446 Prof. R. M. Dadourian on the Temperature Coefficient 

 Making the substitutions 



L = L (l + ^ + ^ 2 ), (7) 



P = P (1 + & + #*), (8) 



and E = E (l+e^ + 7 ^ 2 ) (9) 



in (6), expanding, neglecting the terms containing powers 

 of t higher than the square, simplifying, and setting the 

 coefficients of different powers of t equal to zero, we obtain 



e=-(2# + a) (10) 



and 7= - (2$-36 2 -2ot0 + /3-a 2 ). . . . (11) 



In (11) the last three terms are small compared with the 

 others, therefore we may write 



7 =-(20-3(9 2 ) (12) 



Applying the method of Least Squares to the original 

 data obtained in my experiments on the effect of tempera- 

 ture on the period of tuning- forks, I have obtained the 

 following values for 6 and <$>. 



'0=1-28x10-*, 



cf) = 3-8xl0- 7 . 

 Therefore 



P = P (l + -000128£ + -000,00038f 2 ). . . (13) 



Putting these values of and <£, and 1*1 x 10 ~ 5 for « in (10) 

 and (12), we have 



e= -2-68 xlO- 4 

 and 7=— 7-lxlO" 7 , 



or E = E (l--000268*--000,00071* 2 ). . . (14) 



It would be interesting to compare the accuracy of these 

 results with that of the results of the experiments which 

 were reviewed in the first part of this paper. The following 

 expression for the percentage error of a single observation of 

 € is obtained from (10) 



7 = VWJ + fc)' • ■ • (15) 



Since a is only one-tenth of 6, (15) may be rewritten in the 

 form 



7-VU) + ?t) (16) 



