412 Mr. R. E. Baynes on Saturation Specific Heats, fyc, 



be less than 19/17, which is equivalent to ft/R>8*5. Dalton 

 (Phil. Mag. April 1907, p. 537) has given the condition 

 k< 1*202 by an interpolation method, and the foregoing 

 calculation gives k< 5-95824/4-95824 EE 1-20168. 



(iv.) $—$' is always positive and has a minimum value 

 7-00789R when /&= -262535, which corresponds to v= '445963, 

 v' = 11-8364, 7T='127530, r=-642488 : 



(v.) the work of vaporization has a maximum value 

 1-47215 PV = -55206 RT when ^ = -281990 (as also found 

 by Bitter), to which correspond v = '467237, r/=7'80538, 

 tt = -200617, r=-700110 ; it is when t is either or 1: 



(vi.) the greatest value of both \ and A/ is 9 PV = 27 RT/8, 

 this occurring for /z.=0, v= 1, 7r=0, t=0, and both decrease 

 continuously to the value at the critical point. 



Inversion of the sign of $' occurs where S f = 0, that is, 

 where 3v/7*=fe/R, and we can easily see, as was pointed out 

 by Raveau* and earlier by Duhem, that this is at the points 

 where the entropy along the vapour side of the connode has 

 critical values. 



On the assumption that fe/R=N + i we may therefore 

 determine the temperatures of inversion for different values 

 of N either graphically (i.) from the diagram of the values 

 of (fc— S')/R in terms of t or (ii.) from the diagram giving 

 the values of v, t, it in terms of /jl, by finding the inter- 

 sections of the lines 3v//i — N + t? with the v//,-curve, or thus 

 by calculation. 



If we put n = 3(N—J)/(N+ J), the desired points on the 

 connode correspond to /t* = (3 — n)v and are therefore given 



by 



, (6-»>+l 3y(3~?zy)i(12-w)y — 1} 



0g ('5v-l)(nv-l)-('6v-l){nv + l){(6-n)v + ll' 



and for these we have 



7r=(nv — l){(6 — n)v~l} /4v 3 



We also have for these points 



v' = 2v/(;5i>-l-fJL) = 2vl(nv-l), i.e. *=•/(«•- 2), 

 or 



, a (3v'-l)(nv'-2)_ 3 v '( n v' -3){(Q-n)v' + l} 

 ° g (3-«y + 2 ~ (3v'-l)(W-l){(3— n)v' + 2\ 



ir=(nv'-2){(;d-ny + l\j / ? > 

 t= (Sv'-l)^ -1) {{3 -n)v f + 2\ l$v\ 

 * Journ. de Phys. 1892., p. 461. 



