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.

Example.

Suppose I know the Distance by my Map where the first Shot grazed to be 704 Paces, as you may see by the Figure out of the lowermost Gun of the Castle from S to the graze at A, the mounture of the Piece being 4 degr. how much must I mount the Piece to convey her Shot 900 Paces, as you may see by the Figure B the Gun, to C the Shots graze, or place required.

You must proportion these Distances of Random, to those in the Table following; saying, if 704 Paces require 370 Paces, as is in the Table at 4 degrees of Random, what number will be found against the degree in the Table; I must Mount the Piece unto 900, and work by these Rules.* 1.1

370 × 900/704 = 473

The Logarithm of the Shot made 704 is	284757
The Logarithm in the Table against 4 degr. is 370)	256820
The Logarithm of 900 Paces Random is	295424
The Sum is	552244

gives the Logar. of 473 Paces,* 1.2 which I look for in − 267487 the Table of Randoms, but find no such number there, but the next less is 461, and the next greatest is 550 against 7 degrees, the difference between these two Numbers, is 44 and 461 is 12 less than 473, and 12 is almost the one fourth part of 44,* 1.3 and therefore it shews that the Piece must be mounted at 6 degr. 15 min. or one Quarter to reach the Distance of 900 Paces as from B or b to C.

A Table of the proportion of dead Ran∣ges.

Deg.	Randoms.
0	206
1	225
2	274
3	323
4	370
5	416
6	461
7	505
8	548
9	589
10	630

Here is a Table of Randoms that was made out of the fore-named Saker of 8 Foot long, and loaded with 3 Pound of Powder, and every Gunner is advised, if possible, to get Powder, to make one by his own experience, and always to keep some of the same Powder to try his Proportions by; the Rule in the 24 Section by any other Powder he shall have occasion to use, for this is 1 of the material things belonging to a Gunner, without which knowledg hee an never make a good Shot; for at the time of a Leagure he must expect often to change his Pow∣der, as sometimes you shall have 9 Pound of one sort as good as 15 of another sort, as by Instrument and Shooting you may have expe∣rience.

Notes

• * 1.1

  Extend the Compasses from 704 to 370, the same will reach from 900 to 473.
• * 1.2

  505

  461

  44
• * 1.3

  505

  473

  32