would have amounted to over a kilogramme. The weight of each of the three cylinders, however, showed no measurable change; from which it appeared unlikely that metallic conduction is accompanied by the transport of metallic ions.
The ideas of Thomson, Riecke, and Drude were combined by Lorentz[1] in an investigation which, as it is the most complete, will here be given as the representative of all of them.
It is supposed that the atoms of the metal are fixed, and that in the interstices between them a large number of resinous electrons are in rapid motion. The mutual collisions of the electrons are disregarded, so that their collisions with the fixed atoms alone come under consideration; these are regarded as analogous to collisions between moving and fixed elastic spheres.
The flow of heat and electricity in the metal is supposed to take place in a direction parallel to the axis of x, so that the metal is in the same condition at all points of any plane perpendicular to this direction; and the flow is supposed to be steady, so that the state of the system is independent of the time.
Consider a slab of thickness dx and of unit area; and suppose that the number of electrons in this slab whose x-components of velocity lie between u and u + du, whose y-components of velocity lie between v and v + du, and whose z-components of velocity lie between w and w + du, is
f(u, v, w, x) dx du dv dw.
One of these electrons, supposing it to escape collision, will in the interval of time dt travel from (x, y, z) to (x + u dt, y + vdt, z + wdt): and its x-component of velocity will at the end of the interval be increased by an amount eEdt/m, if m and e denote its mass and charge, and E denotes the electric force. Suppose that the number of electrons lost to this group by collisions in the interval dt is a dx du dv dw dt, and that the
- ↑ Amsterdam Proceedings (English edition) vii (1904-1905), pp. 438, 585, 684
