Closing Years of the Nineteenth Centwy. 459* 



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 con- 

 duction is accompanied by the transport of metallic ions. 



The ideas of Thomson, Kiecke, and Drude were combined by 

 Lorentz* in an investigation which, as it is the most complete r 

 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 t 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 ^-components 

 of velocity lie between u and u + du, whose ^-components of 

 velocity lie between v and v + dv, and whose ^-components of 

 velocity lie between w and w + dw, is 



/ (u t 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 ^-component of velocity will at the 

 end of the interval be increased by an amount e Edtjm^ if ra 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 



