HALL. — THERMAL AND ELECTRICAL EFFECTS IN SOFT IRON. 25 



K being the specific resistance at 0° C, y the temperature coefficient of 

 resistance, t a the mean temperature of the L cm. of a, above 0° C, and 

 t h the corresponding mean for {3. 



Let the specific thermal conductivity of the iron be k ai at the temper- 

 ature t ai , k a „ at the temperature t Ui , k bl at t bl and k bi at t^. 



Let q a be the Thomson effect heat in a x a 2 ; that is, the amount of heat 

 generated per second in a t a 2 in excess of the amount accounted for by 

 Joule's law. Let q b be the Thomson effect heat in 6 X b 2 ; that is, the 

 amount by which the heat generated per second in b x b 2 falls short of the 

 amount given by Joule's law. 



Let the temperature gradient at any point in either bar be called g, with 

 the subscript approximate to the point. The current is to be expressed 

 in amperes, the resistance in ohms, and the heat in calories. 



The heat carried out by conduction at a x must exceed the heat 

 brought in by conduction at a 2 by the amount generated between a x and 

 a 2 . Hence 



SQca^ga, - K9a 2 ) = qa + 0.2387 PK{\ +yt a )L+S, 

 or 



(1) q a = S(k ai9(li - ka iffa2 ) - 0.2387 i 2 K (I + y t a ) L -j- S. 

 For the other bar we have 



(2) q h = - S(k h g bl - h 2 g>,) + °-2387 t 2 K{\ + y t b )Z + S. 

 From (1) and (2) we get 



(3) q — qa ^ qb = %S [(*«, g, h - k bl g bl ) + (h h g h - h at g ch )] 



- 0.1 194 i 2 Ky (t a —t b )L+ S. 



As the difference of temperature between any part of a and the cor- 

 responding part of (3 is likely to be small, always much less than one 

 degree in the experiments to be described, and as the temperature co- 

 efficient of k is small, we may provisionally write in place of (3) 



(4) q = $ Sib (g Ch - g h ) + h (gs 3 - #0] - 0.1 lUPKy (t a -t b )L~ S, 



where £ x is a mean between k <h and k bi , while k 2 is a mean between k a 

 and ki >2 . The magnitude of the error made in the substitution of (4) for 

 (3) will be considered later. It is not very important. 



Of the quantities in the second member of (4), S, L, K, i, and y are easily 

 measured; k x and k 2 can, from previous study of the thermal conduc- 



