president's address — SECTION A. 30 



possible to get anything to correspond to the variation of fx 

 with the amount of the magnetic induction. 



Now I come to another class of theories, analogues of the 

 foregoing — creatures of the imagination merely, but useful in 

 that they furnish us with a simple and easily conceived 

 picture of the other I'eal theories. The simplest is that in 

 which we picture to ourselves a certain medium of jjecuHar 

 character. It is a frictionless incompressible hquid, and, 

 unlike any known li([uid, each unit of vohime of it is so 

 tethered to its position in space that if it be displaced a force 

 of restitution is called into play proportional to the displace- 

 ment. The imagery is curious, but simple enough to think 

 of. It is easy to see that in such a medium the displacement 



\ dV 



d at any point is equal to — ^ x —t—, where P is the 



pressure at that point, and E is the elasticity per unit volume. 

 So d corresponds to electric or magnetic displacement, E 



corresponds to -j^^ or — , and P to electric or magnetic 



d P 



potentials (V or ii). The differential —j— corresponds, of 



course, to E or H. Since the medium is incompressible, 



we have A^ P = : and at any surface separating from one 



another, parts of the medium of different elasticities d on 



^ dV \ dV 



one side=« on the other side, ov-^rr • -^ V^rr- • -,- = <'. 



hi^ du-^ x!i2 du.^ 



Boundary conditions like those of the other theories may be 

 supposed to exist here also : we may suppose P or d known 

 at every point of the boundaries. If, however, we know that 

 P is constant over any bounding surface, it is sufficient to 

 know this value of P or the average value of d. 



Here, then, is the same mathematical problem as before ; 

 and we have in this " strain theory " an exact analogue of the 

 electric and magnetic theories, so far as the data just written 

 down apply to the theories in common. Even the peculiari- 

 ties of these theories are capable of simple rept-esentation. 

 Hysteresis, we may consider, as caused by a certain friction 

 in the displacement of the medium, so that the displacement 

 under force may be hastened by vibration, and the removal 

 of the force does not necessitate the undoing of the strain. 

 In just the same way, tapping a tilted board will hasten the 

 descent of a block resting upon it, or hasten the ascent if 

 the block is under a force tending to raise it. Als©, we iway 



