242 
PROFESSOR CLERK MAXWELL OX STRESSES IX RA HI FI El) 
F = 3E 2 0 2 (l + 2a 2 ) 1 
S =3K»0*a/3 I 
^=B 2 0 2 (l+a 2 +/3 2 ) | 
| 2 T7^=E 2 ^y J 
(5.) Rates of Decay of these Mean Values. 
If any term of Q in equation (20) contains symbols belonging to one group alone 
of the molecules, the corresponding term of the integral may be found from the above 
table, but if it contains symbols belonging to both groups we must consider the 
sextuple integral (20). But we shall not find it necessary to do this for terms of 
not more than three dimensions, for in these, if both groups of symbols occur, the index 
of one of them must be odd, and the integral vanishes. 
We thus find from equations (3), (4), (5), (6), and (7) 
(31) 
|a/3 = — ^a/3. ..(32) 
=^( — 2a 3 -ba/3 2 + a/).(33) 
= - -(a 3 — 8 a/3 2 + ay 2 ) 
b /j. 
(34) 
Py 
(35) 
[Any rational homogeneous function of £ rj £ is either a solid harmonic, or a solid 
harmonic multiplied by a positive integral power of (£ 2 +>r + £ 2 ), or may be expressed 
as the sum of a number of terms of these forms. 
If we express any one of these terms as a function of u, v, w, V and the angular 
coordinates of Y, we can determine the rate of change of each of the spherical har¬ 
monics of the angular coordinates. 
If we then transform the expression back to its original form as a function of 
£i, Uj, £ 1; rj. 2 , £ 2 , and if we add the corresponding functions for both molecules, we 
shall obtain an expression for the rate of change of the original function. 
Thus among the terms of two dimensions we have the five conjugate solid harmonics 
