[coKER A m'kergow] THERMAL CHANGE TO TENSION 9 



found in all cases that it was very closely proportional to tlie 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 



0^ dt — k dt 

 where k is some constant to be determined, the actual decrease of tem- 



perature in the time dt is . dt hence 



^- dt = e^ dt — kd dt 

 dt " 



or ^ + A-^ = e, (2) 

 at 



An integrating factor of equation 2 is obviously kt therefore 



£kf = Oof «*' dt + c 



= do f'--* / A 4- c 

 or e = 8^ / k + c £-kt (3) 



To determine the constant c we have the condition that 8 is zero 

 when t = hence c = — 8^ / k and we have 



8^ = k 8 I I — £-fct 



and if we neglect expressions involving k-, since k is always a small 

 quantity, we easily arrive at a sufficiently approximate equation of the 

 form 



8„ t= 8 (\ -\-kt/2,) 



provided f < 2 / k the latter condition being necessary to ensure con- 

 vergency in expanding (1 — £-^')-i 



Now, 0^ t is the actual decrement of temperature D^ due to the 

 stress up to the time t, and 6 is the observed value Dy, Hence the 

 actual observations must be corrected by adding thereto a quantity 

 D Jit I 2. 



The value of k is easily determined in each case by the second part 

 of the curve, which is found experimentally to be always of the ex- 

 ponential type, showing that the assumption of the loss being proper- 



