OP ARTS AND SCIENCES. 219 



temperatures is much complicated by the existence of the two thermal 

 effects, and by the fact that the direction of these effects is not con- 

 stant for all ranges of temperature. The existence of the Thomson 

 effect venders the curve of the electromotive forces and temperatures 

 a parabola. The electromotive force cannot be considered propor- 

 tional to the difference of temperatures of the junctions. Tait's in- 

 genious method of acting on a differential galvanometer with two 

 elements, gives an arrangement where the deflection is proportional 

 to the difference of temperatures ; but the method is exceedingly diffi- 

 cult in practice. We have also seen that, when an abrupt variation 

 of temperature is produced, the electromotive force is probably pro- 

 portional to the difference of temperatures ; but there is no obvious 

 method of realizing this arrangement practically for the measurement 

 of temperature. The chief difficulty, however, in using the thermo- 

 electric element as a thermometer, is due to the reversal of the heat 

 effects. Every element must first be tested through the ranges in 

 which it is to be used ; and this testing necessitates the use of some 

 other method of measuring temperatures, which is very difficult and 

 inaccurate. 



In regard to the use of the thermo-electric element as a heat engine, 

 there is always a loss of heat, from two causes, which is absolutely 

 unavoidable unless some substance can be procured which has a ther- 

 mal conductivity of zero, and a finite electrical conductivity. Tiiis loss 

 must always be taken into consideration in comparing the efficiency 

 of the thermo-electric engine with that of other heat engines. 



In a bar of section S, and length I, the quantity of heat lost in unit 

 time by conduction is 



That generated in unit time by a current of electricity is 



H, = PkL^E^S^, 



K and .- are the thermal and specific electrical conductivities. Loss 



of heat by radiation from the surface of the bar is supposed to be 

 avoided. If this bar is supposed to form part of a thermo-electric ele- 

 ment, any increase of S throughout the bar, that is, so as to increase 

 the surfaces of contact, will increase H -\- H^. If, however, the cur- 

 rent strength is fixed, that is, if the current is passed through the bar 

 from an outside circuit of large resistance compared with that of the 



