THEORY OP ELECTROMAGNETISM. 
741 
type of stress. It by no means explains all the known facts. It does explain 
satisfactorily such known mechanical actions of real conductors—conveying currents 
and bearing charges—and magnets on one another as are of the nature of apparent 
actions at a distance. It does not at all explain the many known mechanical actions 
of one part of a conductor or magnet on another part which can be tested only by 
observing the (small) strains resulting. In other words, conductors and magnets are 
found to behave mechanically, as they would if Maxwell’s supposed stress acted 
outside them, but not as if this stress existed internally. It need not therefore be 
matter for surprise if, on the present theory, what would appear as the most suitable 
stress to regard as normal should differ from Maxwell’s. It is only necessary that 
just outside conductors and magnets it should be identical with Maxwell’s. 
To see what on the present theory should be regarded as a normal type we must 
discuss, from the physical point of view, the results of §§ 54, <55 above. As far as I 
can see (but this is, of course, largely a matter for personal judgment) on the present 
theory we should recognize two normal types of stress—one for fluids and one for 
solids. The reason is that we may assume fluids to be magnetically and electrically 
isotropic, and that fluids are subject to indefinitely large strains. On the other hand, 
solids, even if magnetically and electrically isotropic when unstrained, cannot be 
considered so when strained and, moreover, their strains cannot exceed a certain — 
usually very small—amount without the form of l being permanently altered. 
For bodies which are electrically isotropic, however large their strain, it is needless 
to say that we must regard the Lagrangian function as given in terms of the dashed 
letters. For such bodies, y of equation (19) § 54 is zero. [For let a", f3" . . . be the 
vectors of which l" is an explicit function. Since the body is isotropic the value of 
l" must remain unaltered if we rotate a", /3" . . . all to the same extent round the 
same axis. In particular, if we increase a", (3" . . . by Yea", Ye/3", . . . where e is an 
infinitely small vector, l" must remain unaltered, i.e., the increment — 2Sea" a V'T' = 0. 
Since e is arbitrary, it follows that tYcc'y'T = 0]. By equation (20) § 54 above, 
we see that the assumption that [<£'] = 0 amounts to assuming that the Lagrangian 
function of unit volume of the body when strained, however largely, is the same as the 
Lagrangian function of unit volume of the body when unstrained. By equation (29), 
§ 55, we see that the assumption fj = 0 amounts to assuming that that part of the 
Lagrangian function which causes the body to differ from vacuum, and which is 
contributed by a given mass of the body, is unaffected by strain. Hence from 
equations (21), § 54, and (30), § 55, we have 
For an isotropic body, of which the Lagrangian function per unit ”j 
volume is unaffected by strain I 
2f = - {2Z' + S3 (t'.VT + a-’,VI')} 
+ 2V{r'( ),VT-a'( )yi'} J 
