( 685 ) 
THE HEATIlSra COEFFICIENTS OF EHEOSTATS AND THE 
CALCULATION OF EESISTANCES FOR CURRENTS 
OF SHORT AND MODERATE DURATIONS. 
By H. Bohle, Cape Town. 
(Read October 20, 1915.) 
Stefan's Law of Radiation. — Stefan's law of radition for black or 
grey bodies in vacuum reads — 
Pk=AS (8/-d,^) . . . . .1. 
where Sc is the radiatinpf surface, 8^ and 8^, the absolute temperatures 
of heated body and surroundings respectively, and A a coefficient which 
varies with the nature of the surface and the surrounding media. 
When 8y differs little from 8„ i. e. when the temperature rise s small, 
we may write 
Pk^4AS cV(6/-36)=A'ScS .... 2. 
where 8=d - S^=: temperature size. 
When is very great, 8^ may be neglected, and 
Pr^AScV • 3. 
For electrical apparatus these formulae hold very approximately only, 
equation 2 being the one which is generally used for machines and rheostats. 
The coefficient A', which may be called the emissivity, or the heat radiated 
per unit cooling surface for a temperature difference of one degree, is thereby 
assumed constant and independent of the temperature. 
Test results indicate that A' is by no means a constant quantity if 
formula 2 is used. Where the air is stationary, formula 1 is more correct, 
{. e. the power radiated varies still with a high power of the temperature. 
For pure radiation the ratios of the powers radiated according to equations 
1 and 2 are given in fig. 1, for temperatures up to 500° C, which clearly 
indicate that the use of formula 2 may give results which are altogether 
unreliable, as soon as the temperature rise exceeds a few degrees, whenever 
the power radiated varies with a high power of the temperature. 
When a current of I amperes flows through a resistance of R ohms the 
heat generated in unit time is 
47 
