16 
Davies.—Some Electric and Elastic Analogies . 
The fact of electrical oscillations in such cases has been sufficiently 
well established experimently by Feddersen, Food, Lodge, Trowbridge 
and many others. Hertz and Lodge have traced out in great detail 
the dissipation of the energy of these vibrations, both in electro-mag¬ 
netic waves and heating of the dielectric. The whole electro-magnetic 
theory of light assumes that when these oscillations are sufficiently 
rapid and the wave lengths correspondingly short, they are capable of 
affecting the retina and of producing chemical change. As we see from 
the expression above given for the time of an oscillation, such rapid 
vibrations and short wave lengths imply very small electro-static ca¬ 
pacity and self inductance, such only as we could look for among mole¬ 
cular or atomic structures. 
The next analogy has reference to the self induction of rods, and the 
magnetic forces within them when they are of other forms than circular. 
It is well known that Coulomb made great use of the torsion balance 
in his establishment of the law of the inverse square of the distance as the 
fundamental law of force between electrical charges mutually acting on 
each other, and also between magnet poles. He appears to have consid¬ 
ered in connection with this work the theory of the torsion of elastic 
threads, of hair, silk, and metals. He likewise appears to have been the 
first who established with reference to them, the simple differential 
equation 
where Mk* is the moment of inertia of the cylindrical thread round its 
axis, and 11 the torsional rigidity. The solution of this equation gives 
the time of an oscillation. This time can also be observed. Thus the 
assumption that the force of torsion is proportional to 0 can be tested 
experimentally. This is found to be the case for small arcs, and we have 
here the fundamental equation so much used in all magnetic and elec¬ 
tric as well as general physical work. 
For circular cylinders (solid or hollow) every straight line “ is turned 
round the axis through such an angle as to give a uniform rate of twist 
(r) equal to the applied couple divided by the product of the moment of 
inertia of the circular area into the rigidity (n) of the substance,” i. e.’ 
the moment of the twisting couple, 
(where d6 is an element of area), and r is rate of twist. 
Now Saint Venant has shown that in all but strictly circular cylinders 
(solid or hollow) there is a warping of each cross section in the vertical 
direction whose amount depends upon the position of the point rela¬ 
tively to the axis and the amount of total twist given to the prism. 
