On the Thermodynamic Efficiency of the Thermopile. 361 



tion. Tt is evident that one extreme wave is accelerated and the 

 other retarded by \ X, and that the phases are now distributed 

 uniformly over a complete cycle. The result is therefore 

 darkness; and the effect of the rotation has been to shift the 

 image through half the width of the central bright band 

 which, with accompanying fringes, is the representative in 

 the Image of a mathematical line *. Such a motion would 

 be visible (with proper arrangements as to magnifying), but 

 the limits of revolving power are being approached. It is to 

 be noticed that the conclusion is independent of the focal 

 length of the mirror and of the employment of a telescope. 

 Provided of course that the full width of the mirror is really 

 used, a motion of its vertical edges through J A, may be made 

 evident. 



A comparison with the method by direct observation of a 

 pointer is now easy ; for, as has been proved by the re- 

 searches of Abbe and Helmholtz, a motion of J \ may be 

 rendered evident in a very similar degree by direct applica- 

 tion of a perfect microscope to the moving object. If, there- 

 fore, we suppose the length of the pointer to be equal to the 

 half-width of the mirror, the two methods are optically upon 

 a level. It is needless to say that it would be easy to give 

 the pointer a great advantage in this respect ; but the direct 

 use of the microscope would often be interfered with by 

 motions in the line of sight, making it impossible to preserve 

 the focus. And besides this, it is sometimes necessary for the 

 observer to remain at a distance. 



XLIII. On the Thermodynamic Efficiency of the Thermopile. 

 By Lord Kayleigh, F.R.S^ 



DURING the last few years the thoughts of many elec- 

 tricians have turned to the question of the possibility 

 of replacing the dynamo by some development of the thermo- 

 pile ; and it is, I believe, pretty generally recognized that the 

 difficulty in the way is the too free passage of heat by ordi- 

 nary conduction from the hot to the cold junction. The 

 matter may perhaps be placed in a clearer light by an actual 

 calculation, accompanied by a rough numerical estimate 

 applicable to the case of German silver and iron. 



If t, t Q denote the temperatures of the hot and cold junc- 

 tions respectively, e the electromotive force per degree Centi- 

 grade, the whole electromotive force for n pairs in series will 



* See u Investigations in Optics,'' Phil. Mag. 1879-1830. 

 f Communicated by the Author. 



