BALANCE ELECTRODYNAMOMETERS. 247 



Joule* applied this method to determine variations of current in 

 his calorimetrical researches. He used the system of three sym- 

 metrical coils whose properties have been studied above (792). 

 The three coils were of equal dimensions, and each formed of a 

 flat spiral. In these conditions the formulae are difficult of appli- 

 cation. Dr. Joule contented himself with observing that, if we only 

 take into account the actions of portions of the adjacent wires, 

 regarding each element as under the action of an infinite parallel 

 current, and if / is the total length of the wire in each coil, S the 

 surface, and p the weight necessary to keep the movable coil at an 

 equal distance from the fixed ones, the intensity of the current is 







in which A stands for a correction depending on the dimensions of 

 the apparatus, and which is determined by comparison with a tangent 

 compass. 



Lallemandf had already used a similar arrangement, with this 

 difference, that the movable spiral was placed at the end of a 

 horizontal lever supported by a metal wire, the torsion of which 

 could be varied. Here the action of the earth is not null, as in 

 Joule's balance; but it is eliminated by placing at the other end 

 of the lever a coil symmetrical with the first, and traversed in the 

 same direction by the current (489). 



Such, also, is the electrodynamometer used by Maxwell! in his 

 investigations on the ratio of the electrostatic and electromagnetic 

 units. A horizontal lever, suspended in the middle to a wire, 

 supports two flat vertical coils. Each of these is placed between 

 two other fixed coils of larger diameter, the distance of which 

 satisfies the condition of the maximum (792). 



On this subject it may be observed that the square of the 

 intensity of a current has the same dimensions (609) as a force. 

 The factor by which the action exerted on the movable coil must 

 be multiplied so as to obtain the square of the intensity of the 

 current is thus an abstract number. We see from the values of 

 in (787) and (792) that we can consider this factor as containing 



* JOULE. British Association Report, 1864. Scientific Papers, Vol. I., p. 584. 

 t LALLEMAND. Ann. de Chim et de Phys. [3], Vol. XXXIL, p. 432. 1854. 

 $ MAXWELL. Phil. Trans. Roy. Soc., 1868, p. 643. 



