124 BELL SYSTEM TECHNICAL JOURNAL 



actual values of log k' should be experimentally in error to an extent 

 sufficient to account for its deviation from the value given by Equation 

 6. Hence Equation 2, is at best only an approximation to a correct 

 expression for dh/dt. 



Of course, Equation 2 is actually quite a fair approximation to an 

 expression for dh/dt, as is evident in comparing the differences A log k' 

 with the differences among the values of log k' themselves. In fact, 

 if values of log k' are plotted against log W for a constant value of 

 V, or against log V for a constant value of W, quite good straight 

 lines are obtained, and the inaccuracy of the approximation can 

 only be brought out by an analysis such as is here given. Whether 

 this inaccuracy is due to the approximations employed in the theo- 

 retical development of Equation 4, or to an error in the basic assump- 

 tion that T ^ \_dv/dx'J-'", cannot, of course, be determined. It is, 

 however, of interest to see if the values of a and c are related to that 

 of h in the manner required by Equation 4. For b = 16.156 (the 

 value of b observed). Equation 4 requires that a = 5.462 and 

 c = 8.693. The observed values of a and c are 1.656 and 6.875 

 respectively. It remains to determine if these differences may be 

 accidental, provided the values of log k' differ from those given by 

 Equation 6 as greatly as observed. Following Fisher (page 133), 

 the probability of a divergence between observed and calculated values 

 ofcofc] — C2 is given by entering Table IV of the text with w = n' — 3, 

 where n' is the number of cases (5), and with / given by: 



IZ - {Z + aY - cX)J nay" 



n — 3 ?i^ax^(Xy^ — i^xyy 



This corresponds to a probability between 0.05 and 0.10, which 

 indicates that the divergence may be due to chance, though it is more 

 likely to represent a real difference. Similarly the probability of 

 obtaining the observed difference ai — Oo is given from the table by 

 entering with n = 2 and with / given by: 



t = _ ^^I"^ = 5.85. 



IZ - (Z -\- aY - cX)J naj" 



n — 3 ti^aj^ay^ — {YlxyY 



This corresponds to a probability between 0.02 and 0.05, which 

 suggests more strongly than does the other case that the divergence is 

 real. For so few observations, however, the distribution theory on 

 which Fisher's method is based cannot give a definite indication when 



