114 Mr. Herschel's account of a series of observations 



character of ordinary good watches, not to speak of chro- 

 nometers. 



The worst case that can happen is where the first signal 

 only at a gives corresponding observations at the stations 

 adjacent, the last only at 6, the first again only at c, and so on. 

 In this case the coefficients of /3 and 7 would each equal the 

 whole interval between the first and last signal at each post, 

 or (in the present case) 1^ so"". The correction here would be 



^2 X 24 — 16 

 In this extreme case, the sum of the deviations of both 

 watches from their assumed rates, need only amount to i'.6 

 to produce an uncertainty of a tenth of a second in the result ; 

 and though such a case as here supposed is in the last degree 

 improbable, yet as a certain approach to it is not unlikely, it 

 may be of use to show how the rates of the watches, if not 

 otherwise known, may be obtained, or if known, verified, by 

 the observations themselves. 



If we consider the observations on two successive nights, 

 at two of the extreme stations, A and B for instance, calling 

 A and B the means of the simultaneous observations on the 

 first night, and A^ B^ on the second, we have, assuming for 

 an epoch some time E = any number of days before either of 

 the night's observations, 

 b^r- P = A— .B + iG(A — E) 



But since this is generally true, if the observations be made 

 in sufficient number on both nights to destroy their indivi- 

 dual errors in the mean result, we must also have 



P = A,-B,+ /3(A,-E) 

 equating which we get 



