ELECTRICAL CONDUCTIVITY OF CERTAIN SALINE SOLUTIONS. 63 
of temperature on the position of the point of minimum resistance. This 
would form an interesting subject of inquiry. 
The above table is given graphically in fig. 2. Excess of density over 
unity is measured along the horizontal ordinates (OX in sketch) ; specific 
resistance along vertical ordinates (OY). 
The curve from the axis of Y to the point of minimum resistance M, we 
find to be an hyperbola, but not rectangular, as BecquEreEL’s formula would 
make it, the lower asymptote DH not being horizontal, but inclined as shown. 
The vertex corresponds to a solution of density 10785. And further, the other 
part of the curve, from M to the point of saturation, is symmetrical with the 
first part about a vertical line passing through M. These two facts enable us 
to give a definite formula, connecting the conductivity and density of solutions 
of this salt. 
If we call 6 the angle of inclination of DH, @ the intercept of DH on the 
axis of Y = OD, we have, since the curve is an hyperbola from Y to M, 
xsecO(y —h —ax tan 0) =e (a constant) ; 
or, generally, 
= a+ be + 2 
y=atbr+—, 
a, b, and ¢ being three constants which can be determined by substituting three 
sets of known values of z and y. Inthe case of this curve, we obtained a and 6 
from actual measurement. In finding 0, the tangent of the angle of inclination 
of the asymptote, in this way, care must be taken to assign to the measured 
lengths in fig. 2 their true values, according to the scales employed. This 
being done, we find that tan @ or d is 16, and fh, or a (the intercept), is 14:4. 
Substituting these values in the above equation, and then finding c, the only 
remaining constant, by means of a known pair of values of # and y, we have 
y= 144+ 160 429°. 
To make this formula more convenient, we may write the density instead of the 
excess of density over unity. Thus— 

ve ae 2-66 
R= 144 + 16(D N+p-4> 
or 
i 2°66 
R=16D+5, ae ue 
where R is the specific resistance and D the density, at 10° C. 
This equation, of course, applies only to the left hand part of the curve 
VOL. XXVII. PART I. R 
