( 448 ) 
. @ly 
yee 
m 
Also, 
dA dh 
== (and) ——— (0) 
Av (a 
so that (21) becomes 
4 cl. le 
p= Sy. 
hm 
Multiplying this by e, we find an expression for the electric current 
per unit area, and in order to find the coefficient of conductivity, 
we must finally divide by /. The result is 
Oe ee te ien Hee 23 
dhm a: 
or, taking into account the relations (18) and (14) and denoting by 
€ 
u a velocity whose square is the mean square Oh of the velocity of 
L 
2 Neu 
6 == —_ . —— o A ° . ° e (24) 
Bh gd 
Drupr gives the value 
heat-motion, 
§ 9. The determination of the coefficient of conductivity for heat, 
which we shall call & (expressing quantities of heat in mechanical 
units) is rather more difficult. This is due to the circumstance that, 
if initially N—O, the equation (21) implies the existence of an 
electric current in a bar whose parts are unequally heated. This 
current will produce a certain distribution of electric charges and 
will ultimately cease if the metal is surrounded on all sides by non- 
conductors. The final state will be reached when the difference of 
potential and the electric force arising from the charges have increased 
to such a degree that everywhere » = 0. 
Since it is this final state, with which one has to do in experiments 
on the conduction of heat, we shall calculate the flux of heat in the 
assumption that it has been established. 
In the first place we have then by (21), putting » = 0, 
A A dh 
2h AX = 2 
da Ch de 
and next, substituting this in (22) and again using the formula (14), 
