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LVIII. A Relation between Coefficients of Expulsion of 

 Liquids and their Critical Temperatures. Py H. Davies, 

 B.Sc, Head of Physics Department, Municipal College, 

 Portsmouth*. 



THE law of the " Rectilinear Diameter," as given by 

 Mathias t, states that 



D| +-D,=a-&T, (1) 



where D v and D^ are the densities o£ saturated vapour and 

 liquid respectively, and T is the absolute temperature. As a 

 deduction from this law Gruldberg % calculated the ratio of 

 the densities at the critical temperature and at the absolute 

 zero, finding a practically constant value 4 for it. 



Let T c , V c , and D c represent the critical temperature, the 

 critical volume, and the density at the critical temperature. 



For T = 0, T> v = 0, and D^ = 4D c . Hence in (1) a = 4D c . 



For T = T c , D Z = D„ = D C , and 2D =4D fl -b <T c , 



b= T7* 



Mathias' law can now be put in the form 



D,+D.=4D.-^,T .... (2) 



At temperatures well removed from the critical temperature 

 D v is negligible in comparison with D^. If V is the specific 

 volume of the liquid, then 



1 1 T 



L\ 2D C 2D C {2V C -T)' ' ' W 



The coefficient of expansion a = == ' -— and is obtained 

 directly from (3), thur 



is 



_1 dV___l_ ... 



*~ V dT ~2T C -T W 



Equation (4) enables one to calculate the coefficient of 

 expansion from the known critical temperatures, or con- 

 versely to calculate the critical temperatures from the experi- 

 mental values of the coefficient of expansion. 



* Communicated by Prof. A. W. Porter, F.Ii.S. 



t Journ. de Phys. (3) vol. ii. 1893, p. 11; (3) vol. i. 1892. p. 53, 



% Ckem, Cent. Bl. 1898, vol. ii. p. 1042. 



Phil Hag. S. 6. Vol. 23. No. 136, April 1912. 2 X 



