40 
Steam Engine, 
the equation just preceding the table, which is more sim- 
ple than that of Bettancourt, as representing the pheno- 
mena and measuring the effects of the expansive force of 
the steam of water with all desirable accuracy. M. Pro- 
ny remarks, that the smallness of the coefficient m, will 
allow the term to be neglected in reckoning be- 
tween 0° and 80® ; and thus from the temperature of ice up 
to that of boiling water, the equation of two terms alone 
will suffice, that is to say y=m^^ r^^^+m^^^ 
M. Prony’s equation for the vapour of alcohol compri- 
ses 5 terms originally : but in most cases tliree of those 
terms will give results sufficiently accurate. The nume- 
ral values of the coefficients are as below : 
r, = IT 1424 - - 
r,, = 1*05714 - - 
r,,, == 0*79943 - - 
=~.0’0021293 - 
772., = +0*9116186 - 
772.. ,= +0*2097778 - 
niiy= ^ 1*1 192671 
log. r, = 0*04697771 
log. r„ = 0*02413079 
^/// = T9027776 
log. 772, = "T3282330 
log. 772,, == T9598132 
log. 772,,, = T3217595 
These numbers cause the experiments and calculus to 
coincide very nearly, when introduced into the equation 
^ = 772, r,-^+772„ r„^+7?2,„7*,„'^+772iv. 
The magnitude of the anomalies will be seen by in- 
specting the following talkie. 
Vol, IL G 
