

282 Mr. William Sutherland on the 



for water at ordinary temperatures is quite abnormal, it would 

 be useless to attempt to apply this equation to them ; but 

 from the " dimensions " of the physical quantities involved in 

 it we may make it yield a correct form of empirical equation 

 for solutions. If we neglect the small term 25R/26, and also 

 the difference between o and r at ordinary temperatures, the 

 equation above suggests the simple form / varies as 1/fip 2 , that is 

 X -1 varies as fip*, say KX _1 = £tp 2 , where K is a constant, 

 and for water KW~ 1 =fi w the compressibility of water, and 

 as before we have 'Kr 1 =(W-\+nAr 1 )/(l + n). But on 

 account of the rapid altera tion of the compressibility of water 

 with pressure, and its anomalous variation with temperature, 

 we must be prepared to admit that the part of the com- 

 pressibility of a solution due to the water in it is altered from 

 its value in pure water, and is more altered the more the 

 water is compressed in the process of dissolving the salt. Let 

 this compression be measured roughly by the total amount of 

 shrinkage that ensues when 1 molecule of salt is dissolved in 

 1000 grms. of water, call the shrinkage A, and let us amend 

 the equation given above to KX _1 =/i/) 2 +/(A). Let suffixes 

 a and b attached to symbols refer them to two different bodies, 

 then 



KX r 1 -KX r i= M y o - /ts pf+/(AJ-/(A 6 ) ) 

 but 



KX-'-KX-i=K«(A : >-A->)/(l + »), 



.-. K«(A^-A r i)/(l + n)=^-^+/(A a )-/(A s ). 

 Hence selecting pairs of bodies for which A = A 6 approxi- 

 mately, we ought to get H> a p 2 a — p b pl proportional to cA~ l — cA"^ 

 the values of the last expression being obtainable from 

 Table XXXL 



To facilitate the comparison I furnish the following broad 

 statements about A founded on the study of data as to the 

 molecular volumes of sails, both solid and in solution, given 

 by Favre and Yalson (Comp. Rend, lxxvii.) Long (Wied. 

 Ann. ix.), and Xicol (Phil. Mag. xvi. and xviii.). The modular 

 property applies approximately to shrinkage on solution ; the 

 shrinkage of a gramme molecule of Li CI is 2, and the shrinkage 

 for a gramme molecule is increased when for Li is substi- 

 tuted 



K. Na. NH 4 . fOa. £Sr. £Ba. 



by 8 7 -5 10 11 12; 



and when for CI is substituted 



Br. I. N0 3 . AS0 4 . £C0 3 . 



byO 8 14. 



