122 BELL SYSTEM TECHNICAL JOURNAL 



from the calculated values of log dh/dt evaluated as recommended 

 by Fisher, 1^ page 118. To determine in each case whether these 

 deviations are significant, they may be compared with those that 

 might be expected on the basis of the estimated precision of measure- 

 ment. As the value of b is approximately 16 in each case, an error of 

 0.004 in log h corresponds to an error of 0.064 in log dh/dt. The 

 values of 5 computed are all smaller than this amount, indicating that 

 the differences between observed values of log dh/dt and those cal- 

 culated from Equation 1 are due to experimental variations. 



The next question to be determined is whether the differences 

 observed in the values of b given by the different runs are significant. 

 In Table IV is included the mean value b of the values of b, together 

 with the estimated standard deviation of the individual values of b 

 from their true mean, taken as given by: 



n — \ 



This estimate of the standard deviation of the actual values of b may 

 be compared with estimates of the standard deviation of b made for 

 each run on the basis of the variability of the data. An expression 

 for such an estimate is given by Fisher (loc. cit.) as: 



2 '^^ 



Values of ah as given by this last expression are included in Table 

 IV. These are larger than the value (0.906) of o-j', computed as 

 described, and it is therefore evident that the data are consistent with 

 the hypothesis that b is constant throughout the series of runs. 



To obtain fairer estimates of log k for the subsequent computation, 

 the mean value of b, b, was taken as giving the slope of the straight 

 line of Equation 5. On this basis the values of log k are given by: 



log k' = Y - bX. 



While the values of 5 are given by: 



i:{Y,-\ogk' -bXiY 



/2 i=l 



S" = 



n — \ 



Values of log k' and S' are given in Table IV. The next step in the 

 computation is to determine if the values of log k thus determined 

 1* R. A. Fisher, "Statistical Methods for Research Workers," London (1925). 



