MAGNETIC FORCE IN IRELAND. 201 



Let t, then, be the observed, and t' the standard temperature, and 

 let #' be the value of corresponding to the latter ; then 



^ <j>' = a ({>' (t t'), (3) 



in which a is a constant to be determined by observation. For 

 Needle L (4) it has been found thaf 



a = -00016. 



But we may proceed in another way, which will perhaps be 

 found convenient in practice. We may correct the observed value 

 of 9 by subtracting the change due to temperature ; or, in other 

 words, we may reduce the value of 9 to that corresponding to the 

 standard temperature, and to the standard condition of the needle. 

 For this purpose it is only necessary to find the relation between 

 the corresponding changes of and 9. Differentiating, therefore, 

 the equation (2) with respect to these variables, and dividing the 

 result by the equation itself, we find 



d cos 8 sin 1' 



d 9 ~ cos 9 sin (8 - 9)' 



d 9 being expressed in minutes. Now it is easy to see that the 

 variations of the second member of this equation, arising from 

 changes in the angles 8 and 9 on which it depends, will be in- 

 considerable for the limited extent of those changes in Ireland. 

 Assuming it to be constant, therefore, its value will be given when 

 we know the corresponding values of 8 and 9 at some one station. 

 Thus, at Dublin, September, 1835, it was found that 



3 = 71 3'-0, 9 = - 13 O'-O ; 



from which we find the value of this constant to be -00010. But, 

 since d = ^ - q>' = - a $' (t - t'}, the first member of the equa- 

 tion is 



-~ ---00016^; 



(/ (/ U 17 



so that the correction is finally 



& - 9 = + 1-6 (t - *. 



* It is obvious that the coefficient in this correction might hare been determined 

 directly, by observing the angles and 9' corresponding to very unequal tenipciuturr.- 

 It did not seem safe, however, to subject the apparatus to the action of high artificial 

 heat, and the thermo-electric currents induced by inequality of temperature would in 

 all probability havo sensibly affected the results. 



