110 



MR, F. E. SMITH ON THE CONSTRUCTION OF 



The sum of the squares of the residual errors is 1571, and since twice the weight 

 was given to the ohservations at C., the number of observations may be resided 

 as 39. Hence the probable error of any single determination is 0'6745 (1571/38)*, 

 which is equal to rt 0'43, a little more than four parts in one million. If the residual 

 errors be written down in the order of their magnitude, the central error is three parts 

 in 1,000,000. With the aid of the data in the three normal equations, the probable 

 errors of the coefficients a and may now be calculated as follows : For 



a, 7 X 10~ 7 (39 - 436-5Y7207-9) 1 = 2 X 10-*, 

 and for 



ft, 7 X 10~ 7 (2323-2)*= 145 X lO' 10 . 



The coefficient of cubical expansion of Jena 16'" glass is 231 X 10~ 7 . Assuming 

 the glass to be isotropic, the variation of resistance with temperature of a constant 

 volume of mercury as deduced from the previous equation, is 



RT = R [l + 0-00088788T + 0'0000010564T 2 ], 



the probable errors being as before. 



Standard M. Verre dur glass. Similar remarks apply to the observations with 

 this tube. Table XIII. gives the results of the resistance measurements. 



TABLE XIII. Mercury Standard M. Verre dur Glass. 



1- 1 I .-. 



As before, twice the weight has been given to the observations at the ice-point. 

 The three normal equations obtained by the method of least squares are 



(A) 40.r + 451'5-Ja + 7677'2174/> = "393913, 



(B) 451-52a; + 7677'2174+ 147255-962* = G7I4!)1'15. 



(C) 7677-2174a; + 147255'962a +804920^-28^ = I2l'02551 It', 



