The smoothing of curves

2 This paragraph will be better understood after Chapter V., 106, has been studied. The reader may then return to this section. 

One of the commonest methods of smoothing a curve is to pin down a flexible lath to points through which the curve is to be drawn and draw the pen along the lath. It is found impossible in practice to use similar laths for all curves. The lath is weakest where the curvature is greatest. The selection and use of the lath is a matter of taste and opinion. The use of French curves is still more arbitrary. Pickering used a bent spring or steel lath held near its ends. Such a lath is shown in statical works to give a line of constant curvature. The line is called an elastic curve (see G. M. Minchin s A Treatise on Statics, Oxford, 2, 204, 1886). 

The vapour pressure of a solid increases continuously with rising temperature until, at its melting point, the vapour pressure suddenly begins to increase more rapidly than before. This is shown graphically in Fig. 60. The substance melts at the point of intersection of the solid and liquid curves. The vapour pressure itself is not discontinuous. It has the same value at the melting point for both solid and liquid states of aggregation. It is, however, quite clear that the tangents of the two curves differ from each other at the transition point, because 

There are two tangents to the jp0-curve at the transition point. The value of dp/dO for solid benzene, for example, is greater than for the liquid. The numbers are 2 48 and 1 98 respectively. 

Critical temperature. Cailletet and Collardeau have an ingenious method for finding the critical temperature of a substance without seeing the liquid.1 By plotting temperatures as abscissae against the vapour pressures of different weights of the same substance heated at constant volume, a series of curves are obtained which are coincident as long as part of the substance is liquid, for the pressure exerted by a saturated vapour depends 

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