There is a staff of another projection, which I find by practice to be an Instrument of very great ease and certainty at Sea, the Sun not being more than 45 deg. above the Horizon, whose use is contrary to the other before demonstrated, for by this Staff the beam of the Sun shadowing upon the Transversary, doth thereby give the height most precisely, not regarding how to place the center of the staff to the Eye, for the correction of the parallax of the sight, and without looking upon the Sun, whose demonstration is thus:
- Draw two right lines, cutting each other at right Angles, as do the lines d.v. and d.s.
- upon the Angle d. describe a quarter circle, as is the ark v.s.
- divide that Quadrant into two equal parts by the line d.n. cutting the Quadrant into point h.
- divide the ark s.h. to every of those divisions, then from the point i. being the third part of the line d.s. upon the Center d. describe the ark of a Circle, as is the ark i.o. which is for the Transversary of this staff, and the line d.s.is for the staff,
- then from the point o. where the upper end of the Transversary toucheth the line d.n. draw a Parallel to the line d.s. as in the line o.y. and as that line doth cut the lines, drawn from the Center k. so must the staff d.s. be graduated, laying it upon the line o.y. putting that part of the staff where the point i. toucheth, upon the point o. and then from the point i. lay down degrees, as are the intersections upon the line o.y. and so is the staff graduated.
The transversary at the point i. must have an artificial hole made for the staff to run in,as the other staves have, also there must be a plate of brass with a sockett to be set to the center of the staff, as is the figure 2. in the middle whereof there must be a slit, through which the light must be conveyed to the Horizon, and this plate must receive the shadow of the transversary, and so the staff is finished.
How is the use of this staff ?
Thus use of this staff is altogether contrary to the other, for the center of this staff where the brass plate is fastened, must be turned so that part of the horizon which is from the Sun. and with your back toward the Sun, by the lower edge of the half cross, and through the slit of the plate you must direct your sight only to the Horizon, and then moving its Transversary as occasion requireth, until the shadow if your upper edge of the Transversary do fall directly upon the same slit or long hole, and also at the same instant you see the Horizon through the slit, and then the Transversary sheweth the height observed.
Finding by practice the excellency of the Cross-staff above all other Instruments, to satisfie the Seamans expectation, & also knowing that those instruments whose degrees are of largest capacity, are instruments of most certainty. I have very carefuly labored to search a good and demonstrable mean how a cross-staff might be projected, not only to contain large degreee, but also to avoid the uncertainty of the sight, by disorderly placing of the staff to the eye, which demonstration I have found, and have had the Instrument in practice, under the Sun as in other Climates but because it hath a large demonstration, with manifold uses, I here omit to manifest the same, purposing to write a particular treatise thereof, notwithstanding his Form and use, by picture I have thought good to expess.
This staff is a yard long, having two half crosses, the one circular, the other strait, the longest not 14 inches, yet this staff doth contain the whole 90 degrees, the shortest degree being an inch and 1/4 long, wherein the minutes are particularly a very sensibly laid down, by which staff not regarding the parallax of your sight, nor looking upon the Sun, but only upon the Horizon, the Suns height is most precisely known, as easily in the Zenith as in any other part of the heaven. As which Instrument (in my opinion) the Seaman whall not find any so good, and in all Climates of so great certainty, the Invention and demonstration whereof I may boldly challenge to appertain unto my self (as a portion of the Talent which God hath bestowed upon me, I hope without abuse or offence to any.