548 
MK, 0. AY. RICHARDSON ON THE ELECTRICAL CONDUCTIVITY 
where is the discontinuity in the potential, and Cq is the saturation current per 
unit area. 
C^alculating in this way we find that for platinum at d=1900 E=8XI0^ 
ergs/centim. sec. The value of S^ggo i® ^ much larger quantity, viz., 2'75 X 10^ 
ergs/centim. sec. The largest experimental values of E were obtained with carbon. 
Since the greatest value of the saturation current attained was Cg = Do ampere 
= 4'5 X 10° electrostatic units per square centimetre and §(!> = 6 volts, we have the 
rate at which energy is lost by the wire =9 X 10'^ ergs/centim. sec. The 
temperature corresponding to this current was not measured, but was certainly 
greater than 2000° absolute. The energy radiated from an absolutely black body at 
2000° absolute would have been 3'36 X 10° ergs/centim. sec. 
We see then that at all the temperatures at which experiments were made the 
loss of energy due to the escape of the corpuscles is much less than that due to the 
emission of ordinary electromagnetic radiation ; on the other hand, it increases much 
more rapidly with the temperature, so that, in the case of carbon at any rate, it 
would become first equal to, and finally great compared with, the electromagnetic 
radiation, at temperatures not much above 2000° C. It must not be forgotten that 
for this calculation the hot conductor is supposed to be placed in a vacuum and 
surrounded by an electric field which removes the ions ; otherwise all the ions diffuse 
back to the metal and there is no loss of eiiergy due to this cause. 
In all these experiments we are a long way from the region where an appreciable 
fraction of the total number of ions which strike tlie surface of the conductor pass 
through. This is easily seen if we calculate the value of the saturation current per 
unit area on the supposition that every corpuscle which hits the surface escapes. Let 
us take n = 10^^ as a probalde maximum for the number of corpuscles in a cubic 
centimetre of, say, caribou ; then, at 2730° absolute ^nu = 3 X 10'®, so that the 
saturation current would be 18 X UD® electrostatic units or 6X10° amperes per square 
centimetre. As the largest current which has been yet obtained is 2'0 amperes per 
square centimetre, it is evident that we are still a long way from the limit. This 
calculation seems to indicate that the region on the current temperature diagram 
when the current begins to be proportional to the square root of the absolute 
temperature is much higher than any temperature which can be reached in the 
ordinary way. 
The magnitude of the currents which have been obtained with low voltages 
indicate that a vacuum bounded by a hot conductor is, at any rate under certain 
circumstances, an extremely good conductor of electricity. In fact, it seems probable 
that such a vacuum is capable of becoming the best conductor that can possibly be 
obtained. The conductivity of metals is limited by the shortness of the mean free 
path of the ions, whereas the mean free path of a corpuscle in an atmosphere of 
corpuscles is probably very laige. All tliat is necessary, them tore, to produce a big 
current is to supply the ions quickly enough at the hot surface, that is, to raise the 
