NO. e]. 



INTRODUCTION. CHRONOMETERS. 



XXXVII 



When the equations are solved according to the method of least squares, 

 but separately for ID, I R, etc. they give the results contained in the following 

 table, where n is the number of equations, the final columns giving x in 

 seconds of arc for the distance 5.20, adopting Barnard's values of r as above. 



An inspection of these numbers gives two results : 



1. For all Satellites the numbers are greater for R than for D. This is 

 only what might be expected, because it is quite natural that the quantity 

 of light necessary for enabling the observer to catch the first glimpse of an 

 emerging Satellite must be on the average greater than what is necessary 

 when he is following a vanishing point of light. 



2. For the three inner Satellites the fraction of the radius that must 

 be outside the shadow at the moment of observation is greater for a smaller 

 Satellite than for a bigger one, which is also what might be expected when 

 the albedo of their surfaces is not much different. 



If the albedo had been the same for all three, the product x V2ro5, with 

 x expressed in seconds, should be nearly constant (but of course different for 

 D and R). An inspection of the last two columns of Table a shows that the 

 values of x are too uncertain to give any information on this delicate point, 

 but it was desirable, in order to diminish the effect of accidental errors, to 

 combine the equations for these three Satellites. The values of x expressed 

 in seconds are not more different than is compatible with the assumption of 

 their identity. For I and II this is not very different from supposing the same 

 albedo, but for III, which is the largest, it would imply the supposition of a 

 somewhat inferior albedo. In this respect it is interesting to compare the rela- 

 tive values of the diameters as found by PICKERING by photometric measure- 

 ments, on the supposition of the same albedo, with those of BARNARD and 

 also with those of MICHELSON which were determined by an entirely different 

 method. The table below contains these numbers. 



