PHYSICAL PROPERTIES OF WATER, ETC. 45 



The numbers for the volume of the fourth solution are so nearly in arithmetical 

 progression that we can hardly use them to approximate, even roughly, to the position 

 of the maximum density point, or the corresponding density. The expansibility has 

 practically (from 0° to 12° C.) the constant value 



0-00036. 

 Thus we have for the various salt solutions : — 



As a good illustration of the analogy at the beginning of this section, let us deal 

 for a moment with fresh water at such a pressure that its maximum density point 

 is — 9° C. , that of the first of the salt solutions. It will be seen later that the requisite 

 pressure is about 4 tons. At that pressure (A) gives 



468 - 3-75t + 0-07;! 2 . 



Hence as the unit of volume at 1 atm. and 4° C. becomes 1 '000136 at 1 atm. and 0° C, 

 it is reduced at 4 tons and 0° C. to 



(1-000136) (l - 609 x 7 468 ) = 1 - 0-0284, 



so that the density has become 



10292. 



At the same temperature, and at 1 atm., the density of the salt solution, which has the 

 same maximum density point, is 



1-0297. 



If we assume the formulae (A) to be applicable to temperatures so far as 9 C below 

 zero (a somewhat precarious hypothesis, inasmuch as water at 4 tons has its freezing 

 point about — 4°'5 C), the maximum densities alike of the compressed water and of the 

 salted water are closely represented by 



1-030. 



