SOME PHYSICAL PROPERTIES OF WIPING SOLDERS 121 



shown in Fig. 1. There were thus obtained for each run a set of six 

 or seven pairs of values of log dh/dt vs. log h. 



The first question to be determined is whether for any run these 

 pairs of values agree with a relation of the form of Equation 1, which 

 can be written: 



log -^ = log k + b log //. (5) 



As sample height readings appear to be reproducible in such tests 

 to within about one per cent, the standard deviation of values of log h 

 about their correct values may be estimated as rather less than 0.004 

 (log 1.01). The time readings being more accurate, values of log dh/dt 

 should vary with a standard deviation of like magnitude. If the data 

 can be fitted by an equation of the form of Equation 5, estimates of 

 k and b can be obtained by minimizing the sum of the squares of the 

 deviations of the experimental points from the straight line, these 

 deviations being measured along normals to the line. As for these 

 data b is large, these normal deviations are nearly equal to their 

 horizontal components, the deviations of the observed from the 

 calculated values of log //, and hence the sum of the squares of the 

 latter were minimized. Writing Xi for values of log // and Fj for 

 corresponding values of log dh/dt, the following computations were 

 carried out for each run (w being the number of pairs of values em- 

 ployed in each case) : 



n n 



E Xi Z Yi 



Gx 



n n 



n _ n 



E {Xi-xy E 



i = \ , i = \{Yi-Y) 



n 



^ ^ na^ iQ^k = Y -bX, 



n 



E Xi Yi - 71 X Y 

 i = 1 



n 



E (Fv-log* -bXiY 

 s? = '~^ . 



n — 1 



Values of b, log k, and S thus determined are included in Table IV. 

 The quantity S is an estimate of the standard deviation of the observed 



