554 



The Earl of Rossc on the 



[June 10, 



sensibility of the thermopile is much increased by reduction of its mass, 

 and more especially by a diminution of the cross section of the elements. 



To obtain a clear idea of the problem before us, which is, how to con- 

 struct the thermopile so that, with a given amount of radiant heat falling 

 on its face, the greatest current may be sent through the galvanometer, 

 let us consider the thermopile under two different conditions : — 



1. With the circuit open. 



2. With the circuit complete. 



In the first case, when radiant heat falls on the face of the pile, the 

 whole mass of metal rises in temperature, the rise being greatest at the 

 anterior face, and less and less as you approach the other end. This rise 

 of temperature will increase till the heat radiated from the anterior face, 

 together with that which traverses the depth of the pile and is radiated 

 from the posterior face, is just equal to that radiated to the anterior face 

 at that moment, or when 



sc 



7c(t + t')=Jct + -j (t—t') = Q, 



where (t, t') are respectively the temperatures of the anterior and posterior 

 face, s, I the cross-section and depth of the pile, c proportional to the 

 mean conductibility of the material of the pile, (Q) the quantity of heat 

 falling on the pile in a unit of time, and (/.:) a constant. 



Let us now suppose the circuit completed, and we shall have, in addi- 

 tion to the above, two causes operating to reduce the temperature of the 

 anterior face, — the abstraction of heat hy the electric current, and propor- 

 tional to that current =LI, where I is the intensity of the current and 

 L a constant, then there will be equilibrium when 



sc 



7c (t+t') + Ll=Jct+ -j-(t-t') + LI=Q. 



It is quite clear therefore that if Q be constant, I will become the larger 

 the smaller the other two terms become ; and therefore as long as the first 

 term continues small compared with the remaining terms, and the resist- 

 ance in the pile is very small compared with that in the rest of the cir- 

 cuit, we shall increase the intensity of the current by every reduction 

 of the cross-section of the elements of the thermopile. 



There is another point which, though less important, cannot be entirely 

 lost sight of, namely, that the more we reduce the mass of the anterior 

 face and adjacent parts of the pile, the more rapidly will the temperature 

 rise to its state of equilibrium, and therefore the more convenient will it 

 be for use where the needle is liable to disturbances from various causes, 

 and where consequently the more speedily the needle can be brought to 

 rest, the more accurately will its observed motion be a measure of the 

 radiant heat falling at that moment on the face of the pile. 



Let us now compare the case of a single pair of small cross-section 

 with a metal disk soldered to the junction of the two bars, and of sum*- 



