


DYNAMICAL THEORY OF HEAT. 281 
subjected to a uniform pressure in all directions, which lead to various remarkable 
conclusions. Such of these as are independent of Joutn’s principle (expressed by 
equation (2) of § 20), being also independent of the truth or falseness of Carnot’s 
contrary assumption regarding the permanence of heat, are common to his theory 
and to the dynamical theory; and some of the most important of them,* have 
been given by Carnor himself, and other writers who adopted his principles 
‘ and mode of reasoning without modification. Other remarkable conclusions on 
the same subject might have been drawn from the equation — ihe 0, express- 
ing Carnor’s assumption (of the truth of which experimental tests might have 
been thus suggested); but Iam not aware that any conclusion deducible from 
his assumption besides that which Carnor gives regarding the motive power of 
heat through finite ranges of temperature, has yet been actually obtained and 
published. 
45. The recent writings of Carnot and CLAustius contain some of the conse- 
quences of the fundamental principle of the dynamical theory (expressed in the 
first fundamental proposition above) regarding physical properties of various 
substances; among which may be mentioned especially a very remarkable dis- 
 ~ covery regarding the specific heat of saturated steam (investigated also in this 
paper in § 58 below), made independently by the two authors, and a property of 
water at its freezing point, deduced from the corresponding investigation re- 
garding ice and water under pressure by Cuausius; according to which he finds 
that, for each 75° cent. that the solidifying point of water is lowered by pressure, 
its latent heat, which, under atmospheric pressure is 79, is diminished by ‘081. 
The investigations of both these writers involve fundamentally various hypo- 
theses which may be or may not be found by experiment to be approximately 
‘true; and which render it difficult to gather from their writings what part of 
their conclusions, especially with reference to air and gases, depend merely on the 
necessary principles of the dynamical theory. 
46. In the remainder of this paper, the two fundamental propositions, ex- 
pressed by the equations 
dM qdN _1dp 
TEE So Te ST Ee . : . . (2) of § 20 
_1 dp 
and. M=7 7p BOF GAL, 
are applied to establish properties of the specific heats of any substance whatever ; 
and then special conclusions are deduced for the case of a fluid following strictly 
the “ gaseous laws” of density, and for the case of a medium consisting of parts 
* See above, § 22. 
VOL. XX. PART II. ; AG 
