432 Mr. W. Sutherland on the 
Drude, and Thomson treat the conduction of heat by electrons 
as practically identical with that by molecules of a perfect 
gas. In the present theory, although the breaking up and 
renewal of doublets causes a free movement of electrons in all 
directions, these movements go on not according to the laws 
of molecules in a gas, but according to the laws of electric 
eyrostats. Just as electric conduction is due to directed 
vibrations of the gyrostats in the direction of electric force, 
thermal conduction is due to thermal! vibrations of the gyro- 
stats maintained equally in all directions. The mean effect 
of a collision between two atoms is to leave each with the 
same kinetic energy but differently directed. The axis of 
rotation of each atom is also changed in direction. Thus, 
there must be set up couples of action and reaction between 
atom and electric gyrostat, just as if the gyrostat were a 
material one revolving round an axis with “bearings in the 
atom. As the kinetic energy of rotation of the atom remains 
on the average constant and only changes the direction of 
its axis, the moment of each couple must on the average be 
proportional to the kinetic energy of rotation, and therefore 
‘to the kinetic energy of translation of the atom. Thus in 
place of the electric couple esX we have a thermal couple 
which we may write Amv’, A being a constant. In place of 
the angular amplitude esX/Cw® of the electric vibration of the 
gyrostat we have Amv?/Cw? for the angular amplitude of the 
thermal vibration of the gyrostat. For the mean velocity of 
each electron due to the thermal vibration we have 
Amv’s/2Co’r. < . sn 
Now each electron which is passed on from one molecule to 
another advances a distance 2a. If there isa fall of tempera 
ture in any direction, one-third of the movements of electrons 
may be assumed to take place only in that direction, the rest 
perpendicularly to it. An electron moves from a place where 
it is in thermal equilibrium with an atom having kinetic 
energy mv’/2 to another place where it comes into thermal 
pauea with anatom having energy mv*/2 + 2ad(mv?/2)/da, 
x being in the direction of motion. The electron carries 
eae such fraction of the energy 2ad(mv*/2)/dz as its own 
energy is of mv?/2. Call this fraction 7, ‘Then the current 
of heat across unit area perpendicular to « is 
26 (Q2aA (mv*s/Cor) f° ey a 
Now mv*/2=a0, where a is generally taken to be constant, 
but we shall see that for the metals it is not quite so. 
