XX Inteoduction to the Makerstoun Observations, 1845 and 1846. 



19. The value of the absolute horizontal intensity is determined from the ob- 

 servations 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 u 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 formula 



m \ ^ , 1 



= — y"* tan u 



where p and q 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 u is obtained from the formula 



tan M = tan fy {{u^ + ^u-u^ + ^u) - /{d^ + ^d-d^ + ^d)] (1 + o) |. '^ ) '^~ "/ 

 L4 J l—q{ta — tv) 



where a is the angular value of one division of the long scale, / is the coefficient for 

 reducing the divisions of the short scale to the value of divisions of the long scale ; 

 Ui and iM 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, u^ and „m are the 

 mean scale readings when the deflecting bar, at the same distance, has its north pole 

 towards the west : d^, id, &c., are the simultaneous mean scale readings of the de- 

 clinometer corresponding to Wi, ^u, &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, k being the coefficient for reducing 

 the scale divisions of the bifilar magnetometer to parts of horizontal force, hd 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, t^ and ty are the 

 mean temperatures of the bar during deflection and vibration respectively. 



The values of log ^ r^ tan u are given for each distance, pages 166 and 167. 



20. The following are the values of the constants used in the previous formula : — 



a = 40"-35 (No. 8.) /= 1-115 (No. 8.) g = 0-000288.* 



In 1845, k = 0-000140. In 1846, k = 0-000135. 



For the thread in the unifilar box and long scale magnet, <I> = 000212. 



21. The comparative observations for u and d were rendered simultaneous thus : 



* See Introduction, 1843, p. xliii. 



