GO 



ELECTRO-MAGNETISM. 



whether this velocity varies in different 

 cases, nor have we any distinct idea of 

 the causes that are likely to produce 

 such variation. We can perceive, how- 

 ever, that the mode of transmission has 

 a considerable influence on the results. 

 The currents transmitted by perfect 

 conductors are continuous; that is, 

 their intensity is either constant, or varies 

 insensibly during two consecutive in- 

 stants. When the conductors are im- 

 perfect, the currents are discontinuous; 

 for the electricity is allowed to accumu- 

 late for a certain time, and until the 

 insulating force is overcome, when it 

 escapes, and passes on with a sudden 

 impulse, analogous to an explosion. 

 The electro-motive power continuing to 

 act, gives rise to a second accumulation, 

 and a fresh explosion, and so on succes- 

 sively. These alternations may become 

 sufficiently rapid to escape our senses, 

 and thus produce the appearance of an 

 uninterrupted current, although it be 

 really discontinuous. The distinctive 

 character of such currents is, that they 

 are incapable of producing a deviation 

 in the magnetic needle. This is the 

 case with the current produced by the 

 common electrical machine, when a com- 

 munication is established between its 

 positive and negative conductors : and 

 also with the currents established in 

 what have been called the secondary 

 piles of Kilter (see Electricity, J 93), 

 or piles constructed with a series of 

 metallic discs separated by humid con- 

 ductors. Discharges from the Leyden 

 vial, in like manner, although they in- 

 duce a degree of permanent magnetism 

 in steel bars near which they pass, yet 

 scarcely leave any traces of their effects 

 on the needle of the galvanometer, when 

 transmitted through the wires of that 

 instrument. 



(177.) The continuity of the electric 

 current being the quality most immedi- 

 ately concerned in the production of the 

 effects that are the subject of our present 

 consideration; and it being impossible 

 for us to discriminate differences of ve- 

 locity or of quantity, in any other man- 

 ner than by the total effects that result 

 from the passage of the current through 

 a conducting body, we shall distinguish 

 continuous currents only in respect to 

 their intensity, and pretend to judge of 

 the degrees of intensity solely by the 

 amount of the effects produced on the 

 galvanometer. 



(178.) In order to arrive at the fun- 

 damental law of electro-dynamic action 



of currents upon one another, it is 

 necessary to consider the total action of 

 each as resulting from the combined 

 actions of every one of its parts. As 

 it is not possible to institute a direct 

 measurement of those elementary forces 

 exerted by each indefinitely small por- 

 tion, the one upon the other, the inquiry 

 can only be made by assuming some 

 hypothesis relative to the law of diminu- 

 tion according to distance, and prose- 

 cuting the consequences of such an 

 hypothesis, when applied to such finite 

 portions of current as occur in our 

 experiments, and to compare them with 

 actual observation, their accordance 

 with which will be a test of the admis- 

 sibility of the hypothesis. 



(179.) Guided by the analogy of all 

 the other known forces in nature, we 

 shall assume that the mutual actions of 

 the elementary portions of electric cur- 

 rents are inversely as the squares of 

 their relative distances ; and this is, in 

 fact, the supposition which agrees best 

 with all the facts that have hitherto been 

 ascertained. If we suppose A, for in- 

 stance (Jig. 97), to be an indefinitely 

 small] portion of the rectilineal current 

 P N, moving from left to right, it will 

 act upon another elementary portion, 13, 



Fig. 97. 



-N 



A. 



of a current placed at a given distance 

 with nine times the energy that it exerts 

 upon a similar portion of current placed 

 at C three times further removed from 

 it. If we call the force of attraction /, 

 the intensity of the first current a, and of 

 the second current b, and the distance 

 between them, or the line B A, d, the 

 following equation will express the law 

 just enunciated : 



/. a b 



/= ^ 



(180.) It may be demonstrated ma- 

 thematically, that such being the law of 

 elementary action, it will follow as a 

 necessary consequence that the total 



