for determining the difference of meridians , &c. iii 



sidereal time since the epoch, their difference reduced to the 



fixed epoch will be 



(B'— C')-(;3-y)(A'_E) 



in which, substituting for A its value above found, we get 



(B'_C')-(/3-y)(P + B'-E) 



neglecting powers and products of jS and y. Putting then 



Q=:mean of all the{B*-- C)-(3'-r/)—meanofall the (P+B'— E) 



we get the most probable value of the difference of the 



chronometers at the epoch which can be obtained from any 



number of such comparisons. 



Finally, if we make a comparison at any time A" (Paris 



Sid. T. ) between the watch at C and the clock at z, and call 



their indications at that moment C" and Z", their apparent 



difference will beC — Z", and their difference reduced to the 



epoch will be 



(C— Z") — y(A'— E). 



But Q being the most probable difference between the chro- 

 nometers B and C at the epoch, and (jS — y) the difference 



of their rates 



Q + i^-Y){A"-E) 



will be their difference at any other moment A"; hence 

 B''-~ C'= Q + (/3 - y) (A"-- E). 

 But by the equation (a:) since B" and A" are correspond- 

 ing times, we have 



B"=A"-P-|-^(A''— E). 

 Consequently substituting this for B" we get 



C'= A"-,P — Q + y ( A"-E) 

 whence A"= P + Q + C"— y { A"— E) 



= P + Q + C"-y (P + Q + C"-E) 

 neglecting the square and higher powers of y : 



