IN RAIUFIED OASES 



one Ml it i batter than that adopted by Professor Reynolds, while I admit 

 I hi* method fe efficient to establish the existence of the phenomena, though 

 not to afford an estimate of their amount. 



Tbe method which I have adopted throughout is a purely statistical one. 

 It eonaider* the mean values of certain functions of the velocities within a 

 givw element of the medium, but it never attempts to trace the motion of a 

 molecule, not even so for as to estimate the length of its mean path. Hence 

 11 the * equations are expressed in the forms of the differential calculus, in 

 which the phenomena at a given place are connected with the space variations 

 of certain quantities at that place, but in which no quantity appears which 

 explicitly involves the condition of things at a finite distance from that place. 



The particular functions of the velocities which are here considered are 

 thoM of one, two, and three dimensions. These are sufficient to determine 

 approximately the principal phenomena in a gas which is not very highly 

 rarined, and in which the space-variations within distances comparable to X are 



not very great 



The same method, however, can be extended to functions of higher degrees, 

 and by a sufficient number of such functions any distribution of velocities, 

 however abnormal, may be expressed. The labour of such an approximation is 

 considerably diminished by the use of the method of spherical harmonics as 

 indicated in the note to Section I. of the paper. 



On the Conditions to be Satisfied by a Gas at the Surface of a Solid Body. 



As a first hypothesis, let us suppose the surface of the body to be a 

 perfectly elastic smooth fixed surface, having the apparent shape of the solid, 

 without any minute asperities. 



In this case, every molecule which strikes the surface will have the normal 

 component of its velocity reversed, while the other components will not be 

 altered by impact. 



The rebounding molecules will therefore move as if they had come from 

 an imaginary portion of gas occupying the space really filled by the solid, and 

 such that the motion of every molecule close to the surface is the optical 

 reflection in that surface of the motion of a molecule of the real gas. 



In this case we may speak of the rebounding molecules close to the surface 

 as constituting the reflected gas. All directed properties of the incident gas 



