W. J. M. Rankine on the Mechanical Action of Heat. 65 
Let H represent the mechanical equivalent of total heat expended ; 
, the motive power developed ; i 
t”, the absolute temperature at which heat is received by the 
elastic substance which works the engine ; 
t,, the absolute temperature at which heat is given out ; 
Then the efficiency of the engine is 
tT, 
aera 
This formula is ascribed by Professor Barnard to Professor 
William ‘Thomson of Glasgow. 
' The formula originally proposed*by Professor Thomson is, 
however somewhat different in form from the above, being the 
following : 
1 4h 
qelse of Baty ss - ee 
where « is the base of Napier’s logarithms; J, ‘ Joule’s Equiva- 
lent” = 1390 foot-pounds per centigrade degree in liquid wa- 
ter; and w, “Carnét’s Function;” being an unknown func- 
tion of temperature only, which has to be determined by ex- 
periment. 
wtea'eh Te peeckged weed ace rad cee aed 
receives and emits heat, divided by the greater of those absolute 
temperatures diminished by a constant which is the same for all 
substances ; that is to say, 

Ww 1 —T, : C. 
HW — # . Z . - ( ) 
The constant x, if not absolutely inappreciable, is so small that 
NO material error in practice can arise from neglecting it in com- 
9 
Soon Sznizs, Vol. XVII, No. 52.—July, 1854. 
