DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
523 
then 
Q = o,0 -f- b, 
and the specific resistance cr equals 
ad -j- b 
na 
Now n will probably depend on the temperature, and will probably in most cases 
increase as it increases, as it seems likely that the molecular aggregations will split up 
more easily at high than at low temperatures. Thus there are two influences which, 
when the temperature increases, oppose each other in the effect they produce upon 
the resistance. On the one hand there is a tendency for the resistance to increase in 
consequence of the greater change in the value of T — Y produced by a given electric 
displacement, and on the other hand there is a tendency for the conductivity to 
increase in consequence of the molecular aggregations breaking up with greater ease, 
and so increasing the number of discharges which take place in unit time. In the 
case of metals the first effect seems to be the most important, as the resistance of 
these substances increases with the temperature. In the case of electrolytes the 
second seems the most important, as the conductivity of these substances increases 
with the temperature. Anything which increases the complexity of the molecular 
aggregations will increase the importance of the second effect relatively to the first, 
hence we can understand why it is that alloys have so much smaller temperature 
coefficients than pure metals, as we should expect the molecular aggregations to be 
more complex in alloys than in pure metals, and therefore the second effect, which 
tends to make the resistance diminish as the temperature increases, is relatively more 
important. 
It is evident that, if the view which we have taken of the electric discharge be 
correct, the specific inductive capacity of metals must alter more quickly with the 
temperature than the specific inductive capacities of dielectrics, as experiment lias 
shown that these vary only slowly with the temperature. 
The consideration of the term 
-iQCT + ^ + n 
which occurs in T — V, leads to many interesting results, of which we shall proceed to 
give one or two examples. 
If we take the axis of x parallel to the electric displacement, and write ana for Q, 
where a is the specific resistance, we may write this term as 
Now the experiments of Sir W. Thomson and Mr. Tomlinson show that the resis¬ 
tance of metals is affected by strain, so that ana must be a function of the strain. 
3x2 
