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III. On the Ideal Re fr activities of Gases. By William 

 Jacob Jones and James Riddick Partington, Assistant 

 Lecturers in Chemistry, Manchester University *. 



r PHE formula deduced by Lorentz f and by Loreuz I 



£=£.£ = - (a constant) = j£.*=-\. . (D 



where jjl denotes the refractive index of a given substance 

 for a given wave-length, and d its density, expresses very 

 accurately the observed relations over a very wide range of 

 densities. When /jl is nearly equal to unity, as is the case 

 with gases, (//, -h l)/(/^ 2 -f 2) approximates to 2/3, and formula 

 (1) degenerates into the formula of Gladstone and Dale § : 



^—=k (a constant) (2) 



We shall designate the excess of the refractive index of a 

 gas over unity, i. e. fju— 1, its ref r activity . The refractivity 

 is therefore the value of k for unit density. 



In their calculations of refractivities from the experi- 

 mental results, investigators have, with the exception of 

 C. Cuthbertson and E. P. Metcalfe ||, and L. Stuckertf, 

 failed to realise the necessity for taking into account the 

 deviations of the gases employed from the ideal state. 



Now the relation between temperature, pressure, and 

 volume of a gas is at pressures less than 5 atmospheres very 

 accurately expressed (at least in the case of permanent gases, 

 and with very close approximation in the case of less perfect 

 gases) by the characteristic equation of D. Berthelot**: 



(p+a£)o 



&) = RT, (3) 



where 27 BS T c 8 , r, 



a= — It- - ; o= - ; 

 o4 p c 4 



T t: , p c , and p^ being the critical constants. If we consider a 



* Communicated bv the Authors. 



+ Lorentz, Wied. Ann. ix. p. 641 (1880). 



X Lorenz, ibid. xi. p. 70 (1880). 



$ Gladstone and Dale, Phil. Trans, cxlviii. p. 887 (1858). 



j| C. Cuthbertson and E. P. Metcalfe, Proc. Roy. Soc. A. lxxx. p. 406 

 (1908). 



f L. Stuckert, Zeitschr.fihr Elektrochem. xvi. p. 37 (1910). 



** 1). Berthelot. Mem. du Bureau internat. des pcids et mesures, xiii. 

 (1907). 



