112 



Mi; F. E. SMITH ON THE CONSTRUCTION OF 



The sum of the squares of the residual errors is 5 '9. Hence the probable error ot 

 any single observation is 0'6745 (5 - 09/39)* = 0'243, a little more than two parts in 

 a million. If the residual errors be written down in the order of their magnitude, 

 the central error is also two parts in a million. The calculated probable error of a is 

 1 X 10- 7 and of ft 8 X 10~ 9 . 



The coefficient of cubical expansion of Verre dur glass being 222 X 10~ 7 , the 

 equation connecting resistance and temperature of a constant volume of mercury is 



RT = R [l + 0-00088776T + '000001 OH76T 2 ], 



the glass being assumed as isotropic. The equation derived from measurements when 

 the standard U was employed is 



RT = R [l + 0-00088788T + "00000 10564T 2 ]. 



The greatest difference between the values derived from the two equations is 

 0-0003 per cent, at 10 C. and O'OOIO per cent, at 20 C. 



For a constant volume of mercury the equations obtained by M. GUILLAUME were* 



(a) R T = R [1 + 0-00088745T + O'OOOOOlOlSlT 2 ], 



(b) R,. = R [1 + 0-00088879T + 0'0000010022T 2 ], 



the temperature being expressed on the hydrogen scale. 

 The equation obtained by KREICHGAUEE and JAGER! is 



R T = R [l + 00008827T + 0'00000126T 2 ]. 



Table XV. gives the values, as calculated from these five equations, of the resistance 

 of a constant volume of mercury at 10 C. and 20 C., the resistance at C. being 

 1 ohm. 



TABLE XV. 



Probably the introduction of yT 3 in the equations would bring the results even 

 nearer together. A difference of O'OOl per cent, corresponds to a difference in 

 temperature of 0'01 C. 



* M. C. E. GTTILI.AUME, 'Bureau International des Poids et Mesures,' 1892. 

 t ' WIF.MKMAXN'S Annalen,' vol. 47, 1892. 



