The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne.

Example.

As 1 to 60 the Inches in Diameter so is 60 to 3600: Again, as 1 to 3600 so is 36 the inches deep to 129600, the Square of the Diameter multi∣plyed by the depth in Inches.

Then lastly, first for Gallons say, as 1 to 0.2785, so is 129600 to 361 ferè, or else, if you please, to Barrels.

As 1 to 0. 775 so is 129600 to 10 Barrels, and a little more.

This Rule is for all Cylender-like round Vessels, but if the sides be streight and taper, then the usual way and somewhat neer the Truth is, to add the Diameters at the top and bot∣tom together, and to take the half for the mean Diameter, which when you have got, work as before.

Or else you may make use of the Gage-point, according to Mr Gun∣ter's way, which by Arithmatick is thus;

Multiply the mean Diameter by the length, and then divide that pro∣duct by 17.15 for Wine-measure, or by 18.95 for Ale-measure, and note the Quotient and his Remainder; A∣gain, Multiply the quotient last found, by the mean Diameter, and the Pro∣duct; divide again by 17-15 for Wine, or by 18.95 for Ale, and the Quotient shall be the Content in Gallons.

This way by the Line of Numbers is very quick and ready. Thus,

Extend the Compasses from the Gage-points either 17.15 for Wine, or 18.95 for Ale, to the mean Dia∣meter, the same extent being turned twice the same way from the length, shall reach to the content in Gallons.

The Extent from 18.95 to 60 be∣ing twice repeated from 36, the In∣ches deep shall reach to 361 ferè, the content in Ale Gallons.

Or if you would have it to Beer-Barrels, then say, as 35.96 the Gage point for a Beer-Barrel is to the mean Diameter 60, the same extent applyed twice the same way from the length, shall reach to 10.002, that is, 10 Barrels.

The Gage-point for an Ale Barrel which contains but 32 Gallons is 33. 91.