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. X. How to Measure a Cone-Vessel, such as is a Spire of a Steeple, or the like, by having the Height and the Diameter at the Base.

SUppose the Diameter at the Base AB be 98 Inches, and the height DC 490 Inches.

Then by the Line of Numbers for Barrels of Ale or Beer.

Extend the Compasses from the Gage-point 169 9/10 unto the Diameter AB 98, the same will reach from the height of the Cone DC 490,* 1.1 turned twice over unto 121 4/10 Barrels ferè.

This is the best Proportion to Work for great Cones to have it in Barrels, but small Cones have it in Gallons.

Then thus Work.

Extend the Compasses from the Gage-point 32 82/100 unto the Diameter of the Base 98, the same will reach from the height of the Cone 490 twice turned unto 4369 547/1009 Gall.

The Arithmetical way. For Gallons.

ABq × DC / 1077 = 4369 547/1000 Gallons.

Which being divided by 36, you have 121 34/100 Barrels.

Or thus for Barrels.

ABq, XDC / 38772 = 121 347/1000 Barrels.

An Example.

The Brewers Tun before measured may be measured, after this manner by Cones, by this Example in this Figure I have proportioned the same Tun in this Cone, as you may prove thus by, the Rule of Proportion to find the Diameter on the top EF 90, it was before.

Work thus.

As CD 490 is to AB 98, so is CG 450 to EF 90 Inches; and so back again, to find the height of the greater Cone, say, as the difference of the Diameters 8 Inches is to the height of the Tun 40 Inches: so is the Diameter of the bottom AB 98 Inches to the greater height DC 490 Inches, from whence substract 40, there remains the height of the lesser Cone GC 450 Inches.

Now Working as before, for the Contents of each Cone.

The greater Cone will be found to be	4369 Gall.	547 Parts.
And the lesser Cone to contain	3384 Gall.	432 Parts.
Which substracted from the greater Cone, there remains 985 Gallons 115/1000 Parts.	985 Gallons	115/1000

For the Brewers Tun, as before found in the 9 PROBL. which is 27 Barrels 13 Gallons. 1/10

Notes

• * 1.1

  See Figure 109 ☜