146 THE ROYAL SOCIETY OF CANADA 



of equilibrating columns as modified by Regnault. As they claimed 

 a high degree of accuracy for their results, the way appeared open 

 for the direct determination of the cubical expansion of fused silica by 

 the use of a mercury-in-quartz dilatometer. 



Accordingly, at the suggestion of Callendar, Mr. F. J. Harlow 1 

 undertook the direct measurement of the cubical expansion of silica 

 by the dilatometer or weight thermometer method. He measured 

 the apparent expansion of mercury, and assuming the values of 

 Callendar and Moss for the absolute expansion of mercury, calculated 

 t he coefficient of cubical expansion of his silica bulbs, from the formula, 



= m . - M t + m 

 M t M t *' 



where a = the absolute coefficient of expansion of mercury, 

 m = overflow, 



M t = Mass of mercury in dilatometer at t°C, 

 g = coefficient of cubical expansion of the silica dilatometer. 

 The mean values of the coefficient of cubical expansion of fused 

 silica obtained by Harlow were — 



betweenO and 100°C, 0-998 x 10- 6 , 

 and " 0° " 184°C, 1-447 x 10- fi ; 



while the values obtained by taking there times the linear coefficient 

 as given by Kaye's mean curves are — 



between 0° and 100°C, 1-49 x lO 6 , 

 and " 0° " 184°C, 1-54 x 10" 6 . 



Harlow used three different transparent fused silica dilatometers. 

 The first was of the ordinary type and was filled by the usual method 

 of alternate heating and cooling, with the open end under mercury. 

 As a larger value of the apparent coefficient of expansion of mercury 



1 Proc. Phys. Soc. London, 24, pp. 30-39, 1911; Chem. News, 104, p. 289, 1911; 

 Nature 88, p. 234, 1911. 



2 This equation is easily deducible as follows: — 



Let Vo = volume of mercury and of dilatometer at 0°C. 

 and V' t = " " dilatometer at t°C. 



Then denoting the density of mercury at 0° and t°C. by p and p t respectively, 

 we have — 



V t = V (l+gt )— -(1) 



Po = PtU+at ) (2) 



Also we can write, V' t p t = M t — ■ — -(3) 

 VoPo = M t +m(4) 

 Dividing (4) by (3) and making use of (1) and (2) we obtain 

 1 + at _ M t + m 

 1 +gt ~ M t 

 whence, solving for a, one obtains the above equation. When t is negative, m will 

 also lie negative, and the formula still holds. 



