694 
Transactions of the Royal Society of South Africa. 
temp, rise if there were no cooling - actual temp. rise_ a 
actual temp, rise "~ b 
as function of ~ . The temperature rise which neglects cooling is given by 
the tangent to the curve, hence with ^ known, we take from the figure the 
t 8 
corresponding ratio — , and then from the first curve the value g-, whence 8^ 
is determined. 
The accuracy of this method depends upon the correct drawing of the 
tangent. The latter can in most cases not be drawn from the initial 
temperature rises, unless the heat capacity is very small. This is clearly 
shown in fig. 6, in which the initial rate is given by the dotted line on the 
left, whereas the correct tangent lies far to the right, for reasons explained 
previously. The tangent must therefore be guessed as correctly as possible, 
which is not very difiicult if one draws a complete set of tangents starting 
where the experiment was interrupted and moving towards the origin, thus 
enveloping the heating curve with tangents. Once the tangent in the origin 
is known, the construction of the whole heating curve is simple, and clearly 
indicated in fig. 7, which is self-explanatory. 
The experimental values of t„ usually lie between 0 and about 50, accord- 
ing to the size and construction of the resistance. For the grid rheostat the 
calculated value was 12 minutes, the experimental one 17 and 19 minutes for 
maximum temperatures of 290° and 210° C. respectively. 
For a known maximum rise the time constant follows from — 
t 
t„ = ^ 
so that only the rise S in the time t has to be noticed. 
