248 
PROFESSOR CLERK MAXWELL ON STRESSES IN RAR1FIED 
If there are no external forces such as gravity, then one solution of the equations is 
u—v=w— 0, constant, 
and if the boundary conditions are such that this solution is consistent with them, it 
will become the actual solution as soon as the initial motions, if any exist, have 
subsided. This will be the case if no slipping is possible between the gas and solid 
bodies in contact with it. 
But if such slipping is possible, then wherever in the above solution there is a 
tangential stress in the gas at the surface of a solid or liquid, there cannot he equi¬ 
librium, but the gas will begin to slide over the surface till the velocity of sliding has 
produced a frictional resistance equal and opposite to the tangential stress. When 
this is the case the motion may become steady. I have not, however, attempted to 
enter into the calculation of the state of steady motion. 
[I have recently applied the method of spherical harmonics, as described in the 
notes to sections (1) and (5), to carrying the approximations two orders higher. I 
expected that this would have involved the calculation of two new quantities, namely, 
the rates of decay of spherical harmonics of the fourth and sixth orders, but I found 
that, to the order of approximation required, all harmonics of the fourth and sixth 
orders may be neglected, so that the rate of decay of harmonics of the second order, 
the time-modulus of which is /x -Fp, determines the rate of decay of all functions of less 
than 6 dimensions. 
The equations of motion, as here given (equation 55) contain the second derivatives 
of u, v, to, with respect to the coordinates, with the coefficient /x. I find that in 
the more approximate expression there is a term containing the fourth derivatives of 
u, v, iv, with the coefficient /x 3 -App. 
The equations of motion also contain the third derivatives of 0 with the coefficient 
/x'-Fpd. Besides these terms, there is another set consisting of the fifth derivatives 
of 6 with the coefficient /rf-r-/rp(9. 
It appears from the investigation that the condition of the successful use of this 
cl d 
method of approximation is that Z— should be small, where — denotes differentiation 
with respect to a line drawn in any direction. In other words, the properties of the 
medium must not be sensibly different at points within a distance of each other, com¬ 
parable with the “ mean free path” of a molecule.—Note added June, 1879.] 
