( 122 ) 



above in fonmilae (9) and (10) iiiul compare the result with the 

 observations. 



Equation (9) yields: 



\ {% - ^) = L/ 6 ^^1 - t) = 3.37 VT^^ 



- P 3 



and equation (10) : 



(.., + v,)-l = -- 



^ t- 30 



(1 — [)= 10.0(1 — r). 



^ P3 



In order to compare these results with the j)aral)olic formulae of 

 Mathias^), formulae must be derived for the reduced densities of the 

 co-existing' phases; representing these reduced densities bv bi and b.^ I 

 find, according lo a transformation employed foi-merly : ^) 



y(^-N) = 3.37 1/1:^ 



Y(&i + ^j-l = (3:37"-10.9)(l_r) = 0,5(l-r). 



In the last formula, however, the co-cflicient 0,5 is somewhat uncertain. 



Matjiias gi\es for the liquid branch, according to the obser\'ations 

 of Cailletet and ^Iathias ''), 



b, = 1 - 2.47 (1 - r) + 4,09 i/l-r, 

 and for the Napoiir branch 



b^ = 1 4- 2,91 (1 — t) — 3,37 i/l — t. 

 f From these formulae it would follow that the two branches of the 

 border curve belong to ditTerent pai'abolae. The co-eflicient of k 1 — t 

 or the vapour branch perfectly agrees wjih the one found, and the 

 fact that Matiiias has found a greater value for the same co-elKicient 

 in the licpiid bi'anch, may clearly be asci-ibed to the uncertainty of 

 the then existing data on this subject. If we neglect this dilTei-ence, 

 the formulae of Mathias give: 



lb, 4- b,) - 1 =: 0,25 (1 - t). 



a sufficient agreement with the co-efficient 0,858 later derived l)y 

 him from A.MAfiAT's observations. The value 0,5 found above is in 

 good harmony with this. 



1) Journ. d. Pliys., (3), 1, 53, 1892. Ann. d. Toulouse, V. 



-) Proc. Royal Acad., 27 June 1896 ; Gomm. no. 28, p. 12. More acurately we have 



1 \ w I 



Q = — =r — =p -— -I {<f"- — 'I») 



i^lc -\- ^ ± (p Vic Vk' Vk' 



-) Juiun. d. Pliys., (3), 2, 5, 1893. Ann. d. Toulouse. VI. 



