SOME PHYSICAL PROPERTIES OF WIPING SOLDERS 123 



vary significantly from those given by Equation 2 above, or by: 



log ^' = log i^ + a log IF - c log V. (6) 



For this purpose there were determined values of log K, a and c for 

 which the sum of the squares of the differences of observed and 

 calculated values of log k' are a minimum, the components of devia- 

 tion due to variations in values of log W and log V being neglected, as 

 these are known to a higher order of accuracy than are values of log k'. 

 Following the usual procedure for calculating partial regression coeffi- 

 cients, the following computations were performed, writing Zi, F,-, and 

 Xi for corresponding values of log k', log IV and log V: 



" n n 



T.Z, EF, Y.X, 



Z = '-^^— , Y = '^^— , X = '■^^— , 



E (Zi - zy E ( Yi -Yf E {Xi - xy 



^=1 9 1=1 , < = 1 



» 0"} •" — . (Tx = 



n n n 



1=1 



Y.xy = E XiYi - nXY, Zyz = E YiZ, - vYZ, 



' ' t=i 



Ezx = E ZiXi - nZX, 



i=i 



logX = Z - aF-f cX. 



The values of a, c, and log K thus obtained are included in Table 

 IV, together with values headed A log k', which are the differences 

 between the values of log k' listed in Table IV and those calculated 

 from Equation 6, using the listed values a, c, and log K. To deter- 

 mine whether these differences are significant or not, the probability 

 of obtaining a value in error to that extent may be calculated for each 

 run from the value {S') of the standard deviation of log k' estimated 

 by the method given by Fisher (loc. cit.). These probabilities are 

 evaluated from Table IV of the text cited, taking n as n' - 3, w^here 

 n' is the number of pairs of values of log dh/dt and log // used to 

 evaluate log k', and taking / as: 



_ A log k'^|n' 

 t J, 



The values of t thus computed range from 5.4 to 16.7 and correspond 

 in every case to a probability less than 0.01, so that not one of the 



