SOLUTIONS. —MACGREGOR. 71 
(2.) As equation (2) may be written : 
Tt ING Ta 
Winwats Ne v= 
we may proceed as follows :— 
1 
Na 
Plot a new curve D 
(Fig. 2) with the same 
abscissee as A and B, 
but with ordinates 
equal to the sum of 
the ordinates of A and 
N,/N, times the or- 
dinates of B. Draw 
K L parallel to the 
ionic-concentration 
a/y axis and at a distance 
Fig 2 1/N, from it, and let 
Tey it eut Din L. Draw 
LQ parallel to the dilution axis and cutting A and B in 
Pand M respectively. P and M are the two points required. 
For they have the same abscissa OQ, and their ordinates, P Q 
and M Q), are such that 
0 
Nes 2 il 
2 2MQ = LQ=—. 
Q + N, Q Q N. 
Then GO 2 Os and-a,.— OOo M@: 
(3) Plot.a new curve 
E (Fig 3), having the 
same abscissze as A and 
B, but with ordinates 
equal to N./N, times the 
ordinates of B. Draw 
RS parallel to the axis 
of ionic concentrations 
and at a distance from 
ay it of 1/(2N,). Find, by 
inspection, the line TY 
parallel to the axis of 
