PLUCKER ON THE THEORY OF DIAMAGNETISM. 34? 



16. In the case of a permanently magnetic bar, which is sub- 

 jected to the action of the earth, and whose south pole is A, we 

 must assume c and c' infinitely great in comparison to r. Ac- 

 cording to this the two expressions (3) and (4) become 



^jsin (</) — a) — sin(</) + a)> = ^sinacos</>, 



-75J sin (<^ — a)— sin (<^ + a) \ == ^ sin acos0. 



The magnetic forces which proceed from the two poles of 

 the earth, unite in driving the needle into the magnetic 

 meridian with a relative force which is inversely proportional to 

 the distance from the poles. The magnetic bar, therefore, in 

 the case of the figure, recedes from the (by reason of its nearness) 

 stronger pole P. The total moment of rotation, if we denote 

 the length of the needle 2r siii a by /, is 



-/^(^ + J2)^C0S(/). 



It decreases, therefore, as cos 0, disappears when the needle 

 has attained the magnetic meridian, and for all positions is pro- 

 portional to the length of the needle /*. 



17. For the case of a bar of soft iron which becomes magnetic 

 under the influence of the two poles P and Q, our formulae are 

 not applicable when one of the two ends A and B is situated at 

 the other side of the axial line PQ. If both ends pass over to 

 the other side they are again applicable; but in this case we 

 must change the sign of //.. In the following we will confine 

 ourselves to the case where the length of the bar, in comparison 

 with the length of the lever and with the distance of the poles 

 from each other, may be neglected. Here our formulae are of 

 general applicability, provided only that we change the sign of 

 /I, when the bar of iron crosses over the axial line PQ. 



18. Inasmuch as the expressions (3) and (4) only change their 

 signs when the sign of a is changed, from the development of 



• The above formula can be applied to the earth only when we assume that 

 the magnetism of the globe is uniformly distributed, and that, besides this, we 

 are situated at the equator. \i. then denotes the force proceeding from each 

 pole projected upon the plane of the horizon. The result deduced from the 

 last form remains applicable when the needle is suspended at any latitude what- 

 ever. The coefficient of I cos alone changes. 



2 B 2 



