156 MR W. J. M. RANKINE ON THE 
The following are some additional values of the constant a for steam, corre- 
sponding to various units of pressure used in practice. 
Units of Pressure. Values of a. 
Armospueres of 760 millimétres of mercury, 
= 29-922 inches of mercury, 
=14°7 lb. on the square inch, 
=1-0333 kilogrammes on the square centimetre, . : 4950433 
Armospueres of 30 inches of mercury, 
=761:99 millimétres, 
= 14-74 Ib. on the square inch, 
=1-:036 kilogrammes on the square centimétre, < 4:949300 
Kilogrammes on the square centimétre, . : : : : : 4:964658 
Kilogrammes on the circular centimétre, : : : : : 4859748 
Pounds avoirdupois on the square inch, ; : ; : : 6117662 
Pounds avoirdupois on the circular inch, - : : : : 6012752 
Pounds avoirdupois on the square foot, : - ; : : 8276025 
All the numerical values of the constants are for common logarithms. 
Section ].—Or tue Muruau Conversion oF Heat anp Expansive Power. 
(1.) The quantity of heat in a given mass of matter, according to the hypo- 
thesis of molecular vortices, as well as every other hypothesis which ascribes the 
phenomena of heat to motion, is measured by the mechanical power to which that 
motion is equivalent, that being a quantity the total amount of which in a given 
system of bodies cannot be altered by their mutual actions, although its distribu- 
tion and form may be altered. This is expressed in Equation XII. of the Intro- 
duction, where the quantity of heat in unity of weight, Q, is represented by the 
height sy , from which a body must fall in order to acquire the velocity of the 
molecular oscillations. This height, being multiplied by the weight of a body, 
gives the mechanical power to which the oscillations constituting its heat are 
equivalent. The real specific heat of unity of weight, as given in Equation XIII. 
of the Introduction, 
qQ _ 8k 
dz 2Cnp 
represents the depth of fall, which is equivalent to one degree of rise of temperature 
in any given weight of the substance under consideration. 
We know, to a greater or less degree of precision, the ratios of the specific 
heats of many substances to each other, and they are commonly expressed by 
taking that of water at the temperature of melting ice as unity; but their actual 
mechanical values have as yet been very imperfectly ascertained, and, in fact, the 
data necessary for their determination are incomplete. 
(2.) Mr Jou.x, indeed, has made several very interesting series of experi- 
ments, in order to ascertain the quantity of heat developed in various substances 
tl 
