138 PROFESSOR W. THOMSON ON THE 



passing from bismuth to copper, when the temperature is kept at 0° Cent, must 

 therefore be ^f^g, or very nearly equal to the quantity required to raise the 

 temperature of a grain of water from 0° to 1° Cent.' " 



119. Example 2. Copper and Iron. — " By directing the electro-motive force of 

 one copper and bismuth element against that of a thermo-electric battery of a 

 variable number of copper and iron wire elements in one circuit, I have found, 

 by a galvanometer included in the same circuit, that when the range of tempe- 

 rature in all the thermo-electric elements is the same, and not very far at either 

 limit from the freezing point of water, the current passes in the direction of the 

 copper-bismuth agency when only three, and in the contrary direction when four 

 or more, of the copper-iron elements are opposed to it. Hence the electro-motive 

 force of a copper-bismuth element is between three and four times that of a copper- 

 iron element with the same range of temperature, a little above the freezing point 

 of water. The electro-motive force of a copper-iron element, with its two junc- 

 tions at 0° and 1° Cent, respectively, must therefore be something greater than 

 one-fourth of the number found above for copper-bismuth w r ith the same range of 

 temperature, that is, something more than 40 British absolute units, and we may 

 consequently represent it by m x 40, where m > 1. We have then by the equation 

 expressing the application of Carnot's principle, [equation (19) of § 116.], 



J 

 ©o t* = ©o 27*7 = m x 40 ' 



Avhence* © = i m nearl y («)• 



" Now, by the principle of mechanical effect, we have 



a 280 \ 



if F 280 denote the electro-motive force of a copper-iron element, of which the two 

 junctions are respectively 0° and 280 D Cent., and a d t, the quantity of heat absorbed 

 per second by a current of unit strength, in passing in copper from a locality at 

 temperature t to a locality at t + dt, and in iron from a locality at t + dt to a 

 locality at t\\ since the Peltier generation of heat between copper and iron at 

 their neutral point, 280\ vanishes \\ and therefore the only absorption of heat is 

 that due to the electric convection expressed byy a d t ; while there is evolution of 



* The value of J now used being 32-2 x 1390 = 44,758, which is the equivalent of the unit of 

 heat in " absolute units" of work. The " absolute unit of force" on which this unit of work is 

 founded, and which is generally used in magnetic and electro-magnetic expressions, is the force which 

 acting on the unit of matter (one grain) during the unit of time (one second), generates a unit of 

 velocity (one foot per second). The " absolute unit of work" is the work done by the absolute unit 

 of force in acting through the unit of space (one foot). 



f That is, if S denote the algebraic excess of the specific heat of electricity in copper, above the 

 specific heat of eleetricity in iron, according to the terms more recently introduced. 



+ See § 123, below. Instead of 240°, conjectured from Regnault's observation when these 

 details were first published, 280° is now taken as a closer approximation to the neutral point of copper 

 and iron. 



