110 



MR J. Y. BUCHANAN ON THE 



§ 42. The following table gives the means of comparing the effect produced by- 

 diluting or concentrating a given solution according as it takes place in terms of the 

 first or the second of these hypotheses. The hypothetical salt MR has a molecular 

 weight 160, which is nearly the mean of those of the ennead MR. The fundamental 

 solution, from which all the others included in the table are derived, is that for which 

 m= 1/2, and it is made by dissolving 80 grams of the salt in 1 kilogram of water. 

 It is assumed that the dissolution of this mass of the salt in the kilogram of water at 

 the standard temperature T, which may be 19 "5° or any other, increases its displacement 

 by 20 grams, so that the displacement of the fundamental solution is r020 kilogram. 

 The concentration of this solution is then supposed to be altered by the addition to, 

 or the withdrawal from, the kilogram of water, of salt so as to produce the series of 

 solutions having the concentrations indicated under m in the first column of the table. 

 From this the weight of each solution, W, given in the second column, follows as a 

 matter of course. 



Hypothetical Case. 

 Table giving the calculated Specific Gravities and Displacements of Solutions of 

 m.MR+ 1 kilogram of Water at T, where MR= 160 and the Displacement for 

 m- 1/2 is 1-020 kilogram of Distilled Water at T. 



m. 



W. 



Sa. 



l-000 + 0-04m 

 = Aa. 



Log A]/2X 2m 



Al. 



Si.. 



Sa-S,. 



10 



2 



600000 



1-857142 



1-400000 



0-1720034 



1-485947 



1-749725 



0-107417 



9 



2 



440000 





794118 





360000 



0-1548030 



1-428346 



1-708390 



85728 



8 



2 



280000 





727273 





320000 



0-1376027 



1-372785 



1-660856 



56417 



7 



2 



120000 





656250 





280000 



0-1204023 



1-319478 



1-606695 



49555 



6 





960000 





580645 





240000 



0-1032020 



1-268242 



1-545447 



35198 



5 





800000 





500000 





200000 



0-0860017 



1-218994 



1-476627 



23373 



4 





640000 





413792 





160000 



0-0688013 



1-171659 



1-399724 



14068 



3 





480000 





321368 





120000 



00516010 



1-126162 



1-314197 



7171 



2 





320000 





222222 





080000 



0-0344006 



1-082342 



1-219473 



2749 



1 





160000 





115384 





040000 



0-0172003 



1-040400 



1-114955 



329 



1/2 





080000 





058823 





020000 



0-0086001 



1-020000 



1-058823 



0-0 



1/4 





040000 





029703 





010000 



0-0043000 



1-009951 



1-029753 



-50 



1/8 





020000 





014925 





005000 



00021500 



1-004963 



1-014963 



-38 



1/16 





010000 





007481 





002500 



00010750 



1-002478 



1-007503 



-21 



1/32 





005000 





003745 





001250 



0-0005375 



1-001238 



1-003757 



-12 



1/64 





002.500 





001874 





000625 



0-0002687 



1-000619 



1-001880 



-6 



1/128 





001250 





000937 





000313 



0-0001343 



1-000309 



1-000940 



-3 



1/256 





000625 





000468 





000156 



0-0000671 



1-000155 



1-000470 



_ 2 



1/512 



1-000313 



1-000234 



1-000078 



0-0000335 



1-000077 



1-000235 



-1 



1 



2 



3 



4 



5 



6 



7 



8 



We now apply our first hypothesis (§ 40), and by means of it we obtain the displace- 

 ment A^ of each of these solutions expressed in terms of the kilogram of distilled water 

 of the standard temperature as unit, and recorded in column 4 of the table. Their 

 specific gravities, the quotients obtained by dividing the weight of each solution 



