PROPERTIES OF MATTER ESI THE GASEOUS STATF. 
803 
The neighbourhood of a solid surface. 
83. In this case we have by the corollary to theorem (II.) 
So-(Q)=S(/(Q)+s{ 1-^/mnJe'j^+m^+n^So-XQ) • • • ( 49 ) 
or as in equation (39) 
<r(Q)=A+s( [^’{l — f{lmn)ef] (ig-f-mg-fn !)SA sin 0d6d(f> . . . (50) 
J o V ct tXy ct y cL & j 
In this case it is clear that the coefficients which correspond to L l3 L 3 , &c., Art. 82, 
will be functions of the position of the point with respect to the solid surface, and will 
depend on the value of f(lmn). f(lmn) will obviously depend to some extent on the 
action between the molecules and the solid surface. It appears, however, that when 
the solid surface extends in all directions in its own plane to distances which are great 
as compared with s, and the variation Q is perpendicular to this plane, the result of 
the integration of equation (50) is the same as that of equation (39). For taking the 
solid surface parallel to xy 
o- / (Q) = o-(Q) + o-(Q), 
and by symmetry, since Q varies only in the direction 2 , for two opposite groups such 
as a, b 
o-(Q) + o-(Q) = o-'(Q) + o-'(Q) 
=A+B.(51) 
Therefore the integral of the last term of equation (50) for A will have the same 
value but the opposite sign as for B. Hence since the solid surface can only be on 
one side of the element, say the side A C G E, fig. 10, Art. 66, and - will be infinite 
for the group B, or for this group equation 50 is identical with equation 39, therefore 
for either of the opposite groups the results of the integration of (50) are the same as 
of (39). 
Near the edge of a solid surface, or when Q varies in some direction parallel to the 
surface, equation (51) no longer holds good, and then the coefficients corresponding to 
L 1; L 3 , &c., will depend on the position of the element with respect to the solid surface 
and on the action between the molecules and the solid surface. 
In dealing with such cases two courses were open—the one was to try and find 
some form for f(lmn) which would satisfy the equations, tbe other course, and that 
which is here adopted, is to introduce arbitrary functions s 1 , s. z , in place of s, and 
subsequently to determine the form of Sj, s 3 , so as to satisfy the experimental results. 
