DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
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magnetic coordinates z, for if it were, a current y l would produce a magnetic force 
proportional to y 1 2 , and thus the force would not be reversed if the direction of the 
current were reversed; as no such forces have been observed we conclude that {yy} is 
not a function of z. It cannot be a function of the temperature coordinates u because 
these are kinosthenic coordinates. 
The question as to whether {yy} is a function of the elastic coordinates w or not is 
one where the experimental evidence is somewhat conflicting. Both AYertheim 
(Ann. de Chun, et de Phys. [3], 12, p. 160, or Wiedemann’s ‘ Lehre von der Elek- 
tricitat,’ vol. ii., p. 403) and Tomlinson (Phil. Trans., 1882) have observed that the 
elasticity of a wire is less when a current is passing along the wire than when it is not, 
and that this diminution in the elasticity is not due to the heat generated by the 
current. Streintz (Wien. Ber. [2], 67, p. 323, or Wiedemann’s ‘ Lehre von der 
Elektricitat,’ vol. ii., p. 404), on the other hand, was unable to detect any such effect. 
Supposing that the passage of a current of electricity along a wire does alter the 
elasticity of it there must be terms in the kinetic energy of the form 
2/ 3 {A(e+/+5r) 3 +B(e 3 H-/ 3 +/—2e/— 2ge—2fg+a*+b 2 +c 2 )} . . (21) 
where e, f g, a, b, c denote as before the six strains; comparing this expression with 
that for the potential energy of a strained solid, and remembering that this energy is 
kinetic and not potential, we see that the rigidity is diminished by B y 2 and the bulk 
modulus by (A—B/3)y 3 . Let us consider what electrical effects this term will indicate ; 
since half the coefficient of y 1 in the expression for the kinetic energy is the coefficient 
of self induction of the circuit conveying the current y : we see that if this term exists 
the coefficient of self-induction of a circuit will be increased by straining the wire 
which forms the circuit; it wall be increased because Wertheim’s experiments show 
that the elasticity was diminished by the passage of a current, and therefore that B is 
positive; so that if a current be flowing along a wire it will be momentarily diminished 
if the wire be twisted. If the coefficients of induction are altered by straining the 
wire the force between two currents or two elements of current will be altered by 
straining the wires along which they flow, even although the intensity of the currents 
is kept constant; this is contrary to Ampere’s hypothesis that the force between two 
elements of a circuit conveying a current depends upon nothing but the strength of 
the currents and the position of the elements. If this term exists we shall see if we 
make a numerical calculation that the alteration in the coefficient of self-induction of a 
coil due to the straining of the wire of which it is made is likely to be much more 
easily detected than the corresponding alteration in the elasticity produced by the 
passage of a current of electricity. For using the C.G.S. system of units the 
coefficients of elasticity are quantities of the order 10 u ; thus, taking copper as an 
example, Young’s modulus is L234 X 10 13 and the coefficient of rigidity is 4‘47 X 10 11 , 
so that we shall be under the mark if we take 10 11 as the value of a coefficient of 
2 t 2 
