1870.] On the Construction of Thermopiles. 553 



small, and this circumstance appears to favour the view that a slow surface- 

 reduction is in progress. " 



XII. " On the Values of the Integrals J* Q„, Q n -, dp, Q n) Q n ' being 



Laplace's Coefficients of the Orders n, n, with an application 

 to the Theory of Radiation." By the Hon J. W. Strutt, 

 Fellow of Trinity College, Cambridge. Communicated by W, 

 Spottiswoode, F.R.S. Received May 17, 1870. 



(Abstract.) 



These integrals present themselves in calculations dealing with arbitrary 

 functions on the surface of a sphere which vary discontinuously in passing 

 from one hemisphere to the other. "When n, ri are both even or both odd, 

 the values of the integrals may be immediately inferred from known 

 theorems in which the integration extends from — 1 to +1> or over the 

 whole sphere ; otherwise a special method is necessary. In the present 

 paper a function of two variables is investigated, which, when expanded, 

 has for coefficients the quantities in question. As an example of the 

 method, the problem is taken of a uniform conducting sphere exposed to 

 the heat proceeding from a radiant point. It will appear at once that 

 the heat received by any element of the surface is expressed by different 

 analytical functions on the two hemispheres — a source of discontinuity 

 which renders necessary a special treatment of the problem. The solu- 

 tion is afterwards generalized to meet the case of a sphere exposed to any 

 kind of radiation from a distance. 



One remarkable result not confined to the sphere is, that the effect of 

 a radiation which is expressed by one or more harmonic terms of odd 

 order is altogether nil, with the single exception of the term of the first 

 order. 



XIII. " Note on the Construction of Thermopiles." By the Earl of 



Rosse, F.R.S. Received June 14, 1870. 



Although in the measurement of small quantities of radiant heat by 

 means of the thermopile much may be done towards increasing the sensi- 

 bility of the apparatus by carefully adjusting the galvanometer and ren- 

 dering the needle as nearly astatic as possible, there must necessarily be 

 some limit to this, and it therefore appears desirable that the principles on 

 which thermopiles of great sensibility can be constructed should also be 

 carefully attended to. 



With the view of obtaining a pair of thermopiles of greater sensibility 

 and of more equal power than I had been able to procure ready made, I 

 made a few experiments with various forms of that instrument, and I was 

 led to the conclusion (one which might have been foreseen) that the 



