450 Mr. J. H. Shaxby on Vapour Pressures 



RT 2T ° bc2 

 §6. The equation p= —r~e ^< can readily be thrown 



into a " Reduced " form : at the critical temperature 



RT,, ^ 



pc = 



p c T c b' 

 Write 7r for — , for 7^-, and yjr for 



Then 



-2( l — 1) 



1 



Replacing 6 by -= 7- and b c by ~-r, and writing 8 for 



— g-r — j we obtain 



77 



= 0S* 



§ 7. The critical density of a substance is difficult to measure 

 accurately, and its magnitude is commonly estimated by 

 using the Oailletet-Mathias linear relation. It may also be 

 calculated as follows : 



d?-df 2Td c 2 

 Let d 1 = qd 2 . Therefore 



los;,? q T c 1 



<W-1) T 2d<? 



or ^ 2 /T /2 log, g / 21og 10 g 



d c ~V T C V f^T * V -4343(3"- 1)' 



Thus d c =-r~z, writing <£ for the last square root. <£ is a 



purely numerical quantity ; to facilitate calculation its 



logarithm can be tabulated for a series of values of log-^ 1 , 



a 2 



say from to 3 in steps of *1, with difference columns 



allowing of estimation for intervals of "001. The values 



thus found for the critical densities of Water and Isopentane 



are given in the last column (11) of Table I. The Cailletet- 



Mathias method gives 0*2344 for Isopentane and fails for 



Water. 



