462 Mr. W. Sutherland on the 



which, with the fact that 1/1*9 = 1/2 + -02632, maybe written 



-45896_ -067485 ... 



P =1 + ^-l-V703-51 + 02682 -I+7^1- * < A > 



To interpret this we must suppose water at 4° 0. to be for 

 the present a standard mixture of the two ingredients in 

 water, and that water at any other temperature is formed by 

 adding a certain proportion of one of the pure ingredients to 

 this standard mixture. Let us denote this standard mixture 

 by S, its density at any temperature by p s , and at 0° by p 8 , 

 while p x and Q p 1 relate to the pure ingredient which we shall 

 call 1. Then for a mixture of 1/2 + g parts by weight of S 

 with 1/2 — q parts of 1 formed without shrinking, we should 

 have a density p given by 



i = V2-_, + v2+, = i +{ , } n_i\ 



P Pi Ps Ps HJ \Pl Ps 1 ' ^ } 



•• P = P s \l-£-<l)(pJPi-l) + (h-qy(Ps/Pi-l) 2 + -...}, 

 Now for S and 1 we shall have approximately 



P,=oP,0--K t )i Pi = oPiO- — ht)t 



, L oPi v. oP« J 



r 1 , i_ ogg/jogi 



-oPs^ + 2 l-t{(3 p l/o p 3 -2)k s ' + ^\ 



^{(g-^-^St*--^}'} • (B) 



where k/ and ky ought to be nearly equal to k s and k x and 

 are used to bring our expansion back to a form suitable for 

 comparison with MendeleefPs empirical equation in its form 

 (A). In the sequel they will be taken as k s and ky. 

 A comparison of (A) and (B) gives 



ps=l, (3) 



op s /2 oPi = -45896 .-. 0^=1-08942, (4) 



(3orV*.-8)#+*i= 1/703-51 



.-. 1-2683*, + *! = -0014214, ... (5) 



-02632- ^fi =gU/^-i)(i-*.0 -t{K-h) Psl oPl 



= --08208^(1-40 -•91792(£ s -£ 1 >. (6) 



