444 Mr. Norman Shaw on Increased A 



ccuracy 



A rough graphical examination showed that the creeps 

 could be represented by formula (8) with the proper value 

 of T inserted. An algebraic method of calculation was 

 adopted so that a full advantage of the observations might 

 be taken. If we denote log (x r + i — x r ) by i/ r for a given 

 value of T we can represent each column of Table II. by 

 the equation 



where m— log (e~ k ) 



and At = log (x 2 — #1) 



for the value of T considered. It will give a sufficiently 

 accurate result for the best possible values of h and D if we 

 find the best representative values for m and At, which will 

 fit each of the series of equations in 



y v = . m + At " 



1/2 = 1 . m + A T 



y 3 = 2 . m + At 



y r — (r — l)m + At. 



By applying the method of Gauss it can be shown that the 

 desired values of m and At are given by a solution of the two 

 equations 



[3/1+^2+^3+ ... +yr] = Tl + 2 + 3-+- ... +(r-l)]m + rA T 

 and 



[y 2 4 2^ + 3y 4 + ... +(r-l;z/ r ] = [l 2 -f2 2 + 3 2 -r ... +(r-l) 2 ]m 



+ [1 + 2 + 3+ ... +(r-n]A T . 



If we solve these for each column in Table II. we can get 

 m and At, and hence the k and D which will best fit each 

 set. If formula (8) holds we should get the same values for 

 k and J) throughout. (It should be noted that At is, of 

 course, necessarily different in every case, but D calculated 

 from At, m, and T should be constant.) Table III. gives the 

 results of this calculation. 



