ELECTRO-MAGNETISM. 



It is also to be observed, that the mo- 

 tion of the wire, whatever be its relative 

 position to the magnet, is always moved 

 parallel to itself; that is, in the direction 

 of a line at right angles to it. 



(-27.) The direction of Ihe electro- 

 magnetic force being thus determined, 

 we have next to ascertain the exact 

 law, according to which its intensity 

 varies, with relation to the distance of 

 the electric current from the point on 

 which it acts. The most reasonable 

 conjecture we can form on this subject, 

 prior to experimental investigation, is, 

 that this law is the same with that which 

 is followed in the case of electric and 

 magnetic actions, namely, that the in- 

 tensity of the force is every where 

 inversely as the square of the distance. 

 But if this be the real law of action, it 

 must apply to the elementary portions 

 of the two agents which thus mutually 

 act apon each other ; or, to adopt the 

 more convenient language of theory, it 

 must obtain only among the elementary 

 particles of the electric and magnetic 

 fluids. In the magnet, the action of the 

 latter may be regarded as concentrated 

 in the points, which are the poles of the 

 magnet ; but in the conducting wire, the 

 electric fluid which is passing through 

 it, acts in an equal degree along the 

 whole line of its motion ; and admitting 

 the hypothesis of the action being in- 

 versely proportional to the squares of 

 the distances of each individual particle, 

 we have to deduce the law which will 

 result from the combined actions of all 

 the points of a line directed upon a 

 point out of that line. Now, it may be 

 mathematically demonstrated, that if the 

 line in question be perfectly straight, 

 and its length be exceedingly great in 

 proportion to the distance of the point 

 on which it acts, then the intensity of 

 action will be inversely proportional, 

 not to the square, but to the simple dis- 

 tance of the point, so that at three times 

 the distance, for example, the force 

 shall be one-third, at four times the 

 distance, one-fourth, and so on. That 

 this law is conformable to observation, 

 has been proved by the experiments 

 conducted by Biot and Savart, in which 

 the intensities of the force at different 

 distances were accurately ascertained, 

 by observing the number of oscillations 

 performed by the needle in a given time, 

 and taking the squares of those num- 

 bers. 



CHAPTER IV. 



Direct consequences of the Law of Elec- 

 tro-magnetic Action. 



(28.) Let us now inquire into the 

 consequences of this law. So different 

 is the action of the electro-magnetic 

 force from that of the other forces in 

 nature, with the effects of which we are 

 more familiar, that a particular train of 

 investigation is required, in order to 

 trace its exact operation under every 

 combination of circumstances. It is 

 not easy, even in the simpler cases, 

 where a single magnetic pole is sub- 

 jected to the action of a conducting 

 wire, at once to pronounce upon the 

 precise motion that will result, espe- 

 cially if the motion of the magnetized 

 body is limited to a fixed plane, and re- 

 strained to mere rotation ; but the diffi- 

 culty is much increased, when, as most 

 frequently happens in actual experi- 

 ment, the investigation is complicated 

 by the necessity of including the com- 

 bined actions of several poles of dif- 

 ferent kinds. The only mode of ob- 

 taining clear views of the subject is to 

 examine the several cases in their order 

 of simplicity, commencing with each 

 force taken singly, and afterwards stu- 

 dying their several combinations. 



$ 1. Effects on the Directive Property of 

 a Magnetic Needle. 



(29.) Confining our attention, then, 

 for the present, to a single magnetic 

 pole, the north pole for instance, we 

 have to examine the effects produced 

 upon it by a conducting wire of indefi- 

 nite length, acting upon it with a tan- 

 gential force inversely proportional to 

 its distance, when the movements of 

 that wire are limited to the circumfer- 

 ence of a circle, in a given plane, per- 

 pendicular to the wire. The case under 

 consideration may, in a great measure, 

 be exemplified, by placing a magnet, 

 SN, fig. 12, on a flat support, AB, 

 resting, at its centre, on the pivot P, 

 and balanced by a counterpoise at the 

 opposite end, so that the south pole, S, 



Fig. 12. 



