PRINCIPLES OF THE MECHANICAL THEORY OF HEAT. 251 



Fig. 5. 



Let us now seek to determine the mechanioal power wliicli is required in 

 order to compress 2956 cubic inches of air, of atmospheric density, to a 

 21.G54-fohi density. For this purpose we will conceive the quantity of air 

 just mentioned to be contained in a tube a h, (Fig. 5, j which is supposed to 

 be 21.051 feet long-, and to have such a transverse section (H.37G square 

 inches) that the contents of 

 a portion of this tube one 

 foot long shall be equal to 

 the contents of the vessel A, 

 (13G.5 cubic inches) ; thus 

 the above compression will 

 plainly ensue if we force a 

 piston from the upper end a 

 down to the point c, which 

 is situated one foot above 

 the bottom of the tube. If 

 now lines be drawn at differ- 

 ent points of the tube per- 

 pendicular to its axis, and 

 of a length always propor- 

 tional to the pressure under 

 which the included air stands, 

 and if the piston be driven 

 to the })oint c, so that the line 

 c g shall be 21.G54 times as 

 great as a /, the curve / h i g, 

 which connects the terminal 

 points of the above lines, will 

 be a j)oi1ion of an equilateral hyperbola, and the hyperbolic surface a c g h J 

 will represent the power v»'hich must have been employed in pressing the piston 

 down from a to c. Let us denote gc hy y,h c by x, and h a by x'; thus the 



x' 

 contents of the surface in question will be H=a;- y- log nat- and if a;=l 



H=^ • log nat x', or 



11=2.2020, ■ y log x' . . . . . (1) 

 if log represent the common logarithm referable to 10 as a base. By the test of 

 experiment the barometer stood at 30.2 English inches, which makes on the 

 transverse section of our tube 1G8.5 pounds. The line fa thus represents to us 

 the pressure 168.5, bat g c the pressure 21.G54 X 168.5=3648.7. Let us nowput 

 in equation (1) a;'=21.654 and j/=3648.7 ; we shall thus have 



11=2.3026 X 3648.7 log 21.654=11220 foot-pounds, 

 as the expenditure of power which is required to compress 2956 cubic inches of air 

 of atmospheric density intoa space 21.654 times smaller, whereby, as has beensecu 

 3.437 units of heat are developed. 



Hence, according to these experiments, 3437 units of heat are the thermic 

 equivalent for an expenditure of power of 11220 foot-pounds, or 1552 kih)- 

 gram-metres. In order, therefore, to produce one unit of heat through compres- 

 sion of the air, an expenditure of poiver of 451 kilogram-metres is needed. 



For the purpose of measuring the absorption of heat which results from the 

 discharge of compressed air, the vessel A, after the air had been couipressed in 

 it to 22 atmospheres, was placed in a reservoir containing 21 pounds of water. 

 As the compressed air was now allowed to escape from the vessel A through a 

 leaden pipe, the temperature of the surrounding water was found to be lowered 

 4.°1 F. With due regard to all necessary correctiou.^, it may be hence com- 

 puted thattlie quantity of heat which disap})ears by the discharge of the air from 



