426 Mr. G. J. Stoney on the Penetration 0/ 



(which, in the simple case we have supposed, will be a plane 

 parallel to A), there will fly the same number of molecules 

 per second in both directions, across an element 8S of this sur- 

 face, the momentum of the two processions which pass through 

 SS in a second will be the same, and their kinetic energy also 

 will be the same. Their number will be the same ; for other- 

 wise the density would be still undergoing change, and we 

 have supposed that the period of adjustment is over. Their 

 momentum will be the same, because the pressure is every- 

 w^here constant ; and their kinetic energy is the same, because 

 there is no transfer of heat across S. 



4. Hence the change of temperature and density in passing 

 along hoc, an element of the normal to SS, must be such as to 

 secure these three conditions. In investigating the law of 

 this variation, we have to take into account : — 



P, the pressure everywhere through the gas ; 



Oj the temperature (measured from absolute zero) on the 

 isothermal surface S ; 



p, the density of the gas on the isothermal surface S ; 



oc, the distance of S from A ; and 



G, a quantity which changes from one gas to another, but 

 is almost constant in each gas, within a wide range of 

 temperature and pressure. 



When the gas and its tension are given, G and P are con- 

 stants ; and p is a known function of G, P, and 6, Hence only 

 two of the foregoing quantities are independent — suppose 6 



OLSC 



and x^ instead of which we may use -y^ and 6. It is easy 



to see, by taking particular instances, that -7^ and Q will 



remain independent of one another, if only two of the condi- 

 tions in § 3 need to be fulfilled ; but if all three have to be 

 fulfilled, we find by experiment that a definite Crookes's layer 

 is formed, and that, therefore, in each gas and at each pressure 



dec 



-T^ is a definite function of Q. In other w^ords, 



g=t(^,G,P), («) 



in which G and P are constants. This furnishes by integra- 

 tion an equation of the form 



x= const. +^(^, G, P), . . . . ifi) 



which represents the law by which the temperature must 

 change across the layer. What we learn from this investiga- 

 tion is, that, besides the uniform distribution of a gas with the 



