Page:Philosophical Transactions - Volume 004.djvu/170

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And if you suppose the Heads of such a Cask to be two Plains erect to the Axis, and alike remote from the Center, cutting off both ends of the figure produced, then, if the middle frustum,, so intercepted, , be computed as

											The Content in Wine Gallons is about
The	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$	Solid Zone	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,}$	of	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,}$	a	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	Sphæroid		$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,}$	126¼
								Parabolical			115½
								Spindle.
						two	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	Cones.	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,}$ Of the same base and height		110⅓
								Parabolical			112 8/10
		Trunci.						Conoids

the Method of Calculation being very easy by either sort of Tables, and of great affinity in all these figures. And whereas the Learned have commonly supposed, Cask to be the midle frusta of Spheroids, and given Rules accordingly for Gaaging them, those suppositions, as Vintners and others upon experience assert, are found too much to enlarge the Capacity, so that a Canary Pipe, that is reputed to hold about 126. gallons, upon Experiment hath been found to contain but 116. gallons: And to determine, what figure is most proper to be admitted, ought to be built upon such an Experiment as this;

Conceive a Caske to lye upon an Horizontal Plain with its Axis paralel thereto; and Perpendiculars on the outside of the smooth boards of the Cask to fall; from the Head, Boung, and some intermediate point between, upon the Plain or Floore; and in like manner the axis to be designed: Then find out such a curved line of some property, that may pass thorough the said Points, which conceive to have a rotation about the Axis-line: the round solid so made may be taken to represent the Cask; and in the Writings of Geometers divers Curves are to be found, that are capable of palling through such Points and their round Solids measured. But if the Reader think this too nice and troublesome, and that the Sphæroid way is too great, and the Parabolick spindle too little, then the Author gives scope enough between; showing how to contrive such Rules, as shall best agree with Experience.

II. HIS-