72 Royal Society : — 



forraulaa for the work of steam which is supplied during its expan- 

 sion with just enough of heat to prevent any appreciable portion of 

 it from condensing, for the expenditure of heat in producing and 

 using that steam, and for its efficiency in producing motive power. 



There is explained a convenient approximation to the exact for- 

 mulae, founded on the facts, that for initial pressures of steam of 

 from 30 to 120 lbs. on the square inch {includimj atmospheric 

 pressure), and for ratios of expansion up to sixteen, the pressure of 

 saturated steam varies nearly as the seventeenth pov^er of the six- 

 teenth root of its density, and that the expenditure of heat in an 

 engine in which dry saturated steam is used, expressed in units of 

 energy, is nearlj' equal to Jifteen-ancl-a-half times the product of the 

 initial pressure and volume of the steam expended. 



Lastly, there are given examples of the application of the formulae 

 to the engines of three steam-vessels lately experimented on by the 

 author. The displacements of those ships are from 700 to 1100 

 tons ; the indicated horse-power of their engines from 226 to 1180; 

 the initial absolute pressures of steam in their cylinders range from 

 32 to 108^ lb. on the square inch, and the ratios of expansion from 

 4 to 10. In each case the difference between the results of calcula- 

 tion and experiment is within the limits of error of observation, and 

 ranges from -ji to y^ of the actual work of the steam. 



The author has computed Tables of the results of the formulae, 

 exact and approximate, which are now in the course of being printed. 



Summary of Formulae. — Notation and Constants. 



t, absolute temperature in degrees of Fahrenheit, = temperature 



measured from the ordinary zero -j- 4(il°'2. 

 jt, pressure in pounds on the square foot. 

 V, volume of one pound of steam in cubic feet, 

 'i' Pv ''i' '"^^^'^" ^^ ^^^^ admission of steam into the cylinder. 

 t.., p^, r.„ to the end of the expansion. 

 r=^v.,-h-i\, ratio of expansion. 

 ^)^= pressure of exhaustion. 

 ^,, absolute temperature of feed-water. 

 J, "Joule's equivalent," or specific heat of one pound of liquid 



water, =772 foot-pounds per degree of Fahrenheit. 

 W, work of one pound of steam. 



|t), expenditure of heat per pound of steam in foot- pounds. 

 rt=:l 109.550 foot-pounds. 

 6 = 540'4 foot-poiuuls per degree Fahrenheit. 

 Efficiency of steam, W-^?^. 



Exact Formulae. 



W=ahyp.log^ -b{t,-t.:) + v.J,p,-p,). 



?t)=«(H-hyp.log^)-^-fJ(^,-0. 



