ASSOCIATED PHYSICAL QUESTIONS. 



X. Theoretical Speculations. 



If instead of the percentage of Nad in the solutions we tabulate the amount of 

 NaCl to 100 of water, and along with it the compressibility at zero, we have — 



s = amount of Average compressibility at 0° C. x 10 7 . 



NaCl to 100 of water. For first ton. First 2 tons. First 3 tons. 



o-o 



40 



9-6 



15-4 



21-4 



The relation between these numbers is very fairly represented by the formula — 

 Average compressibility for first p tons= — — 



It is remarkable that if we put t = in the formula of Section VII., we have — 

 Average compressibility of fresli water for first p + s tons = — — 



which presents an exceedingly striking resemblance to that last written. 



Though these formulae are only approximate, we may assume the true constants to 

 be at least nearly the same in both, and make the following statement as a sort of 

 memoria technica in this subject : — 



At 0° C. the average compressibility, for p tons, of a solution of s lbs. of common 

 salt in 100 lbs. of water, is nearly equal to the average compressibility of fresh water 

 for the first p + s tons of additional pressure. 



The numerical coincidence above is, of course, accidental ; because the formulae 

 are taken for the special temperature 0° C, and the special unit of pressure 1 ton 

 weight per square inch. 



But a coincidence of a much more striking character, and one which does not depend 

 upon special choice of units, is suggested by the common form of the expressions 

 compared. 



