Discontinuity accompanied by breaks

If a cold solid be exposed to a source of heat, heat appears to be absorbed, and the temperature, 0, of the solid is a function of the amount of heat, Q, apparently absorbed by the solid. As soon as the solid begins to melt, it absorbs a great amount of heat (latent heat of fusion), unac-companied by any rise of temperature. When the substance has assumed the fluid state of aggregation, the tem- 

1 Sometimes the word break is used indiscriminately for both kinds of discontinuity. It is, indeed, questionable if ever the break is real in natural phenomena. I suppose we ought to call turning points singularities, not discontinuities (see S. Jevon s Principles of Science, London, 1877). 

This function is said to be discontinuous between the points A and jB, and between C and D. Breaks occur in these positions. f 6) is accordingly said to be a discontinuous function, for, if a small quantity of heat be added to a substance, whose state is represented by a point, between A and B, or C and D, the temperature is not affected in a perceptible manner. The geometrical signification of the phenomena is as follows There are two generally different, tangents to the curve at the points A and B corresponding to the one abscissa, namely, tan a and tan a. In other words, see page 102, we have 

It is necessary to point out that the alleged discontinuity in the curve OABC may be only apparent. The corners may be rounded off. It would perhaps be more correct to say that the 

56 shows the result of plotting the variations in the volume of phosphorus with temperatures in the neighbourhood of its melting point. 

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