202 OBSERVATIONS OF THE TERRESTRIAL 



Now if 0x, 8,, and 0j be the values of $, 8, and at the station 

 with which the rest are compared, we have 

 sin (8 - 0) = |3 cos 0, 

 0o sin (8 - ) = /3 cos ; 



cos sin (8 - ) m 



and dividing - = C08 Oo gin ( g _ 0) > 



which expresses the ratio of the force at the two stations in a form 

 suited to logarithmic calculation. 



The following table gives the results of this computation. It 

 contains the place and date of observation ; the angle corrected 

 for temperature ; and the total intensity at each station, compared 

 in the first instance with Dublin or Limerick, and in the second 

 with London. For the intensity of the magnetic force at Dublin 

 we have the three following determinations : * 



* *' 

 Aug., Sept., 1834, . . Intensity = 1-0194 



Sept., 1835, .... 1-0213 



Oct., Nov., 1835, . . 1-0211 



Mean, . . 1-0206. 



The intensity at Limerick, compared with London, is observed 

 to be 1-0262 ; and the intensity at the same place, compared with 

 Dublin, is 1-0030. Accordingly, for the determination of the 

 values of the total force at Dublin and Limerick, observation 

 furnishes us with three results, in the two former of which the 

 intensities at these two stations are directly compared with that 

 at London, while in the third they are compared together. To 

 s infer from these data, therefore, the most probable values of the 

 force at the two stations, we must proceed precisely as in the ana- 

 logous problem respecting the horizontal intensities, and we have 

 only to substitute in the formulas already given,* for a, b, c, &c., 

 their particular values. We have then 



a = 1-0206, b = 1-0262, e = 1'0030, 



f, = - = 1-0055, c - c = -0025. 

 (t 



And since the comparison of Dublin and London is the mean of 

 three distinct comparisons, while each of the other two results is 



* Page 188. 



