27 
the intensity of magnetic forces , &c. 
vals of 30 minutes, from 74° to 86 ®, by means of the formula 
(G): from these and their several orders of differences, I 
interpolated the values of A (p at intervals of 6 minutes : 
forming these, with their differences, into tables, I obtained 
from them, by inspection, the value of A (p corresponding to 
any observed angle : adding the plus value of A <p to the 
observed angle, when the temperature of the magnets was 
above the mean temperature to which the observations were 
to be reduced, I obtained the value of (p at a temperature of 
the magnets one degree lower than that observed : proceed- 
ing in the same manner with this corrected value of (p, I ob- 
tained another value at a temperature one degree lower than 
the last, or two degrees below the observed temperature : 
with this I proceeded again in the same manner, and so on, 
until the observed value of cp was reduced to its value at 
the standard temperature of the magnets. If the observed 
temperature was below the mean temperature, I successively 
subtracted the different minus values of A (p to obtain the 
corrected value of (p. This will perhaps be better understood 
when I come to the observations and their corrections ; but I 
thought it necessary to explain the use which I made of these 
tables previous to giving them. 
In the observations which I made within doors on the 
daily variation in the positions of the points of equilibrium, 
the distances of the nearest ends of the magnets from the 
centre of the needle were 15.21 inches, or the distances of 
their centres from the centre of the needle 21.21 inches; so 
that, as we have before seen, the equation (C) here becomes 
M — ( .004690814 + . 000829329 cos.“Cp). F = 0 ; (a) 
consequently the equation ( G ) becomes 
