and on Astronomical Refractions. 



565 



J IT ad\ = pa{l+c) —p'a{l' + c) 



+ a{l> + c) j5;(^_i) logS ^ 



for the values of the constants E, y. See p. 511. 



To this must be added the work effected during the course of the 

 piston through I', which is p' a I, and if R is the total pressure ex- 

 erted upon unity of surface of the piston 



pa {I -\- c) —p' ac 



+ a{li + c) {p' y - Ep') 



= aRl 



E{y-l) 



\og< 



y—\- 



1 -Ep^ 



y-~\ 



.1 - Ep' ^ . 



(A)* 



-R ^= (1 + S) r+ jj" +^yis the friction of the machine not loaded, 

 I the increase of this friction due to unity of the charge r, jo" the 

 pressure on the surface of the piston, representing the atmospheric 

 pressure when the machine works without condensation, and other- 

 wise the pressure of condensation in the cylinder. 



If S denote the volume of water converted into vapour by the 

 boiler in unity of time, this volume in the cylinder becomes 



SK 



p' y —Ep' 



K being the same constant as in p. 563. 



It is evident, according to the reasoning of M. de Pambour, in 

 p. 125. of his work, that \^v denote the velocity of the piston 



SK 



= —v.a- 



I' + c 



(B.) 



/y — 



Ep' 



* This equation is equivalent to the equation (A) of M. de Pambour, p. 123, which 

 may be put into the form 



pa{l-Jrc)-p'ac-\--- Nap. log {^TX^} = a E I. 



or pa(l^ c) - p'ac + [6-9505960] - log P±S\^aIiL 



t) \. I -\- c J ' 



the pressure being reckoned in lbs. per square inch. 



