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PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
lienee we have, from equation (79), 
dL . _ 
~dt + P - * 
the ordinary electrical equation if the specific resistance of the substance equals Q/aw. 
From this expression for the specific resistance we see that if Q remains constant, or 
nearly constant, the resistance will vary inversely as n, that is, the resistance will 
be inversely proportional to the number of discharges in unit time. Now, since 
the discharges are caused by the breaking up of the molecular aggregations, the 
number of discharges in unit time will be greater, the greater the ease with which 
the molecular aggregations break up. The formation and breaking up of these 
molecular aggregations in a solid would play in it very much the same part as 
that played by the collision between the molecules in a gas. But, the greater the 
number of collisions in unit time, the greater the rapidity with which inequalities in 
the kinetic energy, momentum, &c., in the different parts of a gas disappear, so that 
we may conclude that, the greater the ease with which molecular aggregations are 
broken up in a solid, the more rapidly will the inequalities in the kinetic energy 
disappear, that is, the better conductor of heat the solid will be. Thus the expres¬ 
sion for the resistance of a solid conductor contains one term which is inversely 
proportional to the conductivity for heat of the substance. Hence we can understand 
why those metals which are good conductors of electricity are also good conductors of 
heat. 
The term 
- IQ (f\ + 0 s + h% 
which we have introduced into the expression for T — V of unit volume of the 
conductor, corresponds to the term 
| (P + + V) 
in the expression for the potential energy of unit volume of a dielectric in which the 
electric displacement is f, g, h. Thus we may look on Q as equal to 47 t/K, where K is 
the specific inductive capacity of the conductor. The rapid way the resistance 
increases with the temperature for metals shows that of the term — TQ (f ~ + g~ + h~) 
the great part must in this case be due to the kinetic energy. Let us suppose that 
in the kinetic energy we have the term 
— \ad (p + r + h 2 ), 
where 0 is proportional to the absolute temperature, and in the potential energy the 
term 
P U ~ + + h 2 ); 
(SO) 
