n 



ELECTRO-BYNAMICS. 



1 : 1 . KCTRO-M4GNETISM. 



81G 



let f, f' be the intensities of the currants ; the mutual action of these 

 two elements will then be represented in all c,w* by the formula 



', sin 1 cos $ I cos cos 



K 5 



Let R 0, R, 8, be the final values of - and for any given current 

 of which St is an element, tt' remaining as before ; then the total 

 ' of this electrical current on the element to in the direction of 



its length will be 



Co0\ 



Iff tr^sr B ; 



This may be easily deduced from the preceding formula. 



Hence an indefinite current, for which R, R, are infinite, exerts no 

 longitudinal action on !' ; only a normal force. This coincides with 

 what has been before shown for the action of an indefinite current on 

 a terminated conductor. The same property holds true for a closed 

 current, since in this case 0, R=H,. 



From hence it is easy to find the total action of a fixed current, or a 

 moveable rectilineal current. 



The action of a closed current, or an element of another current, 

 which is turned in all possible positions round its middle point, lies in 

 an invariable plane. 



The mutual action of two small closed conductors, containing areas, 

 A, A', the centres of which are at a distance v, exercise on each other a 

 force directly as the plane areas, and inversely as the fourth power of 

 the distance. 



The action of a uniform canal of currents indefinitely extended in 

 one way varies inversely as the square of the distance of its extremity 

 from tlie element acted on, and directly as the sine of the angle 

 which that distance forms with the element, and is in a direction per- 

 pendicular to the plane passing through the element and the extremity 

 of the canal. 



When two uniform and indefinite canals of currents act on each 

 other, the canals being supposed terminated at one extremity only, the 

 resultant is in the line joining their extremities, and the force is 

 inversely as the square of this line : hence the action of finite cauals 

 may be easily estimated, as being the difference between two 

 indefinite canals. With respect to the nature of the force, it will be 

 attractive or repulsive as before described. The simplest mode of 

 observing the actions of a canal of closed currents is by twisting a wire 

 in the form of a helix having but small intervals between the succes- 

 sive convolutions, the action of each portion of the helix being then 

 very nearly the same force as that of a portion of a circle or closed 

 current. 



Ampere imagined an ingenious manner of calculating the actions of 

 any plane closed conductors. Conceive one such to be divided into an 

 infinity of small compartments by right lines parallel to the rectan- 

 gular axes of co-ordinates, and the periphery of each compartment to 

 be traversed by currents, in the same manner as the whole curvilineal 

 side which encloses the area; then it is easily seen that all the 

 internal sides of the compartments, being traversed by two currents 

 in opposite directions, will have no electro-dynamical action, and 

 therefore the sole remaining current is that which circulates in the 

 periphery of the given figure ; but by this division into compartments 

 we can calculate the mutual actions of the two closed conductors from 

 the very simple law which we have already given for the action oi 

 small closed conductors on each other. 



Voltaic conductors, of which the centres of gravity are supported 

 undergo terrestrial action, similar to that produced by a canal oi 

 currents. We should infer, by the position which the moveable con 

 ductor takes, that the direction of the terrestrial currents is nearly 

 from east to west, having the north magnetic pole situated on their 

 right. 



Since the action of closed currents on an element of a conductor 

 is perpendicular to that element, hence a straight conductor fixed a 

 one extremity, and free to move in a horizontal plane, will receive a 

 continued rotation from the influence of the currents of the earth ; 1m 

 if the conductor were supported by its centre of gravity, it would be 

 brought by their action into a fixed plane, and an electro-dynamii 

 cylinder would come into a position perpendicular to that plane. 



All these results of theory are confirmed by experiments, and are 

 shown in the lecture-rooms of gentlemen who profess this branch o 

 science. 



With respect to the quantity of the galvanic current, Ohm in 182. 

 advanced the following formula) : 1. For a conductor, into whose 

 extremities the two electricities fiow with a given tension. Let A. be 

 the electrical tension ; K, the conducting power of the wire or other con 

 ductor; ve, the surface of its transverse section ; L, its length; <j, th 



quantity of the current, then q = AKW . 2. For a simple galvani 



L 



circuit: Let A be the electro-motive power of the circuit (or th 

 tension?), R, the resistance which the current meets with in th 

 circuit itself. This is the resultant of the following individual resist 

 anccs : a, resistance of the two metallic plates which the current ha* 



o traverse ; b, resistance of the liquid through which the current 

 lasses. To this, Fechner and Poggerdorff add, c, resistance of transi- 

 ion, or the resistance which exists to the passage of the electric 

 urrent from the metal to the liquid and conversely. Also, let r be 

 be resistance of the conductor which unites the two metals, and Q, 



A 



lie quantity of the electric current which enters it; thenQ = j^- r ; 

 herefore, A = <} (R + r). 3. For the galvanic battery : >i, denoting the 



umber of united simple currents Q = . When the resistance, 



nR + r 



, of the conductor which closes the circuit is inconsiderable in com- 

 parison with the resistance B, in the individual circmt, it nearly 



anishes in the formula, and there remains q = fc^ RI tnat >>- 



uantity of the current is the same, whether it proceed from one \mr 



r from several. But if the resistance of the conductor which closes 



the circuit be considerable, as from the interposition of water, &c., 



hen Q increases considerably with the number of pairs, because then 



; gives a much smaller quotient than n R f . [GALVANISM.] See 



also Gmelin's 'Handbook of Chemistry,' vol. i. ; Cavendish So< 

 "ransactions. 



ELECTROLYSIS. [ELECTRO-CHEMISTRY.] 

 ELECTROLYTE. [ELECTRO-CHEMISTRY.] 

 ELECTRO-MAGNET. [ELECTRO-MAONETISM.] 

 ELECTRO -MAGNETIC MACHINES. [ELECTRO-MOTIVE MA- 

 CHINES.] 



ELECTRO-MAGNETISM. The first important discovery in point 

 jf time, which laid the foundation of this new science, was made by 

 "rofessor Oersted of Copenhagen. By reference to the article ELECTRO- 

 )YNAMICS, it will be seen that when the wires which communicate with 

 he poles of a galvanic battery are connected by a conductor or by being 

 jrought into contact with each other, the opposite electricities thus 

 continually made to combine acquire a power of action on another 

 jonductor under similar circumstances, though latent with respect to 

 jomuion electrical action ; but this discovery of Ampere M;>S preceded 

 >y that of Oersted, who found that the electrical current thus gene- 

 rated acted upon a magnetised bar, and tended to turn it round as if 

 exercising a tangential force. Before this time a connection between 

 electricity and magnetism had been suspected, or rather believed, by 

 franklin, Beccaria, and others, from the well-known circumstance that 

 ,he poles of the compass-needle had been frequently reversed during 

 .hunder-storms, and that the same effect could be produced by elec- 

 trical discharges. In most experiments which were then made these 

 discharges were unnecessarily strong ; but to Oersted's discovery, 

 'ollowed up as it has been by Ampiire, Faraday, Barlow, Arago, &c., 

 we must ascribe the source of those accurate data by which the actions 

 of the earth on magnets, of magnets on each other, of conducting \\iivs 

 on magnets, and of the earth on conducting wires, are reducible to 

 imilar and simple principles of action. 



When a magnetic needle is placed near a conducting wire in the 

 plane of the magnetic meridian, and the battery is powerful, it is 

 observed that the needle will turn round, placing itself at right angles 

 to the direction of the current ; the same effect, which we have seen 

 in the preceding article, would be produced by the same conductor on 

 a canal of currents. If we suppose that a man with his face turned to 

 the needle is himself the conductor, with his feet at the positive pole, 

 the north pole of the needle will turn towards his right. This must 

 be understood as only meant to illustrate the direction of rotation. 



In order to discover the law of action of a current on a magnetic 

 element, Biot and Savart used a small magnetic needle, guarded from 

 the agitations of the air, and having the action of terrestrial magnetism 

 neutralised by a bar, thus subjected only to the immediate action of 

 the conductor. Having acquired the position indicated by Oe 

 the times of its small oscillations were observed, which we know by 

 the principles of Dynamics rfust be inversely proportional ctetent 

 paribue, to the square root of the accelerating force impressed. By 

 ng the times in which, for instance, ten oscillations of the needle 

 took place at different distances, it was deduced without difficulty, that 

 the electro-magnetic force exercised by the whole conductor was in- 

 versely ns the distance of the needle from the conductor ; this of 

 course supposes that the current may be regarded as indefinite, com- 

 pared with the dimensions of the needle. Hence it easily followed, as 

 was shown by Laplace, that the force exercised by each element of the 

 conductor on the magnetic needle must, like all known forces, vary 

 inversely as the square of the distance ; and Biot showed that, when 

 the distance was given, the force was then proportional to the sine of 

 the angle formed by each element of the current with the right line 

 joiring the middle of that element with the middle of the needle. 



It has been shown by means of the multiplier that the electrical 

 intensity of the current at different points of the same conductor is 

 constant. We may observe that the principle of the multiplier con- 

 sists in bending the wire in the form of a helix, but returning upon 

 itself so as to form a closed circuit, the wire being covered with silk 

 to prevent communications at the crossings ; the action of such a spiral 

 being similar to that of closed circular currents equal in number t the 

 spiral convolutions. 



