MATHEMATICAL PHYSICS. 105 
‘ticular, the theory did not lead to Fresnel’s wave-surface, 
which Glazebrook’s experiments showed to be a very close 
approximation to the truth. So Lord Kelvin stepped in 
’ with his theory of a contractile ether—a medium that offers 
no resistance to compression, and, indeed, is such chat it 
tends to move in the same direction as a displacement within 
it. Such a medium has the advantage of getting rid of 
the pressural wave (for if there is no resistance to pressure 
there can be no such wave), and it leads to a wave-surface 
in crystals that is approximately that of Fresnel. Then 
we have the revival in recent times of the method employed 
as long ago as 1839 by MacCullagh. He started out with 
the remark that the success of a dynamical “ explanation ”’ 
of optical phenomena must depend on the proper choice of a 
functiom representing the potential energy of the ether. If 
this be properly chosen, all the rest will follow by the aid 
of the principle of least action. He arrived at the well- 
known expression for the energy in terms of the rotation 
of the elements of the elastic medium, and added—“ Having 
arrived at this value, we may now take it for the starting- 
point of our theory, and dismiss the assumptions by which 
we were conducted to it.’ His method is more philosophical 
than the more pretentious one that is usually followed, and 
the special form of his energy-function has the great merit 
of leading to the same equations as those required by the 
electromagnetic theory. Thus we have gradually modified 
our “explanation,” until we have a medium before our 
minds that enables us to group together a vast number of 
optical and electrical phenomena. Finally, in order to 
make our theory still more comprehensive, we have found 
it necessary to consider the possibility of point-singularities 
(electrons) in the ether. With this addition to the older 
theory, we hope to be able to group together a still larger 
number of facts than before. Some even have faith that 
this idea will enable us to remove mountains of difficulties, 
and ‘ explain”’ the whole worid; but there is clearly little 
real explanation here. 
After all that has been said, I hope it will be admitted 
that physical science does not include within its scope the 
explanation of phenomena. The great end it has in view 
is to sum up everything in one generalisation, and we have 
already more than a glimpse of the end. How, chen, does 
the mathematical physicist set out towards this goal? We 
start with three categories, or fundamenta! ideas—space, 
time, and mass. _ It is useless trying to get behind these, 
and we can never resolve space into time or mass into space. 
