358 
BIGELOW. 
caloric. Carnot knew that heat and work were transform¬ 
able quantities, but, supposing that heat is an indestructible 
substance, he never went beyond the incorrect statement that 
heat is equivalent to the work done. He did not know about 
the entropy function, which connects the quantities of heat 
energy and work energy. Clayperon followed Carnot's error, 
and the differential equation which they adopted as funda¬ 
mental is erroneous, since they supposed they were dealing 
with a true differential, which was not the case. Carnot in¬ 
troduced the fruitful idea of reversible and irreversible cycles; 
Clayperon used the indicator diagrams to measure the value 
of the work expenditure in a complete reversible cycle. To 
Clausius and W. Thomson (Lord Kelvin) belongs the credit 
of the discovery of the entropy function and the analytic 
form of the same. Clausius first used the word entropy in 
1865, but the idea was complete in 1855. Thomson began 
his work on this subject with Carnot's idea, but in 1850 aban¬ 
doned that view of the relation of heat and work. First he 
defined the absolute temperature, then he relinquished 
Carnot's statement that in doing work heat as a substance 
does not lose in quantity, but only in aspect, and accepted 
Clausius , proposition that heat is a molecular movement, 
which in doing work loses quantity as well as changes in 
aspect. Carnot had, however, this correct idea, that the kind 
of medium through which the work is done is not essential, 
but only the initial and final temperatures, for otherwise 
perpetual motion would be possible. Clausius admitted that 
the small changes in the intrinsic energy, the heat energy, 
and the work energy are not true differentials, but only 
small variations. 
A W 6 — & 
Thomson reaches the relation, -ft- = - J —-— 2 where A is 
Ai '2 
the mechanical equivalent of heat; 
W is the work performed ; 
Q 2 is the heat transformed at the higher temperature, 
being the lower temperature. 
