256 ON THE DETERMINATION OF THE HORIZONTAL 



deduced ratio of the number 1'224 to 1. The form of the magnets 

 was cylindrical, their lengths being 3 inches, and 3f inches, and 

 their diameter -fV of inch. The suspended bar was hung by two 

 fibres of untwisted silk, and inclosed in a small wooden box with 

 glazed front. The deflections were observed by means of a mirror 

 attached below the magnet, which reflected the divisions of a scale 

 placed at a distance of nearly six feet from it. As the utmost 

 precaution was required in the experiments, the use of a copper 

 ring or metallic box was dispensed with, and the arc of vibration 

 reduced by means of a magnet, which was always replaced care- 

 fully in the same position after use. The deflecting magnet was 

 placed on the east and west sides of the suspended one, at distances 

 varying from 15 to 30 inches. The distances were observed by the 

 help of a standard scale, a line at the middle of the magnet being 

 made to coincide with the image of the division of the scale, re- 

 flected from its polished side. The observations were made begin- 

 ning with the longest, and proceeding to the shortest distance at 

 one side, and back again in the reverse order at the other, so that 

 the two observations at the same distance were taken at times 

 equally remote from the middle epoch. 



The angles of deflection were calculated by the formula 



tan 2u = I (n e - n w ) k ; 



where n e and n w denote the observed readings of the scale, with the 

 marked end of the deflecting bar to the east and to the west 

 respectively. The value of the constant k is given by the formula 



a denoting the length of one division of the scale, d its distance 



TT 



from the mirror, and the ratio of the torsion force to the 



Jc 



magnetic force. In the present instance, a = '038935 of an inch ; 



JT 



d = 68-52 inches ; and - -000345. Hence log k = 6-75467; and 



the angle corresponding to one division of the scale was conse- 

 quently 



I tan- 1 k = 58"-623. 



The following Tables exhibit the results of the observations. 

 The first column of each contains the distances of the magnets, in 



