60 ON THE CONDUCTIVITY, SPECIFIC GRAVITY AND 
It might be well to note that in each series having a constant 
Concentration of potassium sulphate, the differences seem to 
change from a negative to a positive per cent. 
Considering the many sources of error in the calculations of 
the conductivity. the agreement between the observed and 
calculated values is very satisfactory, and leads one to draw the 
conclusion that the conductivity of mixtures of solutions of these 
1 Note by the communicator of the paper.—Mr. Barnes points out that in series of 
mixtures whose constituent solutions have in the case of one electrolyte the same con- 
centration (74 say) in all,and in that of the other a variable concentration (mg say), the 
excess (e) of the calculated over the observed value of the conductivity increases with 
ny, being usually negative for small values of m2 and positive forlarger values. At 
first sight it might appear that he had over-estimated his limit of error, and that the 
conductivity was thus shown to be calculable only for a particular value of mg in each 
case. There are, however, two sources of error which will account for this regular 
progression in the relative magnitude and sign of the e’s, viz., (1) The employment, 
of the quotients of the specific equivalent conductivity by the specific equivalent con- 
ductivity at infinite dilution (1/20) as the values of the ionization coefficients (a) 
for simple solutions, and (2) the impossibility of drawing with perfect accuracy the 
dilution-ionic-concentration curves. The more concentrated the solutions the greater 
will /Moo differ from @; and the greater the liability to error in the drawing of the 
curves the greater the possible error in the determination of the ionization coefficients 
of the electrolytes in the mixture. The dilution-ionic-concentration curves are-nearly 
rectilinear for very weak and for strong solutions but curve rapidly in the region of 
moderate dilution, and it is in this region that it is most difficult to draw them 
accurately. Hence in the case of strong solutions, the magnitude and sign of the e’s will 
be determined largely by the error due to using values of 1/00 as the ionization coefti- 
cients of the simple soiutions. Inthe case of moderately dilute solutions they will be 
determined by both sources of error. In the case of dilute solutions neither source of 
error will have so large an effect on the result. Hence a regular progression of the e’s 
the same in kind, may be expected in different series of mixtures of strong solutions of 
two given electrolytes; a regular progression may be expected also in series of moder- 
ate dilution, but since the error due to inaccurate drawing of curves will depend on the 
portion of the curve which is used, it may be different in kind for different series; and 
in sufficiently dilute solutions no regular progression is likely to occur, The most of 
Mr. Barnes’ series are of moderate dilution, and in all of them the e’s show a regular 
progression of the same kind, as they would if the errors involved did not conflict in 
sign, or if the error due to the one source were large relatively to that due to the other. 
His series of dilute solutions exhibit the same progression in the e’s, but they consist of 
only two mixtures each. In my calculations of the conductivity of mixtures of 
NaCland KCl solutions (Trans N.S. I. S., 9, 116), the three more concentrated series 
showed a progression of the e’s of the same kind, the two weakest series showed no 
progression. In Mr. McIntosh’s calculations (Jbid.. 9, 132), for HCl and NaCl, 
the two stronger series gave a progression of the same kind, the weakest no progression, 
And in Mr. Archibald’s caleulatiens ([bid., 9, 299), for KygSO4 and NagSO, solutions, the 
four stronger series gave progressions of the e’s, differing in kind, and the three series 
of weaker solutions gave either a very doubtful progression or no progression at all, 
All these results are thus consistent with the assumption that this regular progression in 
the e’s is due ma nly at least to the two sources of error mentioned above. Ae (Ge Mil 
