36 THE SCIENTIFIC PAPERS OF 



lines denote the pressure in Ibs. per square inch, and the figures 

 on the side denote volumes of air, as compared with the volume 

 of the same weight of water. The curve a a a represents 

 Marriotte's law, and is a curve of equal heat. The curve b b 1) is 

 the dynamical curve, representing the real rate of expansion of 

 air, behind a working piston. The difference between the two 

 curves arises from the loss of sensible heat, which is converted 

 into effect. The figures upon the curve show the rate of pro- 

 gression of temperature, in compressing air of atmospheric 

 pressure at 60 Fahr. 



In constructing this curve, the specific heat of air at constant 

 volume has been taken at '267 as determined by Delaroche and 

 Bernard. It furnishes itself at least an approximate proof of the 

 correctness of this number, because the curve agrees with the ob- 

 served fact, that in compressing air, to double its original 

 pressure, its temperature is raised 70 Fahr. The dotted hori- 

 zontal lines limit the uniform fields of power obtained for every 

 10 decrease of temperature. This curve is directly applicable to 

 air, which when reduced to atmospheric pressure has a temperature 

 of 60 Fahr. It can, however, easily be corrected, for any degree 

 of temperature, by adding the difference of temperature at a 

 corresponding pressure throughout, and by adding to each volume 

 the same difference of temperature, divided by 508 (the ratio of 

 expansion of air at 60 Fahr.) * 



Secondly. " On the performance of actual engines, including 

 the air-engines of Stirling and Ericsson." 



* The dynamical theory of heat must not be considered the creation of the last 

 few years, but, like all abstract truths in nature, it seems to have presented itself 

 to the minds of the greatest philosophers in all ages, to be, after them, again 

 superseded by theories moulded, as it were to order, to explain some isolated 

 phenomenon, such as the radiation of the sun, the heating flame of a fire, or the 

 latent heat in steam ; until at length the means of observation were sufficiently 

 perfected to cover with absolute proof, what could before be reached only by the 

 imagination. It may here be mentioned, as instances, a quotation by Baron 

 Humboldt from Aristotle, " who considered the first principle in nature to be a 

 unity in all its manifestations, and the manifestations themselves he reduced 

 always to motion as their foundation." Again, in Lord Bacon's Aphorisms, the 

 chapter on "The first Vintages of the Force of Heat," occurs the following 

 remarkable passage : "From the instances taken collectively, as well as singly, 

 the nature whose limit is heat, appears to be motion." And further on, " But 

 that the very essence of heat, or the substantial self of heat, is motion, and 

 nothing else limited,'' <fcc., &c. Bacon fails, however, in his attempts to prove 

 his philosophy, in confounding the visible motion of heating water, or of fire, 

 with the intrinsic motion of the particles that manifests itself as heat. 



