744 
MR. A. McAULAT ON THE MATHEMATICAL 
Under the same circumstances (?' a function of H' and d' only), equation (29) gives 
<j>' = Yd' ( ) d V7/2 - Sd' ( d VT + d')/2 
-VB'( )H78tt - SrH'/2 + (mo — 1 )H' 2 / 8 tt .... (29a). 
Hence, with the electromagnetic system of units for which /x 0 = 1, 
</>' - <^7.(296, 316), 
in which it should be noticed there is no necessity to assume that the complete form 
of x is — SK'R/lT/2, nor is it assumed, as in equation (28c?, 326) that V has the 
particular form given in equation (3), § 59. 
To sum up, of the two equations (28) and (29), (28) agrees more closely with 
Maxwell as to the electrostatic part, and (29) more closely as to the electro¬ 
magnetic part. On the whole, equation (29) agrees more closely than (28).* 
Of course, the normal stress [eq. (30)] we have adopted for solids is by no means 
the same as Maxwell’s, except for non-magnetic bodies whose specific inductive 
capacities are the same as for a vacuum. But this does not prevent our normal 
stress explaining all that Maxwell’s stress explains, and, indeed, from the remarks 
at the beginning of last section, it is now evident that for all useful purposes either 
the one stress or the other will serve equally well. 
70. We have now compared the results of the present theory with all Maxwell’s 
results contained in equations (5) to (17), § 60, above, except (16). Except for 
equations (12), (13), the agreement is exact, and I think it may now be claimed that 
what the present theory gives instead of equation (12), agrees, as well as (12), with 
known facts, and what it gives instead of (13) agrees better than (13). 
Equation (16) itself is obvious enough since it merely asserts that H' has a potential 
when there are no currents in the field. But it suggests another question—does the 
present theory lead to the ordinary mathematical theory of electromagnetism ? It 
can be easily shown to do so. The mechanical results when expressed in terms of 
IT and I' have just been shown to result in the same forces and moments on conductors 
and magnets regarded as wholes, as does Maxwell’s stress. These are all the 
mechanical demands of the ordinary theory. Equation (19), § 61, shows that the 
relations between the whole magnetic moment per unit volume, the permanent 
magnetic moment per unit volume, and the magnetic force at the point, may on the 
present theory, be regarded as the same as in the ordinary theory. Only one other 
* Notwithstanding this, and the fact that I have in this paper called the stress of equation (29) the 
normal stress, I think equation (28) is to he preferred, partly because of the greater simplicity of the 
assumptions which lead to it, and partly because of the greater simplicity of the electrostatical results 
flowing from it. 
