The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

PROBL. VIII. By the Line of Segments on the Rod or Staff, and also by a Table, How to find the Quantity of Liquor in a Cask that is part full.

SUppose you would know the Quantity of Liquor in a Cask whose depth at the Bong is 23 Inches, as before, and let the Liquor be in height 16 Inches, and the whole Cask to hold 44 85/190 Gallons.* 1.1

By the Line of Numbers on the Staff, the proportion will be, as the whole depth 23 Inch∣es is to the depth in Liquor 16 Inches, so is 1000 to 692 parts.

Which being sought for in the Segment-line on the Staff, you shall have in the Line by it 46 15/1••0 Gallons.

Now if you extend the Compasses from 63 to 46 75/100 Gallons; the same distance will reach once from 44 85/100, the Contents of the whole Cask to 33 6/10, that is, 33 6/10 Gall. of Wine in the Cask.* 1.2

Then by this Rule always as 63 Gallons is to 46 75/100 Gallons, so is 44 85/100 Gallons to 33 60/100 Gallons of Wine in the Cask.* 1.3

By the same Rule Work for Beer or Ale.

To Work this Arithmetically is somewhat tedious; wherefore I have here Calculated a Table whereby you may perform it very easy by help of the Rule of Three.

Example.* 1.4

In the last Vessel whose depth at the Bong is 23 Inches, and depth in Liquor 16 Inches

The first Rule of Proportion.

As 23 is to 16, so is 10000 to 69 21 parts, which sought for in the nearest Number in the table of Segments you shall have against it 46 75/100 Gallons nearest.

Then again.

As the whole Radius 63 Gallons is to 46 75/100, so is the Gage of your Vessel 44 85/100 Gallons to 33 54/100 Gallons near, as before.* 1.5

After this manner of Working you shall have for 7 Inches depth of Liquor 11 22/120 gallons.

And so by these Rules you may work for any other Cask.

Notes

• * 1.1

  See Figure 107 ☜
• * 1.2

  33 − 6/10
• * 1.3

  This table is made to ½ or 50/100 parts of a Gallon: by same Rules you may make him Quarts or Pints.
• * 1.4

  The top or Bong is up∣permost in the Column to the left hand 63 Gal. the bottom is ½ to the right hand Colum.
• * 1.5

  23 − 7:10000 to 3049

  3043 answers 15:76/100

  63; 15.76 so 44 85/290 = 11 22/100 Gall.