
DYNAMICAL THEORY OF HEAT. PATE 
consequently render considerable alterations in my results necessary, I shall still 
continue to use Table I. of that paper, which shews the values of » for the tem- 
peratures 3,14,2} . . . 2303, or, the mean values of yu for each of the 230 
successive centigrade degrees of the air-thermometer above the freezing point, 
as the basis of numerical applications of the theory. It may be added, that any 
experimental researches, sufficiently trustworthy in point of accuracy, yet to be 
made, either on air or on any other substance, which may lead to values of pu dif- 
fering from those, must be admitted as proving a discrepancy between the true 
densities of saturated steam, and those which have been assumed.* 
35. Table I. of my former paper, which shews the values of ps ‘udt 
fort¢=1,t=2,¢=3, ... . t= 231, renders the calculation of the mechani- 
cal effect derivable from a given quantity of heat by means of a perfect engine, 
with any given range included between the limits 0 and 231, extremely easy; 
since the quantity to be divided by J + in the index of the exponential in expres- 
sion (8) will be found by subtracting the number in that Table corresponding to 
the value of T, from that corresponding to the value of S. 
36. The following Tables shew some numerical results which have been 
obtained in this way, with a few (contained in the lower part of the second 
Table) calculated from values of ie ‘udt estimated for temperatures above 230°, 
roughly, according to the rate of variation of that function within the experi- 
mental limits. 
37. Explanation of the Tables. 
Column I. in each Table shews the assumed ranges. 
Column II. shews ranges deduced by means of Table II. of the former paper, 
) 
so that the value of fr pdt for each may be the same as for the corresponding 
range shewn in Column I. 
Column III. shews what would be the duty of a unit of heat if Carnor’s 
theory required no modification [or the actual duty of a unit of heat with addi- 
* I cannot see that any hypothesis, such as that adopted by Crausrus fundamentally inshis 
investigations on this subject, and leading, as he shews, to determinations of the densities of saturated 
steam at different temperatures, which indicate enormous deviations from the gaseous laws of varia- 
tion with temperature and pressure, is more probable, or is probably nearer the truth, than that the 
density of saturated steam does follow these laws as it is usually assumed to do. In the present 
state of science it would perhaps be wrong to say that either hypothesis is more probable than the 
other. 
} It ought to be remarked that, as the unit of force implied in the determinations of is the 
weight of a pound of matter at Paris, and the unit of force in terms of which J is expressed is the 
weight of a pound at Manchester, these numbers ought in strictness to be modified so as to 
express the values in terms of a common unit of force; but as the force of gravity at Paris differs 
by less than 3755 of its own value from the force of gravity at Manchester, this correction will be 
much less than the probable errors from other sources, and may therefore be neglected. 
VOL. XX. PART II, 2F 
