158 Prof. Barnard on the Elastic Force of Heated Air. 
making p’=p, and e=3, gives 6=41, which is the amount of heat 
to be added to t to expand the air-at the constant atmospheric — 
pressure from density 1 and temperature 509° to density ?. ‘The 
air at discharge, therefore, will be a ea 1693° above 50° F., or 
at 219§° F'.—equivalent to an absolute temperature of 678%°, 
which we will represent by 7,. 
Mr. Joule now proposes that the air shall be compressed in the 
supply cylinder to one-fourth its original bulk, which will make 
its temperature 898°'59 (=439°-59 F.); and that the air so com- 
pressed may be expanded to the relative density 2, it must be 
oO. 
further heated S98 99 9990-53, making the total maximum 
temperature =1198°-12 (=739°-12 FE.) which we will represent 
by *’. The heat of compression, 898°'59, may. be put =”. 
By an application of the formula given on page 248 of the last 
volume of this Journal, we find the mean effective pressure of 
the engine working under these conditions to be 9:891 lbs. to the. 
square inch, The absolute pressure will be, in the mean time, 
105-92 lbs. 
It may be objected that Mr. Joule proposes to carry his heat 
extravagantly high. All that can at present be said as to this 
point is, that the difficulty with regard to a high temperature has 
hitherto been to reach it. It has not yet been ascertained what 
degree of temperature would be seriously injurious to the mate- 
rials of the machine. The great liability to loss of heat by radi- 
ation at these high temperatures, is a more serious consideration. 
ut Mr. Joule has undoubtedly placed his minimum tempera- 
ture too low. Sixty degrees of Fahrenheit, which is the usual 
temperature to which scientific determinations are. referred, is 
quite as low as we are justified in assuming the ordinary atmos- 
pheric temperature to be, in our estimates regarding a machine of 
this description. For though the mean temperature of the year 
may in northern latitudes be lower, yet as the engine is expected 
to work in all seasons, we ought rather to assume a temperature 
above the mean than below. 
If we adopt 60° as the atmospheric temperature, we shall have 
P (mean pressure) = 9°846 lbs. to the sq. inch, 
p (absolute press. )= 105-92 “ = as before. 
The conditions here supposed are highly favorable to economy 
of heat, and do actually convert into useful labor, as will present- 
ly be shown, forty-three and a third per cent. of the caloric im- 
parted to the air from the furnaces. They are not however alto- 
