370 Royal Society : — 



posterior faces, s, I the cross-section and depth of the pile, c pro- 

 portional to the mean conductivity of the material of the pile, Q 

 the quantity of heat falling on the pile in a unit of time, and h a 

 constant. 



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

 addition to the above, two causes operating to reduce the tempera- 

 ture of the anterior face — the abstraction of heat by the electric cur- 

 rent, and 'proportional to that current =LI, where I is the intensity 

 of the current and L a constant ; then there will be equilibrium when 



k(t+t f ) + hl=Jct+~ («-*')+ 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 resistance in the pile is very small compared with that in 

 the rest of the circuit, we shall increase the intensity of the current 

 by every reduction of the cross section of the elements of the ther- 

 mopile. 



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 sufficient size to catch all the radiant heat required to be 

 measured, with that of a pile of n pairs, each of equal dimensions 

 with those of the single pair, the area of face being the same in the 

 two cases. 



By increasing the number of elements from one to n, we increase 

 the number of solderings in that proportion ; consequently the ave- 

 rage amount of heat reaching any soldering is - as great as that 



reaching the soldering of the single pair ; therefore, if the same 

 percentage of the total heat be lost by conduction, the total electro- 

 motive force is the same in the two cases. But inasmuch as the 

 total cross section of metal to conduct the heat away from the an- 

 terior face is n times as great in the pile as in the pair, and the 

 resistance of the pile is n times as great as that of the pair, the 

 pile will be inferior in power to the pair, unless these two causes of 

 inferiority are counterbalanced by the loss due to the greater average 

 distance to the soldering from the points where the heat reaches 

 the face, in the case of the pair, than that of the pile of n pairs. 



The experiments already referred to were made with three differ- 

 ent thermoelectric pairs. These consisted each of a pair of bars of 



