Page:Reflections on the Motive Power of Heat.djvu/278

third, or a quarter of the stroke. The piston completes its stroke, therefore, under a constantly diminishing pressure. The first engines working on this principle date from 1778. Watt conceived the idea of them in 1769, and took out a patent in 1782.

We give here the Table appended to Watt's patent. He supposed the steam introduced into the cylinder during the first quarter of the stroke of the piston; then, dividing this stroke into twenty parts, he calculated the mean pressure as follows:

Portions of the descent from the top of the cylinder.				Decreasing pressure of the steam, the entire pressure being 1.
	0.05	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right\}\,}$	Steam arriving freely from the boiler.	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	1.000	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right\}\,}$	Total pressure.
	0.10				1.000
	0.15				1.000
	0.20				1.000
Quarter.....	0.25				1.000
	0.30	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,}$	The steam being cut off and the descent taking place only by expansion	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$	0.830
	0.35				0.714
	0.40				0.625
	0.45				0.555	$\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$	Half original pressure.
Half........	0.50				0.500
	0.55				0.454
	0.60				0.417
	0.65				0.385
	0.70				0.375
	0.75				0.333		One third.
	0.80				0.312
	0.85				0.294
	0.90				0.277
	0.95				0.262
Bottom of cylinder...	1.00				0.250		Quarter.
			Total,		11.583
Mean pressure ${\dfrac {11.583}{20}}$ = 0.579.