TRANSACTIONS OF THE SECTIONS. 17 



cause the wheel to rotate in the cUrection towards A. According to Faraday's 

 Wfll-kuo\^Ti discovery, a cuirent is induced iu the circuit in such a direction that 

 the mutual electromagnetic action between it and the fixed magnet resists the 

 motion of the wheel. Now the mutual electromagnetic force between the por- 

 tions AB and CT of the circuit is reiiulsive, according to the well-known elementary 

 law of Ampere, and therefore resists the actual motion of the wheel ; hence if 

 the magnet be removed there will still be electromagnetic induction tending to 

 maintain the cm-rent. Let us suppose the velocity of the wheel to" have been at 

 first no greater than that practically attained in ordinary experiments with Barlow's 

 electromagnetic disk. As the magnet is gradually withdrawn let the velocity be 

 gradually increased, so as to keep the strength of the cm-rent constant, and, when 

 the magnet is quite away, to maintain the current solely by electromagnetic in- 

 duction betweeu the fixed and moveable portions of the circuit. If, when the 

 magnet is away, the wheel be forced to rotate faster than the limiting velocity of 

 our previous supposition, the cm-rent will be augmented according- to the law of 

 compound interest, and would go on thus increasing without limit were it not 

 that the resistance of the circuit would become g-reater in virtue of the elevation of 

 temperature produced by the cm-rent. The velocity of rotation, which gives by 

 induction an electromotive force exactly to that required to maintain the current, 

 is clearly independent of the strength of the cm-rent. The mathematical deter- 

 mination of it becomes complicated by the necessity of taking into account the 

 diffusion of the current through portions of the disk not in the straight line between 

 C and T ; but it is very simple and easy if we prevent this diffusion by cutting the 

 wheel into an infinite number of infinitely thin spokes, a great number of whicli 

 are to be simultaneously in contact with the fixed conductor at T. The linear 

 velocitj' of the circumference of the wheel in the limiting case bears to the velocity 

 which measures, iu absolute measure, the resistance of the circuit, a ratio (deter- 

 minable by the solution of the mathematical problem) which depends on the pro- 

 portions of the rectangle CTAB, and is independent of its absolute dimensions. 



Lastly, suppose the wheel to be kept rotating at any constant velocity, whether 

 above or below the velocity determined bj' the preceding considerations ; and sup- 

 pose the cm-rent to be temporarily excited in auy way, for instance, by bringing a 

 magnet into the neighbourhood and then withdrawing it; the strength of this current 

 will diminish towards zero or will increase towards infinity, according as the velo- 

 city is below or above the critical velocity. The diminution or augmentation 

 would follow the compound interest law if the resistance in the circuit remained 

 constant. The conclusion presents us with this wonderful residt : that if we 

 commence with absolutely no electric current, and give the wheel auy velocity of 

 rotation exceeding- the critical velocity, the electric equilibrium is unstable : au 

 infinitesimal current in either direction would augment until by heating the cir- 

 cuit, the electric resistance becomes increased to such au extent, that the electro- 

 motive force of induction j ust suffices to keep the current constant. 



It will be difficult, perhaps impossible, to realize this result in practice, because 

 of the great velocity required, and the difficidty of maintaining good frictional con- 

 tact at the circumference, without enormous liictioU; and consequently frictional 

 generation of heat. 



The electromag-netic augmentation and maintenance of a cm-rent discovered by 

 Siemens, aud put iu practice by him, with the aid of soft iron, and proved by 

 Maxwell to be theoretically possible without soft iron, suggested the subject of 

 this communication to the author, and led him to endeavoiu- to arrive at a similar 

 result with only a single circiut, and no making and breaking of contacts ; and it is 

 only these characteristics that constitute the peculiarity of the arrangement which 

 he now describes. 



On Volta-Convection hy Flame. By Sir W. Thomson, LL.D., F.Ii.S. 



In Nichols' Cyclopedia (2nd edition), article " Electricitj', Atmospheric," and in 

 the Proceedings of the Royal Society, May 1860 (Lecture on Atmospheric Elec- 

 tricity), the author had pointed out that the efi'ect of the fhime in an insulated 

 lamp, is to reduce the lamp and other conducting matej'ial connected with it to the 



1S67. 2 



