714 Proceedings of Royal Society of Edinburgh. [sess. 
for platinum and zinc when paired with any of the three former 
metals had to he multiplied by 5 to bring it up to that observed, 
seeming to show that some factor acted with 5 times the influence 
on zinc and platinum as on silver, copper and aluminium; but 
when gold is paired with either zinc or platinum the multiplier is only 
2J, being in the same proportion as the multiplier of the former 
metal with silver, etc., as that of platinum and zinc with them. 
And so of all the others. The observed resistances quoted are the 
relative resistances of wires of chemically pure substances of the 
same length and sectional area at 0° Cent. I believe that the 
resistances for wires of the same length and weight can be found 
on the same lines if allowance be made for the difference in surface 
area for radiation of heat. I only tried one example, viz., silver 
and aluminium, and the result was very close to the observed 
resistance. My powers of calculation are very limited, and so also 
is the time I can spare. 
39. It may not be amiss to put down in succinct form the 
rationale of the above rule, as it may not be perfectly obvious to 
everybody ; indeed, I am rather in danger of forgetting it myself, 
and did forget it for a time, and had some difficulty in recalling it, 
so I will put it down once for all for the general benefit. Well, 
then, 1st, the reason for the resistance to be inversely as the squares 
of the cube roots of the atomic weights is that the mean radii (see 
pars. 6 and 35) of atoms of the same atomic volume are proportional 
to the cube roots of their atomic weights ; * and since the molecules 
of the lighter element at the outward limit of their swing must 
occupy the same space as those of the heavier, if their mean radii 
are small, the greater must be the amplitude of vibration ; and as 
the energy of vibration is proportional to the square of the 
amplitude, the heat radiated must be in this proportion, and the 
conduction inversely, as the heat radiated. Or resistance will be 
proportional to radiation of heat. 
2nd. The reason for resistance being directly as the melting 
points is that the higher these latter the broader or deeper must be 
the bonds uniting the molecules, with a consequent greater radiation 
of heat per vibration. And 3rd, that it should be directly as the 
* Assuming, of course, that when atoms have the same atomic volume their 
particles move with the same speed. 
