256 The Rev. H. Lloyd on the mutual Action of permanent Magnets. 



direction of the force exerted by the magnet a (in that position) upon the point 

 D. This temporary adjustment of the magnet a may be at once effected by 

 means of a line drawn on the supporting pedestal ; and it is obvious that it 

 may be accomplished v^'ithout removing the magnet from its stirrup, or inter- 

 fering in any vpay with its permanent adjustments. 



The building required to receive the magnets, in the arrangement repre- 

 sented in Fig. 5, may be still simpler ; consisting only of a single room, 26 feet 

 in length, and 16 feet in width, and having a portico with a second door, to 

 prevent draughts of air, (Fig. 7). 



To find a suitable place for the inclination instrument, we have only to 

 determine the point on the line ab, at which the action of the magnet c is per- 

 pendicular to ab. Then, the action of the magnet b being perpendicular to 

 AB at every point of this line, the forces exerted by b and c will be perpendicular 

 to the meridian, and will therefore be destroyed by the reaction of the sup- 

 ports ; and, in order that the same thing should hold also for the magnet a, 

 we have only to turn that magnet, temporarily, into a position perpendicular to 

 the meridian. 



Let D (Fig. 5) be the point sought, and do a line perpendicular to ab ; 

 then the condition requires that tan cdo :=. ^- tan ocd ; or, denoting the angle 

 CDA by x, cotan x = 7]- tan {x — 58° 17')- Whence, developing and substituting 

 the value of tan (58° 17')» we have the following quadratic for the determi- 

 nation of tan X, 



tan -X — 4.854 tan a; — 2 = 0. 



Accordingly, tan 3; = 5.236, or =: — 0.382 ; and :r = 79° 1 1', or r= — 20° 

 54', Of these solutions the former is that adapted to the present purpose ; the 

 latter giving the point a itself. 



The pedestal erected at the point d will likewise serve to support the reading 

 telescope of the magnet b, which may be inserted in a groove cut in the top, so 

 as not to interfere with the other instrument. The supporting pedestal of the 

 telescope of the magnet a should be on the line da, its centre being four or five 

 feet from the point d, so as to admit the observer's chair between the two 

 pedestals. 



