358 MESSRS. R. T. GLAZEBROOK AND T. C. FIT/PATRICK 



length of the column was measured with the reading microscopes. The ebonite plugs 

 were then removed, and the full length of the mercury column measured. The 

 difference between these two gives us $1 directly ; for one tube 1'9 mm. in diameter 

 the mean of a number of determinations which were in fair agreement gave 



81 = -45 mm. ; 

 and for this tube we have, therefore, 



81 = '47 X a. 



For a tube such as those used for the half units, for which the diameter was 1'57 mm., 



we found 



81 = '35 mm., 



and this gives 



SI = '4.1 X ". 



It is, therefore, clear that for these tubes we may, without serious error, use the 

 value given by the above theory, viz., 



81 = -4(5 x ". 



and this has been done in the calculations. 

 Thus, the equation to determine r becomes 



WR x 10* 



r = 



pp. (L + SL) (I - SI 



and, as will be seen when the values of the various quantities involved are introduced, 

 this may be written 



WR x 10* T, SL , SI 



In this expression temperature corrections are necessary to p, L, aud /, while the 

 weight W will require reducing to its value in vacua. 

 Let 



t' = temperature at which the length L is measured ; 

 b = coefficient of linear expansion of measuring rod = '000017 ; 

 t = temperature at which the thread of length / is measured ; 

 p* = density of mercury at = 13 "5 957 grammes per c.c. ; 

 y* = coefficient of expansion of mercury = '000182 ; 

 g = coefficient of cubical expansion of glass = '000025. 



* These values are taken from the ' Travanx et Memoires da Bureau International des Poids et 

 Mesnres,' vol. 2. See ' Nature ' for April 3, 1884. 



