240 PROFESSOR E. G. COKER ON 
curve showing the relation of the thermal change to the stress is, however, influenced 
by losses due to conduction and radiation, and hence it is necessary to correct for these 
in order to obtain a correct relation. If it be allowed that the lag of the galvanometer — 
is not a factor in this correction, the required result may be obtained as follows. Let 
6, be the diminution of temperature per second due to the application of a stress 
increasing uniformly with the time, and let @ be the actual difference of temperature 
at any time ¢ from the commencement of the application of stress, then 0<6)t, since 
there is a loss due to conduction and radiation, depending on the difference of 
temperature between the specimen and surrounding bodies. The loss due to this 
cause can be very approximately determined by observation of the subsequent readings 
when the application of stress has ceased, and it was found in all cases that the loss 
was very accurately proportional to the first power of the difference of temperature. 
In an interval of time dt, therefore, the diminution of temperature for a tension specimen — 
under uniformly applied stress will be 6dt—k0-dt, where & is a constant to be 
determined. The actual decrease of temperature in the time dt is wea 
Hence 
oe 
Ft kb=% (1), 
an integrating factor of which is obviously «™. 
Hence 
. &'= 6, [Mdt-+c 
= So c 
or 0=6,/k+ce™. 
To determine the constant c we have the condition that 0 is zero at the commencement 
of the application of the load; hence c= —9,/k, and we have 
6 =6,/ke(1 — e-*) 
or 6, = k/(1 — e~™) 
k6 itt cate 
6,t= (Gee ~ ete.) 
Now the denominator can be expanded provided the value of the variable ¢ is such 
that the expression in the bracket remains convergent, and it is evident if kt/2<1 ie. 
t<’/k this condition will be satisfied. Hence we obtain as a sufficiently near 
approximation 
1 a 
af= (1 +520) 
and since k is a very small quantity, this reduces to 
on! kt 
6,t= 0(1 + =) . 
Now 6,¢ is the actual decrement of temperature D, due to the stress up to the time t, 
