84 PROCEEDINGS OF THE AMERICAN ACADEMY. 



These equations do not involve the (A) electrons, and they must hold 

 irrespective of these electrons, if we have, as we still suppose, condi- 

 tions very close indeed to those of equilibrium. But as soon as we 

 begin to consider actual flow, however slow it may be, we must take 

 into account the (A) electrons and the amount of heat energy they 

 absorb from the metal. 



The Thomson Effect: — Let us consider, as before, what happens at 

 and between two equipotential and isothermal surfaces, separated by a 

 distance dl and a temperature interval (IT. If we let A a represent, as 

 before, the part of the specific electric conductivity which depends on 

 the (A) electrons, A 6 that part which depends on the (B) electrons, 

 and A* = K a + K^, we shall have (K a -4- A) as the (A) fraction of 

 the current and (A fc -5- A) as the (B) fraction. 



Let the ratio (A a -r- A) be called (1 — x), and (K b -r- A) be called 

 x, just as in a mixture of water and water vapor the proportion of the 

 latter is commonly called x. In the passage of electrons from the 

 bound state to the (B) state we have, in fact, a process similar to the 

 evaporation of water, and this analogy is helpful in the present argu- 

 ment. 



x 

 The total energy of - electrons (B) at the temperature T is made up 



x 3 x 



of the kinetic energy - X ^RT, the pv potential energy -AT, and 



x 

 the attraction-repulsion potential energy - F. 



The total energy of electrons (^4) at the same temperature 



is made up of kinetic energy, which I shall assume for the present to 

 be the same 19 as that of an equal number of (B) electrons, namely 



i ,r 3 . 1 — .r 



— X ^RT; of attraction-repulsion potential energy, - - F; and 



l—x 



of another quantity of potential energy, - - $ due to the attraction 



of the particular metallic atoms to which the (A) electrons individually 

 belong. $ is a negative quantity ; that is, (—<£>) is the amount of poten- 

 tial energy which an electron gains in being freed from an atom. 

 Let$ = k v T*, where k v and -k are constants, h v being negative and ir 



19 The (B) electrons may be regarded as individuals which have dropped out 

 of the (A) class by going astray from the short path leading from one atom to 

 the next atom. 



