( B61 ) 



unknowns AA/, A/cv, A,r/, and is not removed from them by the 

 subsequent apj)roximations. Tlie coefticients of these unknowns consist 

 of a constant and a periodic |)art, of which the former amounts on 

 an average to three times the latter. (See e.g. Cookson, Cape XII.4, 

 p. 102). If tliis periodic part is neglected, the three unknowns cannot 

 be separated, and they represent together only one unknown, which 

 I have called Fi (see my dissertation, p. 69), foi- each satellite. Thus, 

 if the systematic pai't of dVfj had been introduced as an unknown 

 the equations of condition would have been : 



|/--rf..,+ ... = o-c. 



Thus it would not be possible to separate F and (fo;^,. Whether 

 the unknown rü'^ is actually written down in the equations or not, 

 does not affect the result; in any case the value which is found for 



/ dx 

 F is not F itself, but F — ^^'^pjj^^ ^"^ ^he residuals div , and there- 

 fore also their mean (\x^, do not contain the systematic part of the 

 error of pointing on the disc of the planet. 



If we assume that the values of F found from the simultaneous 

 heliometer observations (see above, sub 2), are the true ones, then 

 the differences P — H, which are given by Cookson in Cape XII. 4, 

 page 102 (where for 7^^ — 0.0295 should be read instead of — 0.0395) 



dx 

 are proportional to this systematic error, and we have öx^j = — ^ (P — H). 



dr 



We thus find for the four satellites : 



6x^ = — 0".19 ± 0".04 \ 



mean — 0".21 = — 0'.0035. 



The agreement of the four values is remarkable. The probable 

 errors, of course, would only be a true measure of the accuracy, if 

 it could be assumed that the periodic parts of the coefficients of Nii 

 etc. have been entirely without any influence on the final results, 

 which is very far from being true, especially for the fourth satellite, 

 of which only a small number of revolutions is included in the period 

 of observations. The mean systematic error of ])ointing on the disc 

 is of the sauie order of magnitude as the errors which I found to 

 exist in the measures by Renz (see below, sub 6). So there can 

 be little doubt that this is the true explanation of the large and systematic 



