16 The Philippine Journal of Science 



1913 



Taking different intervals of time from the experimental data 

 in Table V, we can form as many independent equations as we 

 please. Six different intervals were taken; namely, 

 t=600-65=535 min., t=540-65=475 min., t=480— 65=415 

 min., t=600-185=415 min., t=600-245=335 min., and t=600 

 —305=295 min. 

 The differences between the corresponding values of x were 



divided into 10 equal parts and the values of 



computed. For example, the equation for t=535 min. is 





600 a oocqq 



dt=535=^^[ ( Y + Yio) +2 ( Y 2 + Y 4 + Y 6 + Y 8 ) 

 65 6 



+4(Y 1 +Y 3 +Y 5 +Y 7 +Y 9 )] 



The values of y , y lt etc., are 



K 2 (0.0613) + K 3 (0.00376) 

 -, etc. 



K 2 (0.054) +K 3 (0.00292)' 



In summing up the values of y, the denominator was factored 

 in such a way as to make one factor the same as the numerator 

 and the other containing K 2 and K s to the first power. Of course, 

 factoring exactly is impossible, but the difference between the 

 numerator and the first factor of the denominator was very 

 small and canceling them with each other allowable. 



To illustrate: 



_ = q 1 00567r l -'. 



3 LK 2 (0.0008067) +K 3 (0.00001398) _', (14) 



t=41 r = 0-00543r 1 "I 



3 LK 2 (0.000877+K 3 (0.0000178) J. (15) 



Solving for K 2 and K 3 between these equations 



K=0.00454, K3=0.0223. 



Proceeding in this way with the other equations, a set of values 

 of K s and K 3 may be determined. 



Since in the expression for y the effect of K z is very small 

 compared with that of K 2 , K 3 being multiplied by the square of 

 the coefficient of K 2 , a small quantity in itself, we are justified 

 in assuming its value as correct and substituting it in the four 

 other equations to determine K 2 . 



