354 RICHARDSON— DYNAMICAL EFFECTS OF [April 22, 



the average kinetic energy should be the same as the average kinetic 

 energy of a molecule of any gas at the temperature of the enclosure. 

 In fact the laws of the kinetic theory of gases can be applied 

 without change to the atmospheres of electrons ; and the above asser- 

 tions are simply statements of a theorem in the kinetic theory of 

 gases called, after its discoverers, the Maxwell-Boltzmann Law. 

 According to this law if a large number of molecules are selected 

 at random out of any gas the proportion of them which have speeds 

 lying between certain assigned values let us say // and u' is a certain 

 definite function of n and u'. The value of this function, which in 

 addition to it and u' depends only upon the temperature of the gas 

 and the mass of its molecules, was first deduced by Maxwell. Max- 

 well's deduction of the value of this function, though sufficiently con- 

 vincing to those who are familiar with the methods of mathematical 

 physics, was, neverthless, a highly abstract piece of reasoning; and 

 it has been impossible up to the present to make anything in the 

 nature of a direct test of it by experiment on gases. With the 

 atmospheres of electrons we are, however, able to do a great deal 

 more than we could with a gas made up of uncharged molecules. By 

 placing them in a suitable electric field we can bring forces to bear 

 on each individual electron which are enormous compared with the 

 forces exerted on a molecule by the earth's gravitational field. For 

 example if the electrons are being emitted from a heated flat plate 

 we can place another flat surface a little in front and charge it up, 

 so that the electric field tends to drive the ions back into the surface 

 at which they originated. Under these circumstances only those 

 electrons will be able to cross from one plate to the other if their 

 kinetic energy is greater than a certain value depending on the elec- 

 tric field between the plates ; thus the current that gets across will be 

 a measure of the number of electrons emitted whose kinetic energy 

 exceeds a known value. By experiments of this kind, and others 

 based on similar principles, we have succeeded in determining the 

 law of distribution of speed among the individual electrons which 

 are emitted. It is found to agree in every particular with that pre- 

 dicted by ^Maxwell for the case of a gas whose temperature is the 

 same as that of the metal emitting the electrons and whose molecular 

 weight is equal to the mass of an electron. In particular the average 



