with van der Waals' and Clan sins 1 Characteristics. 409 



all real when t<1, is always a maximum when v=l what- 

 ever the value of t, the maximum value for r being ~Rt/(t— 1) 

 and the corresponding reduced pressure being 4t — 3; that 

 K — fe has also a minimum value R when v = ^, this being 

 also its value for any value of r when v= x . 



If the isopiestic for rr cuts the isothermal for t in three 

 points and v. v", v denote the corresponding volumes in 

 ascending order of magnitude, then, if fi is defined as above 

 strictly with reference to v, 



v" = vV, v' = v/B. 



and the heat-capacities corresponding to v', expressed in 

 terms of v, are given by 



I'/F = ABD V 3 , (K'-fc)/B = AD/^G, 

 L'/V=-ADE/S>BG. 



( ise oj Saturation. 



Now, if it is the saturation-pressure at t. we have also the 

 relation 



3(w+3/n0(^-v) = «rlog{(3/-l):(3^-l) 



fj 



so that, in the case of saturation, v and fi are connected by 

 the relation 



Iog(E/AB) = 3fGH/ADE, 



which may be looked upon us the equation of the liquid side 

 of the connode or boundary curve. 



[The equation of the vapour side of the connode is of the 

 same form but with the sign of fi changed ; for we similarly 

 obtain 



l :V + 1-m = .VC. i l-.V-/ t / )(9y , -l-^) 



0g (3v'-lX3v'-lHV) (3v , -l)(3v' + H-/)(3»/+l-^) 



if /= +*/{(3/-l) 2 -4*V»}.] 



From the above equation we may determine the value of v 

 for any value of /*, or vice versa, and then at once obtain the 

 corresponding values of the saturation pressure, temperature, 

 and vapour volume w, r, v', as well as of v" , .-o that we can 

 easily plot the curves connecting these magnitude- with yu,, 

 or indeed with v or t, &c. 



We easily find that fi = for both v= J and v = l and that 

 it has a maximum value -iiOGot)")^ to which correspond 

 v=-54309G2. v'= 3*3^713. 7r = -471354:>, t='8371466. 



