690 Transactions of the Royal Society of South Africa. 
Fig. 4 gives the coefficients for asbestos-woven rheostats, forming sheets, 
about f in. apart, the area of the sheets being taken for the evaluation 
of A". 
Fig. 5 holds for a grid resistance, the cross section of the conductor being 
9x5 mms.^ The grids were closely packed, the distance between the con- 
ductors being about equal to their thickness. As was to be expected, the 
emission of heat was rather poor, and for high temperatures very irregular 
for different parts of the grid. The curves give average values. 
In all experiments the rheostats were quite open at the top, so that the 
hot air could get away. When the asbestos -woven resistance and the grids 
were turned over, so that the top was shielded by an iron plate, the tempera- 
ture rose much higher, showing that a generalisation of values for heating 
coefficients is absurd. For every particular type data should be obtained 
experimentally, and the position and manner of fixing should be clearly 
stated. 
The heating coefficient A', being a function of the temperature, may be 
expressed by an equation. For fig. 2 we get 
On the whole, it will be more convenient to use equation 10, and to take 
A', or better ^„ from the curves. 
A 
~, indicates the size of the cooling surface per watt lost for 1° C. rise. 
Eheostats for Loads of Short Duration. — The time in which a 
resistance reaches its final temperature for a given load depends upon the 
heat capacity and the ventilation. The freely suspended coils used for 
fig. 2 required 2^ minutes, when wound on the porcelain rods 45 minutes, 
while the cast-iron grid rheostat took 92 minutes. This time does not vary 
much with the load, but the time constant does, as A' increases with the 
temperature. It will thus be impossible to say offhand what constitutes a 
load of short duration. For freely suspended coils of thin wire even a 
minute is a load of long duration, as its temperature will then be near the 
maximum, whereas for the same wire wound on porcelain the cooling effect 
during this time is negligible. Oil-insulated rheostats do not reach their 
steady temperature until hours have passed. 
The initial rise is expressed by 
A'= 0-0026S°-i^« 
whence — 
Compared with Stefan's law we get 
PR=ASc(Sf ^— af'*) where A is now constant 
and Sj- and are absolute temperatures. 
