163 
1889-90.] Sir William Thomson on Ohmic Resistance. 
small as 80 ; on the other hand, for moderately strong currents and 
correspondingly high electromotive forces, we may have sr greater 
than 3000.* We shall take it as 300 merely by way of example 
and illustration, hut as the permeability varies enormously with the 
amount of the magnetising force, and in a manner desperately com- 
plicated by magnetic retentiveness, hysteresis according to Ewing’s 
designation, no accurate mathematical investigation is practicable 
with only our present knowledge of the requisite data for the 
diffusion of electric currents through an iron or steel conductor. 
Taking for iron or steel 37 = 300, and, as above, a = ' 7, b = 7, we 
find A.= 1/130 of a, or 1/187 of a centimetre. Now, because A. is 
so small a fraction as 1/130 of the radius of the rod, we see that 
the current-density at the surface (or surface-temperature in the 
thermal analogue) drops nearly to zero, while there is still but a 
relatively small diminution of current-density (or temperature in 
the thermal analogue) farther in from the surface than a distance of 
1/10 of the radius. Hence, for the roughly approximate investiga- 
tion with which we must be content, we may be satisfied with the 
very simplifying supposition of X = 0. 
If we take 10,000 c.g.s. (or square centimetres per second) as 
the resistivity f of steel or iron, we must divide this by 300 x 4 ir 
to find the diffusivity for electric current (thermal diffusivity, or 
conductivity divided by thermal capacity of unit volume, in the 
thermal analogue), which therefore is 2*7 square centimetres per 
second. This is only about 12 times the thermal diffusivity of 
heat in iron (which is ‘225 of a square centimetre per second). 
Hence in 1/4300 of a second (if A = 0), the state of things as 
regards falling off of the strength of current towards the final zero, 
at different distances from the surface, would be that represented 
by number 0T curve of my diagram of laminar diffusion.]; That 
is to say, the diffusion curve would be curve number 1 with its 
* Rowland for one specimen of iron found the magnetic susceptibility as 
high as 3595 for magnetising force 1’317 (see Phil. Mag., Aug. 1873). 
t This seems to me a much better word than specific resistance to denote 
the resistance per centimetre of length of a bar of a square centimetre of cross- 
section of any substance. The resistivity of Lord Armstrong’s steel bar I have 
found by measurement to be 14,000 c.g.s. 
+ See British Association Report, Bath, 1888, p. 571 ; or Yol. III. of my 
collected Papers, to be published in May. 
