430 Prof. Thomson on the Mechanical Theory of Electrolysis, 



same unit the mechanical equivalent of the unit of heat. Hence 

 if the mechanical equivalent of the thermal unit be denoted by 

 J, the work done in any time by W, the total quantity of heat 

 evolved in the same time throughout the circuit by H, and the 

 thermal equivalent of the chemical effect produced by 0, we have 



W 

 H=y-e; (1) 



an equation which may also be written in the form 



W=JH + M, (2) 



if M be used to denote the value of J@, or, as it may be called, 

 the mechanical equivalent of the chemical effect produced in the 

 stated period of time. 



3. To avoid the necessity of considering variable or disconti- 

 nuous currents, let us suppose the " machine " to consist of a 

 metallic disc, touched at its centre and at its circumference by 

 fixed wires, and made to revolve in its own plane about an axis 

 through its centre, held in any position not at right angles to 

 the direction of the earth's magnetic force*. If these wires be 

 connected by contact between their ends, there will, as is known, 

 be a current produced in them of a strength proportional directly 

 to the angular velocity of the disc, and inversely to the resistance 

 through the whole circuit. Hence there will be between the 

 ends of the wires, if separated by an insulating medium, an elec- 

 tro-motive force the intensity of which will be constant and pro- 

 portional to the angular velocity of the disc. 



4. Let us now suppose the wires to be connected with the 

 electrodes of an electro-chemical apparatus, for instance a gal- 

 vanic battery of any kind, or an apparatus for the decomposition 

 of water ; and let us conceive the electro-motive intensity between 

 them to be sufficient to produce a current in its own direction. 

 The preceding equations, when applied to this case, will have 

 each of their terms proportional to the time, since the action is 

 continuous and uniform, and therefore it will be convenient to 

 consider the unit of time as the period during which the amounts 

 of work and heat denoted by W and H, and the amount of che- 

 mical action of which the thermal and the mechanical equivalents 

 are denoted respectively by and M, are produced. If r denote 

 the radius of the disc, co the angular velocity with which it is 

 moved, F the component of the earth's magnetic force per- 

 pendicular to its plane, and 7 the strength of the current 

 which is induced ; the work done in a unit of time in moving 

 the disc against the resistance which it experiences in virtue 



* This is in fact the " new electrical machine " suggested by Faraday in 

 the Bakerian Lecture of 1832. (Experimental Researches, § 154.) 



