MAGNETICAL OBSERVATIONS IN IRELAND. 
147 
in which a is a constant to he determined bv observation. For 
needle L (4) it has been found* that 
a = ' 00016 . 
But we may proceed in another way, which will perhaps be 
found convenient in practice. We may correct the observed 
value of 0 by subtracting the change due to temperature ; or, 
in other words, we may reduce the value of 0 to that corre¬ 
sponding to the standard temperature, and to the standard con¬ 
dition of the needle. For this purpose it is only necessary to 
find the relation between the corresponding changes of and 0. 
Differentiating, therefore, the equation (2) with respect to these 
variables, and dividing the result by the equation itself, we find 
d <p _ cos 8 sin l' 
$ d ~0 cos 0 sin (8 — 0)’ 
c/0 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 0 on which it depends) will be 
inconsiderable 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 0 at some one 
station. Thus, at Dublin, September 1835, it was found that 
8 = 7l°3 / *0, 0 = — 13° 0'*0 ; 
from which we find the value of this constant to be ‘00010. 
But, since d == — a (t —t r ), the first member of 
the equation is 
t -V 
0 - 0 ' 
so that the correction is finally 
0' - 0 = + 1*6 (t - t 1 ) f. 
Now if <p p 8„ and 0 y be the values of 4>, 8, and 0 at the station 
with which the rest are compared, we have 
sin (8 — 0) = /3 cos 0, 
<Pj sin (8, — 0 y ) = /3 cos 0,; 
and dividing 
<p __ cos 0 sin (8y — 0 y ). 
cos 0, sin (8 — 0) ? 
* Trans. Royal Irish Academy , vol. xvii. p. 452. 
f It is obvious that the coefficient in this correction might have been deter¬ 
mined directly , by observing the angles 6 and & corresponding to very unequal 
temperatures. It did not seem safe, however, to subject the apparatus to the ac¬ 
tion of high artificial heat, and the thermo-electric currents induced by inequality 
of temperature would in all probability have sensibly affected the results. 
