The Second Book of the Cross-Staff

Chap. IV.
The use of the Line of Numbers in Gauging of Vessels.

The vessels which are here measured are supposed to be Cylinders, or reduced unto Cylinders, by taking the mean between the Diameter at the Head and the Diameter at the Bongue, after the usual manner.

1. Having the Diameter and the length of a Vessel with the Content thereof, to find the Gauge point.

Extend the Compasses in the Line of Numbers to half the distance between the Content and the length of the Vessel, the same extent will reach from the Diameter to the Gauge point.

I put this Proposition first, because these kind of measures are not alike in all places.

Here at London it is said that a Wine Vessel being 66 inches in length, and 38 inches in Diameter, would contain 324 Gallons, which if it be true, we may divide the space between 324 and 66 into two equal parts, and the middle will fall about 146, and the same extent which reacheth from 324 to 146, will reach from the Diameter 38 unto 17,15, the Gauge point for a Gallon of Wine or Oyl after London measure.

The like reason holdeth fro the like measure in all other places.

2. Having the mean Diameter, and the length of the Vessel, to find the content.

Extend the Compasses from the Gauge-point to the mean Diameter, the same extent being doubled, shall give the distance from the length to the content.

So the mean Diameter of a Wine Vessel being 20 inches, and the length 25, the Content will be found to be 34 Gallons after London measure.

For extend the Compasses from 17.15 unto 20, the same extent will reach from 23 unto 29.15, and from 29.15 unto 34.

In like manner, if the mean Diameter were 16 inches, and the length 23, the Content will be found to be about 20 Gallons.

For the same extent which reacheth back from 17.15 unto 16, will reach from 23 to 21,45, and from 21,45 unto 20.

So that if the mean Diameter shall be 17 inches and 15 Centesmes or parts of 100, the number of inches in the length of the vessel, will give the number of Gallons contained in the same Vessel: if the Diameter shall be more or less than 17,15, the Content in Gallons will be accordingly more or less than the length in inches.

3. Having the Diameter and Content, to find the length.

Extend the Compasses from the Diameter to the Gauge-point, the same extent being doubled, shall give the distance from the Content to the length of the Vessel.

So the gauge-point standing as before, if the Diameter be 38 inches, and the Content 324 gallons wine-measure, the length of the Vessel will be found about 66 inches.

4. Having the length of a Vessel, and the Content, to find the Diameter.

Extend the Compasses to half the distance between the length and the Content, the same extent shall reach from the Gauge-point to the Diameter.

So the length being 66 inches, and the Content 324 Gallons wine measure, the Gauge-point standing as before, the Diameter of the Vessel will be found to be about 38 inches.