Prof. Thomson on the Dynamical Theory of Heat. 385 



being respectively 90° — w and w, their strengths per unit of area 

 of this plaue^ obtained by multiplying their intensities by the 

 cosine of those angles respectively, will be each equal to 

 i cos o) sin oj. 



Hence the absorptions of heat which they will produce at the sur- 

 face of separation of the metals per unit of area per second will be 



— Y-i cos (o sin (otO, and y" * cos ay sin ait<^, 



respectively. According to the general principle of the super- 

 position of thermo-electric actions stated above, the su.m of these 

 is the rate of absorption of heat per unit of surface when the two 

 systems of currents coexist. But the resultant of these systems 

 is simply the given longitudinal current in the bai% vith no flow 

 either out of it or into it across any of its sides. Hence a simple 

 current of intensity i, parallel to the sides of the bar, causes 

 absorption of heat at the side CD amounting to 



-=- i cos ft) sin o)t{(fi — 6), 



per unit of area per second ; and the same demonstration shows 

 that an equal amount of evolution must be produced at the oppo- 

 site side CD'. These effects take place quite independently of the 

 matter round the bar, since the metal carrying electric currents 

 which we supposed to exist at the sides of the bar in the course 

 of the demonstration, can exercise no influence on the phse- 

 nomena. 



152. If / denotes the length of the bar, the area of each of the 

 sides perpendicular to the plane of the diagram will htla; and 

 therefore the absorption over the whole of the side CD, and the 

 evolution over the whole of the other side CD', per second, will be 



-p ila cos ft) sin wt{(^ — 6), 

 J 



'' ^7 — cosft)sina)^((^ — ^). 



It is obvious that there can be neither evolution nor absorption 

 of heat at the two other sides. 



153. An investigation similar to that which has just been 

 completed, shows that if the actual current enter from a con- 

 ductor of the standard metal at one end of the bar, and leave it 

 by a conductor of the same metal at its other end, the absorption 

 and evolution of heat at these ends respectively will amount to 



■Y y{t0 cos^ o) + t^ sin^ <b) 



per second. 



