xlii Introduction to the Makerstoun Observations, 1843. 
of observation ; the mean of the two readings gives the position of the needle at 
the minute. The readings increase negatively or positively as the north pole of the 
needle moves above or below the horizontal wire ; the readings are generally nega- 
tive. The quantities given in the magnetical observations are obtained thus : — 
n being the observed reading of the needle, t that of the thermometer, -| = 7*90 the 
temperature coefficient, It the quantity in the Tables, 
R = 700+ | (*-26°) +n 
increasing tabular quantities, therefore, indicate increasing vertical force. 
§ 7. Determination of the Temperature Coefficients of the Deflection, 
Balance, and Bifilar Magnets. 
Deflection Magnet. 
59. The magnet used for deflections in observations of the absolute horizontal 
intensity was placed in a copper trough, resting on a beam of the deflection appa- 
ratus (25.) ; the temperature was varied by means of ice and water of different tem- 
peratures ; a thermometer lying on the magnet indicated its temperature ; the 
declination magnet was observed simultaneously with the deflected (or unifilar) 
magnet ; and the bifilar magnet before and after each change of temperature. 
60. If m be the moment of the magnet, X be the horizontal intensity of the 
earth's magnetism, 8 be the westerly declination, a the angle which the deflected 
magnet makes with the astronomical meridian, then 
m = X tan (u — 8) 
differentiating, all the quantities being variable, and reducing 
Am Au — A 8 a X 
m J sin 2 (it —8) X 
or if u and u Q are the unifilar readings, d and d 0 the declinometer readings, b and b 0 
the corrected readings of the bifilar magnetometer when the temperatures of the 
deflecting magnet are t and t Q ; D is the mean deflection, in this case small ; / the 
coefficient for reducing the declinometer scale divisions to values of unifilar divisions, 
k the bifilar coefficient, then since — — = q (to — t) 
_ u - u 0 -fd - rf 0 k (b — 6 0 ) 
q ~ D (f 0 - t) + 
The quantities in the last column of the following Table have been obtained from 
this formula. 
