334 
MR. J. J. THOMSON ON SOME APPLICATIONS OF 
since y is constant along the wire, the expression may be written 
so that at each point of the rod there is a force tending to increase a equal to 
From the form of this expression we see that the force should increase with y, which 
increases indefinitely with the time the current has been flowing, so that theoretically 
this expression, and therefore the stress, should increase indefinitely with the time; in 
this case, however, other considerations will come in to modify this result. If we 
imagine that the strain is constant along one of the wires the expression (79) becomes 
%/( e ) 
eve 
els 3 
(80) 
but by the theory of the conduction of heat cl' 2 0/ds 2 varies as dO/dt if there is no loss 
by radiation, so that in this case the force per unit length of the wire varies as 
yf(4 .(«> 
so that if we have a current flowing through a wire, one half of which is heated to 
redness and if necessary strained, if the temperature of the wire be allowed to 
equalise itself by conduction there will be forces along the wire tending either to 
stretch or compress it, and if the parts which are losing heat are compressed, the 
parts where the temperature is rising will be extended. 
§ 9. Effects of Heat upon Magnetism. 
The magnetic properties of bodies are very much affected by heat, thus a very high 
temperature seems to destroy altogether both the magnetic susceptibility and the 
power of retaining magnetism. This shows that {uu} the type of the coefficient of 
the squares of the differential coefficient of the us must involve the coordinates which 
fix the magnetic configuration ; these coordinates are of two kinds : one, which is of a 
geometrical type, we shall denote as before by y, the other, which is a kinosthenic 
coordinate, will, as before, be denoted by £, and the momentum corresponding to it by 
£; the coefficient of u 2 cannot contain the kinosthenic coordinate, because if it did it 
would not be of the dimensions of kinetic energy, it must therefore contain the 
geometrical coordinate y only. Suppose that in the expression for the kinetic energy 
there is, using the same notation as before, a term of the form 
