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. I. The true Content of a Solid Measure being known, To find the Gage-Point of the same Measure.

THe Gage-Point of a Solid Measure is the Diameter of a Circle whose superficial Content is equal to the solid Content of the same measure; so the solid Content of a Wine-Gallon according to Win∣chester measure, being found to be 231 Cube-Inches: if you conceive a Circle to contain so many Inches, you shall find the Diameter thereof to be 17:15 by this Rule. Example. A Wine-Vessel at London is said being the 66 Inches in length, and 38 Inches in the Diameter, would contain 324 Gallons. If so, by the Line of Numbers we may divide the space be∣tween 324 and 66 into two equal parts, the middle will fall about 146, and that distance will reach from the Diameter 38 unto 17:15 the Gage-point for a Gallon of Wine or Oyl after London measure: the like reason holdeth for the like measure in all places. Thus likewise you may discover the Gage point for Ale-measure, an Ale-Gallon, as hath been of late discovered containing 282 Cubique-Inches; for as 1 is to 1:273, so is 282 to 356, 3 whose square-root is 18:95 the Gage-point for Ale-measure, because of Wast and Soil exceeding that of Wine above two Inches: or you may find it as before by the Content 256, 3 and the length 66, and the Diameter 38, as before. There are several other Rules to find it, but these may satisfy to save Prolixity, Mr. Phillips, and others, have found and proved by Example. That there is 288 ¾ Cubique Inches in an Ale-Gallon, which I believe is the Truth: But that which is received by Autho∣rity, are these sorts of measures, the Wine-measure is 231 Cubique Inches, and for Ale 282 Cubique-Inches or Beer; and for Drie things, as Corn 272 Inches. These Rules are undeceivable with Authority.

Therefore take notice you must be very careful in all your measures of all sorts of Vessels, their length, breadth, and dephth, as also of the Head and Bong; for all small Errours in them may increase too much in the Content: for the mistake of a quarter of an Inch in a large Vessel, may make you misreckon a Gallon in the Content; therefore how to be careful is best known to the Practicioner more than I can declare by many words.