MERCURY AND GLASS 2 1 



While the value of ft' fi" varies perhaps from 1.48 x io -6 to 

 1.28 x JO -6 in a range of 600 atmospheres, it is nevertheless sufficiently 

 constant to make possible a simplification of equation (1) on page 

 15 without the introduction of appreciable error. Noting that 

 ft' = 0.0000038, fi' (i" = 0.0000014 and d the density of glass 

 = 2.5 we have 



' '3-55 



0.000 001 4 w" (P x - P t )\ ur D 

 + M ) (^W^V (4) 



Since both fi' P x and the second term within the parentheses are very 

 small, the value (1 fi' Pf) rnay be removed outside of the parentheses 

 without introducing appreciable error." The equation thus becomes : 



fi fi' = \w w' 

 + 0.0000076 , (/>,-/>,)] -g^^... ( 5 ) 



This equation was used in calculating all the results. When the 

 inner thin glass bulb was omitted, in the case of liquids not attacking 

 mercury, w" becomes zero and the third term within the first paren- 

 theses drops out. The equation then assumes the form of equation 

 (3) on page 17. 



The value of iv' used in the equation above must of course corre- 

 spond to the same range of pressure (P x P t ) as that observed in the 

 case of w. The value is easily found from equation (2). 



w' = W'P X (/3' fi") = W (P x P 2 ) (/5' - /3") where P' = I\ - P % . 



The value of /?' j8" also must correspond to the given range of 

 pressure. This last designation is necessary because fi' /j" changes 

 in value with changing pressure, as is shown on page 20. w' may 

 also be found directly from the results given on page iS by graphic 

 interpolation, or from the diagram of ,5' fi" by multiplying the 

 ordinate value corresponding to the difference between two pressures 

 by W. All these methods give of course essentially the same results; 

 they were used to verify one another in the tables given below. 



Among the other quantities involved in the equation, the volumes, 

 being found by weighing quantities of mercury determined by the 



1 For a table of formulae giving the permissible abbreviations of equations 

 involving small quantities in the presence of large ones, the reader is referred to 

 Nernst and Schonfliess, Math. Behand. der Naturwiss., p. 303 (1895). 



