420 Dr. C. V. Burton on the Sun's Motion 



(ii.) There will also necessarily be some slight uncertainty 

 as to the epoch of the actual eclipses, and r s will on this, 

 account be liable to a small constant error (7). 



(iii.) In determining the apparent time of mid-eclipse, an 

 error of observation is incurred; let the error thus introduced 

 into the value of r s be called v 6 ; we have accordingly 



t,= (t ), + x, + 7 + v« (7) 



0. For any single eclipse-observation,, to a sufficient 

 approximation, 



Vr-r = v> - r + Y(v s + %> + 7) + rv - for. . . (8> 



Without, in the first place, taking account of the motion of 

 the solar system through the aether, we may make 7 ver}' 

 small by making nse of a number of eclipse-observations 

 extending over at least one Jovian year. Moreover, 7 only 

 enters into our results in association with factors which tend 

 approximately to disappear in the long run ; its effect may 

 therefore be disregarded. For similar reasons our final 

 results will not be appreciably affected by the small errors v 

 and k. (When the numerical values of a, b, e have been 

 found from (5), it will be possible, without much additional 

 labour, to determine more definitely the influence of given 

 errors 7, v, k on the values found for a, b, c, as well as the 

 probable errors in a, b. c arising from an assumed " all 

 round " value for the probable observational error corre- 

 sponding to a single eclipse. For the present we must be 

 content with a more tentative estimate of the accuracy to be 

 expected.) 



10. Finally, since the residual effects for which we are 

 searching depend on the direction of the line drawn from 

 the earth to Jupiter, and have thus a principal period of 

 about 12 years, it is especially important for our purpose 

 that the Jovian system should be free from any influence 

 having an approximately equal period, and capable of affect- 

 ing the times of eclipse of the first satellite. Prof. Sampson 

 kindly went into this question with me, and found that no 

 disturbing influence of the period in question was to be 

 feared. We may accordingly confine our attention (in this 

 preliminary discussion at least) to the errors typified by 



11. Referring now to equations (5), we find that the error 

 Xs + V s in a single observation gives rise to an error in a 

 equal to 



D 



7] s %rj 2 £77 £| ; where D 



a lit sr 2 i 



SP XSn Sff 



2^7) trf 2r}% 



s?i trt s? 2 



