ON THE MECHANICAL EQUIVALENT OF HEAT. 337 
in each of these expressions with the several absolute standards which exist for such 
factors. 
These standards are the standards of mass, length, and force, on the one hand, and 
of mass, quality of matter, and temperature, on the other. 
Thus, work being* defined as the mean product of force multiplied by the distance, 
and the standard of force being the force of gravitation on the unit of mass wherever 
it occurs, the work is represented by W.h, where W expresses the number of units of 
mass, and h the number of units of length through which it has been raised. Taking 
(M) and (L) as expressing these units, the unit of work is expressed as (ML). 
Again, the unit of heat is defined to be one part of that quantity which is 
required to raise one unit of mass (M) of a standard substance (pure water) from one 
definite state of temperature to another definite state. And calling this interval 6, 
the unit of temperature is defined to be Bln. And, taking S to express the ratio 
of the number of units of heat required to raise units of mass of matter from 
Ti° to T 3 ° compared with W„ (Tg® — T^®), the heat expressed by SW^ (Tg — T^) is in 
units (M 
e 
n 
So that, from the physical equivalence of the absolute energy expressed in the 
respective forms, it appears that the unit of heat, as defined by (M — j, is equivalent 
to 
27rNRW 
SW,(T3-L) 
units of work as defined by (ML), 
or that the heat required i o raise one unit of mass of pure water through the definite 
interval of temperature B is equivalent to 
27rNEW 
Qw rv -W units of work (ML). 
This is the definition ol’ the mechanical equivalent of heat in Manchester, adopted 
by Joule if n = i, and B is 1° Fahr. between 50 and 60, as determined on his 
thermometer. But, since the absolute kinetic value of the unit of force as here 
defined varies with the latitude and height of the place, while that of the unit of 
heat is constant, this mechanical equivalent varies from place to place with 1/p, 
where g is the expression, in kinetic units, for the unit of force (M). 
Thus, expressing the work in kinetic units, the unit of heat, as already defined, is 
equivalent to 
27rNRW 
^ SWATg - L) "" 
where the dimensions of C are (T/T“%0“^). 
VOL. CXC.—A. *2 X 
