178 
ME. MACQUOEIs" EA1^KI^^: ON THE THEEMO-DYNAmC THEOET 
cylinder and finishes in a larger, the usual practice is to have steam-jackets round both 
cylinders ; but in a few examples in which the smaller cylinder alone is jacketed, the 
liquefaction is found to be almost wholly prevented, shoeing that the steam during its 
passage from the smaller to the larger cylinder receives sufficient heat, either directly 
from the small cylinder or indirectly by conduction from the smaller to the larger 
cylinder (which is in close contact with the small cylinder), to prevent any appreciable 
portion of it from condensing. 
The only exact formulse hitherto published for the work performed by the steam on 
the piston, viz. those contained in a paper on thermo-d)mamics by the author of this 
paper, which was received by the Royal Society in 1853 and published in the Philoso- 
phical Transactions for 1854, and those contained in a paper by Professor CiArsirs. 
published in Poggendoeff’s ‘Annalen’ for 1856 (the same results haring been inde- 
pendently arrived at in both papers), are adapted to cylinders without steam-jacMs. 
It is obviously desirable that exact formulae should be deduced from the principles of 
thermo-dynamics, for the action of steam in jacketed cylinders also; and the present 
paper is intended to supply that want. In the first place, those fundamental equations 
of thermo-dynamics, to which it is afterwards necessary to refer, are biiefiy recapitulated: 
then the exact formula for the action of steam, and the corresponding expenditm-e of 
heat, in jacketed cylinders are deduced from them, and exemplified b) numeiical 
results : — then is explained a convenient approximation to the exact formulae, founded 
on the facts, that within the limits usual in practice, the pressme of satmuted steam 
varies nearly as the seventeenth power of the sixteenth root of its density ; and that the 
expenditure of heat in a jacketed cylinder is nearly equal to fifteen and a half times the 
product of the initial pressure and volume of the steam: -and, lastly, ai-e ghcii 
examples of the application of the formulae to the engines of three steam-vessels recently 
experimented on by the author, and a comparison of the results of the formulte uith 
those of experiment. 
Summary of 'premously-lcmwn Principles and Formulce. 
The following is the Genekal Equation op Theemo-dynamics which has been known 
since 1849-60^: — 
( 1 -) 
H denotes the quantity of heat which must be communicated to a mass ot matter m 
order to make it undergo a given series of changes of volume and elastic pressure, 
expressed iv. foot-pounds of energy, of which 772 are equivalent to one degree ot Faurex- 
HEiT in one pound of water, as proved by Mr. Joule 
t is absolute temperature, reckoned from the absolute zero which corresponds to total 
privation of heat. It has from the first been conjectured that the scale of absolute 
temperature coincides with that of a perfect-gas thermometer, the absolute zero being 
Ediubiirgli Tnuisactions, vol. xx.; aud PoGGE>'DOKFr s ‘Annaleu, 1850. 
t Philosophical Transactions, 1850. 
