the intensity of magnetic forces , ^c. 33 
These tables are calculated for the distance 21.21 inches, 
that at which the centres r ''the magnets were from the centre 
of the needle during the observations which I made in-doors, 
and they would, without any great error, serve also for the 
correction of the observations in the open air, where the dis- 
tances were 21.52 inches; but I would not, for the sake of 
avoiding the labour of computing fresh tables, which how- 
ever was by no means inconsiderable, leave any doubt on 
the nature of the diurnal changes in the two cases. 
We have already seen that, when R — 21.52, the equation 
(C) becomes, 
M — F . ( .004480432 + . 0007664093 COS.®(^)) =; o, 
so that in this case the equation G becomes 
COS.®((p + A(p)= — ^6— 3 } X .0007664093 COS.®(p-f- . 0000000014 
T . 1 23 X ( .004480432 -f .0007664093 COS.® <p) ® I = o (<y J 
where .0000000014 is the value of ^ ‘ in all the values 
of (p between 74° and 86°, the values which I had in this case 
to compute. 
From this formula I calculated the following tables, as in 
the preceding case, excepting that, as in the observations in 
the open air, the temperature of the magnets varied more 
considerably, I had, in correcting ^-hem, more frequently to 
repeat the additions and subtractions, and therefore from 
82° to 86°, where the values of A(p change rapidly, I calcu- 
lated the values of A (p at intervals of 15' for the fundamental 
tables, and interpolated at intervals of 3' for the tables to be 
applied to the correction of the observations. 
MDCCCXXV. 
F 
