Practical applications of the Heat Theorem

Practical Application of the Heat Theorem—As a practical rule for the application of our Heat Theorem we have made use on page 81 of a method of expressing the equations 

It was pointed out that the expression following the sign of integration was to be integrated indefinitely, and the upper limit to be introduced into the expression so obtained. 

It has been objected by a very eminent mathematician that this method of writing it is not compatible with the nature of integration it is quite easy to put the matter right, but, on the other hand, the rule for calculation given by formula (30) is perfectly correct in its operation, so that it appears to me to be not unsuitable. It may readily be seen from a simple example, such as formula (41), that no lower limit can be indicated for the integral of equation (39). 

As Professor Byk was kind enough to inform me, and as may readily be checked, the expression  

In 1915 Gans and Pereyra Miguez,f on the one hand, and Dragert on the other, independently and simultaneously described an apparatus which depends on the construction described on page 84, and draws the A-curve automatically, when the U-curve is traced from the absolute zero with the pointer of the apparatus. Particular attention may be drawn to this very ingeniously contrived thermodynamical integrator. 

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The assumption that all specific heats (even those of gases) become negligibly small near the absolute zero appears to have been so well established both by theory and also, in so far as it was possible, by experiment, that no serious objection is now likely to be raised against it. Thus every distinction between the above conceptions has now disappeared for the practical applications of the Heat Theorem, in which only changes of entropy are concerned, none has ever existed. 

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