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.

SECT. XXXV. How to find the Right-Line, or Right-Range of any Shot discharged out of any Piece, for every elevation by one Right or Dead-Range given for the Piece assigned.

FIrst, you must have the help of this Table of Dead-Ranges,* 1.1 which was made by Experience of Mr. Norton, and the Table of Point-blanks, or Right-Ranges, was the same Shots in a Right-line at every degree of Mounture, as this Table is the Dead-graze of the Bullet at the same Shot with the same Gun, for he made 200 Shots for tryal.

Now although it be a thing very difficult, and likewise uncertain to arrive herein to exactness, without some Experiments made with the assigned Piece and Powder; yet to come to a necessary nearness at first, far surer than by uncertain guessing by this Table, or by my Scale, and the Rules therein directed.

As for Example.

Admit you were to seek the Right-Range of a Bullet, that the Piece was fired at 30 degrees Mounture, and the Dead-Range of the Bullet was known to be 2200 Paces.

2200 × 693/2150 = 710 Paces.

A Table of Pro∣portion of Dead-Ranges.

Degr.	Paces.
0	192
1	298
2	404
3	510
4	610
5	722
6	828
7	934
8	1044
9	1129
10	1214
11	1296
12	1394
13	1469
14	1544
15	1622
16	1686
17	1744
18	1792
19	1849
20	1917
25	2013
30	2150
35	2249
40	2289
42 ½	2296
45	2289
52 ½	2283
60	1792

Or look in this Table of Dead-Ranges against 30 degrees is 2150)	333243
And the Dead-Range given or known for 30 degrees to be 2800 Paces.	334242
The Number against 30 degrees in the first Table of Point-blanks 693	284073
The Sum	618315
Gives the Logarithm of 710 Paces for the Right-Range of	285072

The Bullet carryed violently in a Right-Line at 30 degr. Moun∣ture.

But admit the Level Right-Range is given, and the Right-Range of 30 degrees Mounture be sought.

Work by these Rules.

The Logarithm of Point-blank 0 degr. is 192	228330
The Num. against 30 d. is 693 in the Table Point-blank	284073
The Level Right-Range of this Piece is 197 Paces	229446
The Sum	513519

Gives the Log. of 711 Paces for the Right-ranges required 285189

And as the Numbers are in the Logarithm, so you may do by the Line of Numbers.

693 × 197/192 = 711 Paces the Range in a Right-Line.

Notes

• * 1.1

  You may make use of this Ta∣ble by the same Rules in the 32 Sect. and Table of dead-ranges,