ps INTRODUCTION TO THE MAKERSTOUN OBSERVATIONS, 1845 AND 1846. 
19. The value of the absolute horizontal intensity is determined from the ob- 
ser vations as follows :—If r be the distance from the centre of the suspended magnet, 
at which the centre of the deflecting bar is placed on the wooden beam, its axis being 
in the line at right angles to the magnetic meridian passing through the centre of the 
suspended magnet; and if w be the resulting angle, through which the suspended 
magnet is deflected, then since, by Gauss’s theory, the ratio of the magnetic moment 
m of the deflecting bar to X, the horizontal component of the earth’s magnetic force, 
is given by the following for mula 
m 1 
af 
—=—-'* tan u 
x 1 a 
He r 
where p and ¢ are quantities depending on the mode of distribution of the magnet- 
ism in the magnetic bars, the value of the ratio may be determined from observa- 
tions at three distances; tan wis obtained from the formula 
1+k (bs—b,) 
1g (ta—t) 
tan w=tan fi {(a, + yu uy + uw +t) —f (d,+,d-d, dj+,d)} + *)|- 
where a is the angular value of one division of the long scale, fis the coefficient for 
reducing the divisions of the short scale to the value of divisions of the long scale ; 
v, and ,v are the observed mean scale readings of the unifilar magnetometer, the de- 
flecting bar, with its north pole towards the east, being at a given distance to the 
east and west respectively of the suspended magnet; similarly, ~, and ,w are the 
mean scale readings when the deflecting bar, at the same distance, has its north pole 
towards the west: d,, 1d, &c., are the simultaneous mean scale readings of the de- 
clinometer corresponding to wm, yw, &c.: (1 + ©) is the torsion factor. ['The quan- 
tity within brackets is given for each distance in the column of the observations, 
“ Deflection corrected for Torsion.” ] The last factor reduces the value of the tangent 
to the value of X and m at the time of vibration, & being the coefficient for reducing 
the scale divisions of the bifilar magnetometer to parts of horizontal force, bz and 6, 
are the mean scale readings of the bifilar at the times of deflection and vibration re- 
spectively ; q is the temperature coefficient for the deflecting bar, ¢, and ¢, are the 
mean temperatures of the bar during deflection and vibration respectively. 
The values of log 47° tan w are given for each distance, pages 166 and 167. 
20. The following a are the values of the constants used in the previous formula :— 
a = 4035 (No. 8.) f = 1115 (No. 8.) = 0:000288.* 
In 1845, & = 0:000140. In 1846, & = 0:000135. 
For the thread in the unifilar box and long scale magnet, ® = 0:00212. 
21. The comparative observations for u and d were rendered simultaneous thus : 
* See Introduction, 1843, p. xlii. 
