( 442 ) 
the number of electrons which, at the time {+ dé, satisfy the condi- 
tions that they themselves shall be found in the element dS’ at 
the point (e+ Sdt.y+ydt,2+6d2) and their velocity-points in 
the element d2’ at the point (§-+ Xdt,y-+ Ydi,é+Zdt). Hence, 
since dS’ = dS and dd’ = da, 
f(&n § 2 Ys 2 t) + (6 — a) dt= 
=f (§ + Xdt, 4 + Vdt,$ + Zdt, x + §dt, y + dt, 2 + Sdt, t + dt), 
or 
òf òf 
6b—-az=—X+ 
Of i Often Oe ONE 
5 On 
st SF 3 2 Ze 
En aes 
This is the equation we wanted to establish *). 
(7) 
Ger 
It is easily seen that, in calculating the numbers of collisions 
adSdadt and 6dSdidt, we need not trouble ourselves about 
the state of the metal varying from one point to another; we may 
therefore understand by adàdt the decrease, and by bdadt the 
increase which the group of electrons characterized by dà would 
undergo, if we had to do with a piece of metal occupying a unit 
of volume and being, in all its parts, in the state that exists in the 
element dS. 
§ 4. We are now prepared to calculate the values of a and 5. 
Let Rk be the sum of the radii of an atom and an electron, 7 the 
number of atoms in unit space, and let us in the first place con- 
fine ourselves to encounters of a definite kind. I shall suppose that 
in these the line joining the centres falls within a cone of the infinitely 
small solid angle dw. 
Taking as axis of this cone one of the straight lines that may be 
drawn in it, and denoting by & the acute angle between the axis 
and the direction of motion of the group (6), I find for the number 
of electrons in this group undergoing an encounter of the kind chosen, 
DL (Sy ACO ONC CLD 5 ny 5 (sh) 
per unit time, a result which leads to the value 
DNA IAN EP oo oe co. 0 os (OO) 
if we take into account a// encounters, whatever be the direction of 
the line joining the centres. 
Now, if we ascribe to a metallic atom so large a mass, that it 
is not sensibly put in motion by an electron flying against it, the 
velocity of the latter after the encounter is given by a very simple 
rule. We have only to decompose the initial velocity into one 
1) See Lorentz, Les équations du mouvement des gaz et la propagation du 
son suivant la théorie cinétique des gaz, Arch. néerl. 16, p. 9. 
