328 
MR. J. J. THOMSON ON SOME APPLICATIONS OP 
which we established equation (53), we find that if 81 be the change in the intensity 
of magnetisation when the twist in the bar is increased by an angle So, and h the 
coefficient of magnetisation, then 
sr=- 2 «n^ 8 «.(57) 
Now since a soft iron wire untwists when the magnetisation is increased, dco/dl 3 is 
negative, so that SI and ct have the same sign if h be positive; hence we see that the 
magnetisation is increased by twisting the rod: this agrees with Wiedemann’s result. 
He found, however, that when the twist exceeded a certain value the magnetisation 
was diminished instead of being increased by twisting. Equation (57) shows that in 
this case dco/dl 2 must be positive, or when the original twist is great the bar will no 
longer be untwisted when it is magnetised but twisted. Professor G. Wiedemann’s 
experiments show that this is the case/" There are many other relations between 
magnetism and torsion which can be investigated in this way, but we have no space 
to consider them here. 
§ 7. We must now go on to consider the part of the kinetic energy which depends 
upon the temperature, and which we denote by { uu ) id. We considered before a way 
of fixing the temperature by means of coordinates : we supposed that it was fixed by the 
coordinates u x , u. 2 , . . . u n . Since the temperature depends upon the whole of the terms 
involving u, and not in a special way upon any one term in particular, we see that 
if one of the u’s enters into any term it must be because the whole of that part of the 
kinetic energy which depends upon the differential coefficients of the u’s enters into 
the term. Let us, as before, call this part of the energy ©, then if v v v 2 > v «> • • • 
be the momenta of the type u lf u 2 , . . . u„, we have by equation (8) 
e= H_a!_ + _^_ + ... 
2 1K, {u 2 , u°}' 
As © is the energy in unit of volume the total amount of energy 
of this kind is 
f[ 
©dxdydz 
(58) 
As the consideration of the terms of the tyj>e { uu}u 2 is somewhat difficult, in order 
to simplify it we shall neglect all the effects due to radiation, which is equivalent to 
supposing that the bodies are incapable of radiating or absorbing heat. 
If this is so { uu } cannot be a function of the geometrical coordinates x, for if 
it were it would be possible to alter the temperature of a body by merely moving it 
about. 
* ‘ Die Lebre von cler Elektricitat.’ Dritter Band. S. 688. 
