Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

SECT. I. Of Gauging any Beer, Ale, or Wine-Cask, also any manner of Brewers Tuns.

PROP. I. To find the Solid Content in Inches of any Cask.

I Shall follow Mr. Oughthred's method, which is, Take the Diameter of the Cask both at Head and Bung, by which find the Area's of their Circles, which done, then take two thirds of the Area of the Bung, and one third of the Area at the Head, which added together, shall be the Mean Area of the Cask; which multi∣plyed into the length of the Vessel, it will shew how many solid Inches are contained therein.

Example: Suppose the Diameter at the Head of a Vessel be 18, and at the Bung 32, and length is 40 Inches.

Now I find the Aggregate of the two Circles to be 620, and 989, Cubick Inches: which mul∣tiplyed by 40, the length, produceth 24839, 56/100 Cubick Inches, for the whole Content of that Cask in Cubick Inches.

PROP. II. To find the Content of a Vessel in Wine, or Ale Gallons.

The Wine Gallon is established by the Con∣sent of Artists, in these and other Nations, to contain 231 Cubick Inches* 1.1. Yet Dr. Wybard affirms it to be somewhat less, to wit 225, at most: The Ale Gallon contains 282 Cubick Inches, accor∣ding to the Establish∣ment of Excise. Here∣in Artists differ somewhat in their Experi∣ments.

Now having already shewed how to find the Content in Inches of any Cask, I now come to shew how to find the Content in Gallons, of any Beer, Ale, or Wine Cask, which is thus: Divide the Number of Inches given by 231, for Wine Measure, and 282, for Ale Measure. In the former Example I find the said Cask to con∣tain 107, 53 Wine Gallons, and 88, 8, &c. Gal∣lons in Ale Measure.

PROP. III. How to Gauge or Measure Brewers Tuns, &c.

Those Tuns are most commonly Segments of Cones or Pyramid, whose Basis is either a Square Parallelogram, Circle, or Oval; to measure which,

let their form be what it will you must do thus. By the former Rules of Measuring such Seg∣ments or Bodies, you must find their Solid Con∣tent in Cubick Inches, (as in prop. 3. §. 2. chap. 10.) which Content divide by 282 Inches, (the Inches in one Gallon) it sheweth the Content in Gallons, and dividing the Gallons by 36, (the number of Gallons in a Barrel) it shews the Content in Barrels.

Notes

• * 1.1

  See Mr. Oughthred in his Book of the Cir∣cles of Proportion, page the 57. and Mr. Edm. Gunter in his Book of the Cross-staff, part 21. chap. the 4.