of these years, 

 while in the period 1890—1910 the relation is just the opposite. 



Further it is seen that the mean discordances I, remaining after 

 the empirical term was also applied, are considerably smaller than 

 the values II. If the former are to be attributed to accidental errors 

 alone, they must be about equal to the mean errors in h and k 

 deduced from the equations for each year 



r z=i c -\- li sin (J -j- k cos g 



These mean errors were calculated for the three years 1893, 

 1901, and 1908, and we found: 



We may therefore take for this mean error on the average the 

 value ± 0"30, while for the mean residual discordance in h and k 

 for the years 1890—1910 we find ± 0"38, which agreement may 

 be considered satisfactory. 



We may therefore conclude: 



1. That the reality of our empirical term is established ; 



2. That, when its influence, together with that of all the 

 theoretical terms, is applied to the results for h and k, deduced 

 from the observations, (he residuals may probably be ascribed to 

 accidental errors. 



