140 



The Rev. Dr. Robinson on the Difference of Longitude 



Were we to suppose the results of each night of equal weight, and take the 

 arithmetical mean, we should find, 



K = 1". 14'. 44 

 E = . 14 44 

 F = . 14 38 



but this condition cannot be assumed ; for a greater number of signals are 

 observed on some nights, and the clock correction is concluded with unequal pro- 

 bability. The probable error of the difference of observed times is, denoting by 

 e that of the transit of a single star supposed the same at each observatory (as it 

 is at Armagh and Dublin in fact), and by s the number of stars, 



If the number of rockets be r, and the probable error of the observation of 

 one at both observatories be ± em, that of the mean of the night is ± -7=, 

 and therefore that of the night's result 



(e) = ±eX>/i+i,-|-^^ 



By examining these results, I find e = ± 0'. 065 and em = dz 0'. 23 for 

 E and E, F being greater, and hence the probable weight of each night 



