264 PROFESSOR WILLIAM THOMSON ON THE 
8. The sowrce of heat will always be supposed to be a hot body at a given 
constant temperature, put in contact with some part of the engine; and when 
any part of the engine is to be kept from rising in temperature (which can only 
be done by drawing off whatever heat is deposited in it), this will be supposed to 
be done by putting a cold body, which will be called the refrigerator, at a given 
constant temperature, in contact with it. 
9. The whole theory of the motive power of heat is founded on the two 
following propositions, due respectively to JouLE, and to Carnot and Ciaustus. 
Prop. I. (Joute).—When equal quantities of mechanical effect are produced 
by any means whatever, from purely thermal sources, or lost in purely thermal 
effects, equal quantities of heat are put out of existence, or are generated. 
Prop. I. (Carnor and Craustus).—If an engine be such that, when it is 
worked backwards, the physical and mechanical agencies in every part of its 
motions are all reversed; it produces as much mechanical effect as can be pro- 
duced by any thermo-dynamic engine, with the same temperatures of source and 
refrigerator, from a given quantity of heat. 
10. The former proposition is shewn to be included in the general “ principle 
of mechanical effect,” and is so established beyond all doubt by the following 
demonstration. 
11. By whatever direct effect the heat gained or lost by a body, in any con- 
ceivable circumstances, is tested, the measurement of its quantity may always be 
founded on a determination of the quantity of some standard substance, which it 
or any equal quantity of heat could raise from one standard temperature to 
another; the test of equality between two quantities of heat being their capa- 
bility of raising equal quantities of any substance from any temperature to the 
same higher temperature. Now, according to the dynamical theory of heat, the 
temperature of a substance can only be raised by working upon it in some way 
so as to produce increased thermal motions within it, besides effecting any modi- 
fications in the mutual distances or arrangements of its particles which may 
accompany a change of temperature. The work necessary to produce this total 
mechanical effect is of course proportional to the quantity of the substance raised 
from one standard temperature to another; and therefore when a body, or a 
eroup of bodies, or a machine, parts with or receives heat, there is in reality 
mechanical effect produced from it, or taken into it, to an extent precisely pro- 
portional to the quantity of heat which it emits or absorbs. But the work which 
any external forces do upon it, the work done by its own molecular forces, and 
the amount bywhich the half cis viva of the thermal motions of all its parts is 
diminished, must together be equal to the mechanical effect produced from it; 
and consequently, to the mechanical equivalent of the heat which it emits (which 
will be positive or negative, according as the sum of those terms is positive or 

