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PROFESSOR CLERK MAXWELL OX STRESSES IX RARIFIED 
cipal phenomena in a gas which is not very highly ratified, 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 he 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 con¬ 
stituting the reflected gas. All directed properties of the incident gas are reflected, 
or, as Professor Listing might say, perverted in the reflected gas ; that is to say, the 
properties of the incident and the reflected gas are symmetrical with respect to the 
tangent plane of the surface. 
The incident and reflected gas together constitute the actual gas close to the sur¬ 
face. The actual gas, therefore, cannot exert any stress on the surface, except in the 
direction of the normal, for the oblique components of stress in the incident and 
reflected gas will destroy one another. 
Since gases can actually exert oblique stress against real surfaces, such surfaces 
cannot be represented as perfectly reflecting surfaces. 
If a molecule, whose velocity is given in direction and magnitude, but whose line of 
motion is not given in position, strikes a fixed elastic sphere, its velocity after rebound 
may with equal probability be in any direction. 
Consider, therefore, a stratum in which fixed elastic spheres are placed so far apart 
from one another that any one sphere is not to any sensible extent protected by any 
other sphere from the impact of molecules, and let the stratum be so deep that no 
molecule can pass through it without striking one or more of the spheres, and let this 
stratum of fixed spheres be spread over the surface of the solid we have been con¬ 
sidering, then every molecule which comes from the gas towards the surface must 
strike one or more of the spheres, after which all directions of its velocity become 
equally probable. 
When, at last, it leaves the stratum of spheres and returns into the gas, its velocity 
