34 PROCEEDINGS OP THE AMERICAN ACADEMY. 



5 = 0.785, 



L = 16, 



l\ = k,. above = 0.1543, 



k, = k h " =0.1461, 

 9a, — 9b — &c last given = 0.03363, 

 9 bt -9a\=-^H " " -0.03733, 

 i = 25.15, 



iT= 11365 x 10" 9 , 



y = 0.005, 

 t a — t b = 0.21, 



we get, as the first approximation to the value of the Thomson effect 

 heat, 



(5) q = 0.002037 + 0.002142 - 0.000018. 



In this evaluation of q we have taken full account of the temperature 

 gradients; but we have, in using a mean k l for the cold couples and a 

 mean k 2 for the hot couples, ignored the fact that the thermal conduc- 

 tivity is slightly less at any point in the warmer bar than at the corre- 

 sponding point in the cooler bar. In fact, if there were no difference of 

 gradient at the cold couples, the difference of temperature, about 0.055° , 

 between the bars at the section c would, with the temperature gradient 

 4.6, which is, approximately, the general gradient along each bar, send 

 about 0.000020 calorie per second more along the cooler bar than along 

 the other, and accordingly the first term in the second member of equa- 

 tion (5) should be diminished by half this amount. At the h section the 

 excess of temperature of the warmer bar is apparently about 0.145 ° , 

 and accordingly, if there were no difference of gradient in the two bars 

 at this section, the cooler would here transmit about 0.000056 calorie 

 per second more than the warmer. Therefore the second term of the 

 second member of equation (5) should be increased by half this amount 

 The result is, 



(6) q = 0.002027 + 0.002170 — 0.000018 = 0.004179. 



This would be the final value of q, if there were no correction for loss 

 of heat by lateral flow from the bars a and fS. Unfortunately such a 

 correction is necessary and is large. It is estimated by the following 

 method : When both ends of both bars have been for several hours in boil- 

 ing water, the couples, K K', NN', MM 1 , and P P' indicate a perma- 



