The First Book of the Cross-Staff
The Cross-Staff, is an Instrument well known to our Seamen, and much used by the ancient Astronomers and others, serving Astronomically for observation of the Altitudes and Angles of distance in the Heavens; Geometrically for Perpendicular Heights and Distances on Land and Sea.
The Description and several Uses are extant in Print by Gemma Frisiess in Latine, in English by D. Hood. I differ something from them both, in the Projection of this Staff, but so as their Rules may be applied onto it, and all their Propositions be wrought by it; and therfore referring the Reader to their Books, I shall be brief in the Explanations of that which may be applied from their unto mine, and so come to the Use of those Lines which are of my Addition, not extant heretofore.
The necessary parts of the Instrument are Five; (1) the Staff; (2.) the Cross; And (3.) the three Sights. The Staff which I made for my own use, is a full Yard in lenght, so that it may serve for measure.
- Description of Lines
The Cross belonging to it is 26 Inches 1/5 between the two outward sights, If any would have it in a greater form, the proportion between the Staff and the Cross, may be 360 unto 262.
The Lines described on the Staff are of four sorts: One of them serves for Measure and Protraction; One for the observation of Angles; One for the Sea-Chart; and the other four for working of Proportions of several kinds.
The Line of Measure is an Inch Line, and may be known by ist equal quarts, the whole Yard being equally divided into 36 Inches, and each Inch subdivided first into ten parts, and then each theth part into halfs.
The Line for observation of Angles may be known by the double Numbers, set on both sides of the Line, beginning at the side at 20, and ending at 90: on the other side at 40 and ending at 180: and this beiong dived according to the degrees of the quadrant, I call it the Tangent Line on the Staff.
The next Line is the Meridian of a Sea-chart, according to Mercators Projection from the Equinictial to 58 gr. of Latitude, and may be known by the letter M, and the numbers 1, 2, 3, 4, unto 58.
The Lines for working of proportions may be known by their unequal divisions, and the number at the end of each Line.
- The Line of Numbers noted with the Letter N , divided unequally into 1000 parts, and numbered with 1, 2, 3, 4, unto 10.
- The Line of Artificial Tangents is noted with the Letter T, divided unequally into 45 degrees, and numbered in both ways, for the Tangent and the Complement.
- The Line of Artificial Sines noted with the Letter S, divided unequally in 90 degrees, and numbered 1, 2, 3, 4, unto 90.
- The Line of Versed Sines for more easie finding the hour and Azimuth, noted with V, divided unequally into about 164 gr. 50 m., numberd backward with 10, 20, 30, unto 164.
Thus there are seven Lines inscribed on the Staff: there are Five Lines more inscribed on the Cross.
- A Tangent Line of 36 gr. 3 ms. numbered by 5, 10, 15, unto 35; the midst whereof is at 20 gr.and therfore I call it the Tangent of 20; and this has respect unto 20 gr. in the Tangent on the Staff
- A Tangent Line of 49 gr. 6 m. numbered 5, 10, 15, unto 45; the midts whereof is at 30 gr. and hath respect unto 30 gr. in the Tangent of the Staff, whereuopn I call it Tangent of 30.
- A Line of Inches numbered 1, 2, 3, unto 26; each Inch equally subdivided unto ten parts, answerable to the Inch Line upon the Staff.
- A Line of several Chords, one answerable to a Circle of twelfe Inches Semidiameter, numbered 10, 20, 30 unto 60, another a Semidiameter of a Circle of sic Inches; and a third to a Semidiameter of three Inches, both numbered 10, 20, 30, unto 90.
- A Continuation of the Meridian Line from 57 gr. of Latitude uto 76 gr., and from 76 to 84 gr.
For the Inscription of these Lines. The first for measure is equally divided ito Inches, and theth parts of Inches.
The Tangent on the Staff for observation of Angles, with the Tangent of 20 and the Tangent of 30 on the Cross may all three be inscribed out of the ordinary Table of Tangents.
The Staff being 36 Inches in length; the Radius for the Tangent on the Staff will be 13 Inches and 103 parts of 100: so for the whole Line will be a Tangent of 70 gr. and must be numbered by their Complements, and the Double of their Compliments, the Tangent of 10 gr. being numbered with 80 and 160.
The Radius for the Tangent of 20 on the Cross, will be 36 Inches, and the whole Line between the Sights a tangent of 36 gr. 3 m according as it is numbered, The Radius for the Tangent of 30 on the Cross will be 22 Inches and 695 parts of 1000: so the whole Line between the sights will contain a Tangent of 49 gr. 6 m. in such sort as they are numbered.
The Meridian Line may be inscribed out of the Table which I set down for this pupose in the Use of the Sector.
The Line of Numbers may be inscribed out of the first Chiliad of Mr. Briggs Logarithms: and the rest of the Lines of Proportion out of my Canon of Artificial Sines and Tangents, and in recompence thereof this book will serve as a Comment to explain the use of my Canon.