64 Sir W. Thomson on Volta- Convection by Flame. 



ductor at T. The linear velocity of the circumference of the 

 wheel in the limiting case bears to the velocity which measures, 

 in absolute measure, the resistance of the circuit, a ratio (deter- 

 minable by the solution of the mathematical problem) which 

 depends on the proportions of the rectangle CTAB, and is in- 

 dependent of its absolute dimensions. 



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

 velocity, whether above or below the velocity determined by the 

 preceding considerations ; and suppose the current to be tempo- 

 rarily excited in any 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 velocity 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 re- 

 sult : that if we commence with absolutely no electric current, 

 and give the wheel any velocity of rotation exceeding the critical 

 velocity, the electric equilibrium is unstable : an infinitesimal 

 current in either direction would augment until, by heating the 

 circuit, the electric resistance becomes increased to such an 

 extent that the electromotive force of induction just 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 diffi- 

 culty of maintaining good frictional contact at the circumference, 

 without enormous friction, and consequently frictional generation 

 of heat. 



The electromagnetic augmentation and maintenance of a cur- 

 rent discovered by Siemens, and put in 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 commu- 

 nication to the author, and led him to endeavour to arrive at a 

 similar result with only a single circuit, and no making and 

 breaking of contacts ; and it is only these characteristics that 

 constitute the peculiarity of the arrangement which he now 

 describes. 



VII. On Volta- Convection by Flame. 

 By Sir William Thomson LL.D., F.R.S.* 



IN NichoPs Cyclopaedia, article " Electricity, Atmospheric " 

 (2nd edition) , and in the Proceedings of the Royal Institu- 

 tion, May 1860 (Lecture on Atmospheric Electricity), the author 



* Communicated by the Author, having been read at the Meeting of the 

 British Association, Dundee, September 1867. 



