270 W. WEBER ON THE ARRANGEMENT AND 



of two minutes. The two magnetometers may be so placed re- 

 latively to each other in a large room, that the mean declination 

 may remain unaltered, and the changes of the declination 

 and of the intensity be only so far affected, that the determina- 

 tion of the value of the divisions of the scale is somewhat dif- 

 ferent from what it would otherwise have been. This is the 

 case when the pillar supporting the theodohtes forms with the 

 two magnetometers a triangle, of which one side (viz. that be- 

 tween the pillar and the declination-magnetometer) is situated 

 in the magnetic meridian, while the other side, viz. the line 

 which connects the central points of the two magnetometers, 

 forms an angle of 35° 15' 52" with the magnetic meridian*. The 



* Prof. Gauss has given, in a very simple geometrical construction, the com- 

 plete solution of the problem of the reciprocal action of two magnets at a great 

 distance, in any given position relatively to each other. It is as follows : 



C Let A be the centre of a small 



magnet, ns; A B the prolonga- 

 tion oi 7is; C a. particle of free 

 magnetism of theother bar; /fC5 

 aright angle ; AD=^^AB; then 

 C D is the direction of the force 

 which acts upon C, when C is a 

 north magnetic particle ; (when C 



is a south magnetic particle, the 



n A s D B direction of the force is, on the 



contrary, in the prolongation of Z) C beyond C) -^-^ . -Tqz^^ the magnitude of 



the force, M designating the magnetism of n s, and m the magnetism at C. This 

 simple proposition, which is useful in numberless cases, is especially applicable 

 to this case, in which the most advantageous reciprocal position of the mag- 

 netometers to be placed in the same room is required ; i. e. that position in which 

 they will least disturb each other, and in which, whatever slight disturbance may 

 be produced can easily be brought into calculation as a correction. The ap- 

 phcation of Gauss's proposition to our case shows that in the position above 

 described, 1st, the mean declination remains unchanged ; 2nd, the value of the 

 divisions of the scale, not only for the variations of the declination, but also of 

 the intensity, are only altered in so far as the directive force of the two apparatus 

 undergoes a change ; for the value of the divisions of the scale changes with the 

 directive force, and in the same proportion. This may all be seen from the 

 geometrical construction of the reciprocal action of two magnets at a great di- 

 stance, without its being necessary to give a detailed development of the theory 

 of the two magnetometers. 



The first assertion is evident from the consideration of the above figure, 

 where A is the central point of the intensity-bar n s, C the central point of the 

 declination-bar situated in the line CD, CD the magnetic meridian, and where 

 the straight line A C, which connects the centres of the two bars, forms the 

 angle A C Z) = 35° 15' 52" with the magnetic meridian C D, — or, more accu 

 rately, forms such an angle, A CD, that 



sin A C D ^ Vi 

 cotan ACD= ^./2 

 cosec A C D =: \/3 



According to the above proposition, C D is the direction of the force which 



!U- 



ch " 



