16 ROYAL SOCIETY OF CANADA 
Let A B or A B’ be the true curve showing the relation of equiva- 
lent depression (0) to ionization coefficient (@), for a given electrolyte. 
Such curves sometimes bend in the one way sometimes in the other. If 
A C have the length unity, the point A will indicate extreme dilution. 
With the true values of k and J, applicable at extreme dilution, and with 
true values of the ionization coefficients, the line 6 = k (1—a) +la 
will be A #, the tangent to A B or A B’ at A. Since for a = i, 6 = l, 
the line A D must have the length /; and since for a = 0, 6 = k, the 
line O Æ must have the length %. With observations ranging in 
dilution from P to Q or P’ to Q’ and affected by errors, the line 
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3 
determined will be say A’ #’ or A’’ #”’ instead of A H. The value we 
obtain for k will thus be the length of O #’ or O E”', and for / the length 
A' Dor A" D. Obviously if P Q or P’ Q’ is not far from À, / will in 
general be determined with a much closer approximation than k, and the 
error in its determination will be smaller the more dilute the solutions on 
which observations are made and the more accurate the observations. 
Unfortunately owing to the wide limit of error in measuring the 
depression in very dilute solutions, it is not possible to use observations 
corresponding to parts of the curve in the immediate neighbourhood of A. 
The fact also that in drawing the experimental curves, we must use 
electrically determined ionization coefficients may possibly introduce 
another source of error of appreciable magnitude ; but at the dilutions at 
which it is possible to make trustworthy depression observations the 
error due to the difference between electrically determined coefficients 
and actual coefficients will probably be small. 
While therefore the determination of even the depression of the free 
ions, per gramme-ion, from the value found for J, may be affected by 
a considerable error, it is worth while to find what it would be in the 
