The Rev. H. Lloyd on the mutual Action 0/ permanent Magnets. • , 253 



ferior to those represented in Figs. 2 and 3. Of the latter, the arrange- 

 ment (Fig. 3) is to be preferred, where our object is to diminish as much as 

 possible the residual action upon the declination magnet, A ; and, on the other 

 hand, the arrangement (Fig. 2) should be chosen, if we prefer to diminish the 

 action upon the magnet b. 



There is still another particular disposition which deserves to be considered : 

 that, namely, in which the magnet c is equally distant from the other two. This 

 condition is expressed by the relation, 



a + p^lSO"; 



and eliminating, by means of it, the angle /3 in (10), we have 



cos 2a -|- ^ sin 2a 



sin 2a cos 2a — ^ ' 



whence cos'' 2a — sin* 2a zz ^, sin 2a ^ ± ^, and 



a = ± 20° 54'. 

 Again, substituting this value in (10), we have 



tan f = -i-^- = d= 1.6180, f = 58° 17', or = 180° - 58° 17'. 

 ^/5 — 1 



Accordingly, the arrangement of the magnets is that represented in Fig. 5, 

 or the reverse arrangement, in which the magnet c is in the corresponding 

 position on the opposite side of the line ab. 



Let us now consider, briefly, the corrections required for the residual actions, 

 and the manner in which they are to be experimentally determined. 



In virtue of the equations (6) and (7), the action exerted by the magnets b 

 and c upon a, in the magnetic meridian, is null ; the disturbing action is, there- 

 fore, perpendicular to the meridian, and operates only as a deflecting force. 

 The amount of the deflection produced by this resultant force is easily deter- 

 mined ; for we have only to reverse the magnets b and c simultaneously, and it 

 is obvious that the difference of the readings of the magnet a, in these two 

 positions of the deflecting magnets, is double the deflection sought. In order to 



