( 717 ) 



TABLE VI. RECIPROCAL OF THE MASS OF THE SYSTEM. 



The mean by weights is 1047.394 ± .026. Tiie simple mean is 

 1047.412. The mean of the detei-minations from the planets alone is 

 1047.380, and the mean of the determinations from the satelliles is 

 1047.417. The value which I propose to adopt is 



:U = 1047.40 ± 0.03. 



The probable ei-ror was derived from the residuals. The distribution 

 of these residuals, each compared with its own probable error as 

 totaled l)y the observers, is in excellent agreement with the theoretical 

 distribution according to the law of errors. The adopted p.e. can 

 therefore be considered to be a trustworthy measure of the real 

 accuracy 



I may be allowed to state as my conviction that it will not be 

 possible in the near future materially to improve the value here 

 adopted. In order to attain from observations of satellites a smaller 

 probable error than ± 0.03, or \'s5„oo. ^l^e scale-value must be 

 known within less than Vuoooo- I^ thus appears useless to attempt a 

 new determination of the mass from observations of the satellites, 

 until we are in the possession of means as well of tixing the distance 

 of a pair of standard-stars with this accuracy, as of transferring the 

 scale-value determined therefrom to other (smaller) distances without 

 the possil)ility of systematic errors. Investigations of modern heliometers 

 point to the conclusion, that the ti-ansferring of the scale-value from 

 a distance of, say, 7000" to one of 700" is still subject to uncertainties, 

 which may reach an amount ecpiivalent to an error of 0".l in the 

 larger distance, and which therefore may amount to \/-oooo ^f ^''^ 

 scale-value. On the other hand it seems a liigh demand on our present 

 observational means to fix a distance of about 2° of two stars with 

 an uncertainty smaller tluiu O'.Ol = 0\()05 '). 



1) The accuracy of the distance of the standard stars used in 1891 was + Veoooo- 

 (See my dissertation, page 8). 



