ELECTRO-MAGNETISM. 



the phenomenon in question. But the 

 subject has been investigated with all the 

 rigour of mathematical analysis, and the 

 results determined with all the precision 

 that can be required for comparison 

 with actual experiment. We have pur- 

 posely omitted several of the minuter 

 details which were even compatible with 

 the popular view we have presented, but 

 which would have required more com- 

 plicated diagrams for their exposition, 

 and considerably lengthened the inquiry, 

 but which have no material influence on 

 the ultimate conclusions. Thus, if the 

 straight conductor, instead of being 

 indefinite in length, were terminated, 

 and wholly above the horizontal prism, 

 it would be found that there is no longer 

 that exact compensation between the 

 currents in the upper and lower surfaces ; 

 for when the conductor is immediately 

 above the prism, the upper currents 

 have a much more considerable influ- 

 ence on it than the lower currents, and 

 urge it on its revolution in the same 

 direction as that in which it was moving 

 from the effect of the other forces in 

 operation. At the remotest part of the 

 circle, the lower currents come more into 

 operation from their acting with less 

 obliquity than the upper currents, and 

 concur, in their turn, in augmenting the 

 tendency to revolution in the same di- 

 rection. 



(249.) The following laws are ob- 

 tained as the results of the mathema;- 

 tical investigation of the subject: 



i. The action of a very slender electro- 

 dynamic cylinder upon an elementary 

 portion of a current may be resolved 

 into two forces, acting in directions per- 

 pendicular to the direction of the cur- 

 rent, and also respectively perpendicu- 

 lar to the lines drawn from it to each of 

 the extremities of the axis of the cylin- 

 der ; each of these forces being inversely 

 as the squares of these distances. 



ii. The action of an electro-dynamic 

 cylinder upon an indefinite conductor, 

 perpendicular to its axis, may, in like 

 manner, be reduced to two tangential 

 forces, as in the former case ; but these 

 forces are in the simple inverse ratio of 

 the distances from the extremities of the 

 cylinder. 



iii. If the length of the electro-dynamic 

 cylinder be supposed to be indefinite, its 

 action upon an elementary portion of a 

 current will depend entirely upon the 

 relative positions of the element, and 

 that extremity of the cylinder to which 

 it is referred, and is influenced in no 



respect by the relative position of the 

 axis of the cylinder. 



iv. The action of this cylinder upon 

 conductors, of whatever form or magni- 

 tude, is subject to the same conditions, 

 being dependent solely upon the posi- 

 tion of that extremity, which is referred 

 to the conductor, and remains the same 

 whatever be the direction of the axis of 

 the cylinder *. 



(250.) The conclusions thus deduced 

 from the evidence of observation, com- 

 bined with the deductions from theory, 

 indicate the strongest analogy, and 

 almost perfect identity, between the 

 agency of electro-dynamic cylinders and 

 that of magnets. The law of their ac- 

 tion upon an electric current, and of the 

 reaction of the latter upon botb, is pre- 

 cisely the same ; so much so, that if we 

 had the command of sufficiently power- 

 ful currents, the electro-dynamic cylin- 

 der might be substituted for the mag- 

 net in all the experiments we have de- 

 scribed in the last Chapter, and the 

 same results, whether of attraction, re- 

 pulsion, or revolution, would be obtained 

 from them. The two extremities of an 

 electro-dynamic cylinder exhibit all the 

 properties possessed by the poles of a 

 magnet : that end in which the current 

 of positive electricity is moving in a 

 direction similar to the movements of 

 the hands of a watch, acting as the 

 south pole of a common magnet ; and 

 the other end, in which the current is 

 moving in a contrary manner, manifest- 

 ing a northern polarity. 



(251.) It will be readily anticipated, 

 from the known resemblance between 

 the action of electro-dynamical cylin- 

 ders and of magnets on electric currents, 

 that two such cylinders will act upon 

 each other precisely in the same way 

 as magnets do. Theory confirms the 

 exactness of this general conclusion ; for 

 the following is the law to which mathe- 

 matical examination conducts us, namely, 

 that the mutual action of two electro- 

 dynamic cylinders may always be repre- 

 sented by four forces, having the direc- 

 tions of lines drawn from each extremity 

 of the one to both extremities of the 

 other, and being to one another in the 

 reciprocal ratio of the squares of. these 

 lines, provided these distances be not 

 exceedingly small t. 



* .Ampere, Recueil d' Observations Electro-dyna- 

 miques, p. 343. See also Demonferrand's Manuel 

 d'ElectriciteDynamique ; or Cumming's Translation, 

 pp. 60, 67, 138, and 140. 



f Ampere, Recueil d'Observations Electro-dyna* 

 rniques, &c. p. 343. 



