1893 - 94 .] Prof. Tait on Compression of Ordinary Liquids. 289 
coincide. The first cuts the axis of x at h and cajic + a), the second 
at a and hcfh + c), so that the second lies wholly within the first 
while y is negative. They intersect in the single point whose 
abscissa is abcl{ah-\- hc + ca). These parabolas are shown in the cut 
opposite. 
The values of yjq are the ordinates of the chief curve. This has 
three asymptotes : — two parallel to y, and cutting xat a and bc/(b + c) 
respectively; and the third at a constant distance, 2T712, from the 
axis of X. Its maximum ordinates are given by the equation 
or 0 = (ab -hbe + ca)x^ - 2abc x . 
Thus the maximum (at A in the cut) is on the axis of y ; and the 
minimum (at P>) corresponds to x = 0‘6321. Their values are 2 ’228 
and 2 '8 16 respectively ; and the ordinate of the point of intersection 
of the construction-parabolas lies midway hetw^een them. 
Thus, since the minimum numerically exceeds the maximum, the 
curve has no ordinate intermediate to these values ; and therefore 
no selection of real constants can make Yan der Y^aals’ equation 
applicable to a liquid in which the pressure, required to reduce its 
volume by 10 per cent., exceeds that required for a 5 per cent, 
reduction, in any ratio between 2 '2 2 8 and 2 ’8 16. 
Moreover, in accordance with what has been said above about the 
term A/?;^, it is only while the ratio of pressures exceeds the higher 
of these limits that this term represents a pressure, and not a 
tension. For the graph of Ajq in terms of /5 is easily seen to be a 
rectangular hyperbola whose asymptotes are parallel to the axes ; 
cutting X at bcjib -f c), and y at b’^d^fb^ — c^). The curve cuts x at 5, 
and so its ordinates are positive from bcjib + c) to &, only. 
VOL. XX. 
23 / 7 / 94 . 
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