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.

CHAP. IV. How to Correct the Account, when the Dead Latitude differs from the Observed Latitude.

WE are come now to make good what was promised in the second Chapter, to prescribe four Precepts for correcting a Single Course.

I shall be brief, in regard Mr. Collins, in pag. 22. of his Mariner's Scale new Plained, hath imitated Moetius a Hollander, a Latin Author, in these Exam∣ples; but good Rules, the oftner writ, the more they get.

The First EXAMPLE.

IF a Ship sail under the Meridian, if the Difference of Latitude be less by Esti∣mation, than it is by Observation, the Ship's Place must be corrected and enlar∣ged under the Meridian; and the Error is to be imputed either to the Judgment in estimating the Distance run, in making it too little; or if the said Distance be estima∣ted by a sound experienced Judgment, it is to be supposed you stem some Current.

Admit a Ship sail from A, in the Latitude of 36 deg. directly South, 70 Leagues, or 3 deg. 30 min. and by Estimation is at B, but by Observation he is in Latitude 32 deg. The Reckoning rectified, the Ship's Place is in the Point C; but if the Difference of Latitude be more by Estimation, than it is by Observation, the Judgment may err, in supposing the Distance run to be too much. In this Case, the Distance is to be shortned, and the Correction must be made according to the Latitude observed under the Meridian.

Admit a Ship sail South from A, in the Latitude 36 deg. untill she have altered her Latitude 3 deg. 30 min. by Estimation being at B, in Latitude 32 deg. 30 min. and if the observed Latitude be 33 deg. 00 min. the Ship's Place corrected is at C, and not at B.

RULE II.

SUpposing no Current, If the Dead Latitude differ from the Observed Latitude, the Error is in misjudging the Distance run, which is to be made longer or shorter, as the Case requires.

Admit a Ship sail from A, S. S. E. ¾ Easterly 70 Leagues, and is by Estimation at P in the Latitude of 33 deg. but if the observed Latitude be 32 deg. 30 min. ad∣mit at B, then a Line drawn through B, parallel to NA, crosseth the Line of the Ship's Course at Q, which is the Corrected Point where the Ship is: So that the Di∣stance is inlarged 10 Leagues 4/10, the whole Distance AQ is 82 Leagues 4/10.

[illustration] geometrical diagram

The same manner, If the Ship had sailed 94 Leagues on the same Course, and by Estimation were at the Point R, in the Pa∣rallel of 32 deg. and by Observa∣tion the Latitude were found to be 32 deg. 30 min. In this Case the Ship's Distance is to be short∣ned, by drawing the foresaid Line BQ parallel to NA; and it will cross the Line of the Ships Course at Q, the Corrected Point where the Ship is.

By the Traverse-Scale.

EXtend the Compasses from 100, to 94; the same Di∣stance will reach from 2 ¾ Points, to 82 4/10 Leagues in the Line of Numbers.

RULE III.

SUppose there is some Current, and you can depend upon the Observed Difference of Latitude, and Log-distance, as both true; then the Error may be imputed to the Rhomb, which alters by reason of the supposed Current.

Especially when you sail in Rhombs near the East and West; for then if the Dead Latitude differ from the Observed Latitude, the Error is to be imputed either wholly to the Rhomb, or partly to the Rhomb, partly to the Distance.

If wholly to the Rhomb, then retain the observed Difference of Latitude, and Di∣stance by Observation, and thereby find the Departure from the Meridian, by draw∣ing a new Rhomb-line.

But if your Judgment would allot the Error partly to the Rhomb, partly to the

Distance, keep the observed Difference of Latitude: And for the Departure from the Meridian, let it be the same as was by the Dead Reckoning.

Suppose a Ship sail East by South ½ a Point Southerly 72 Leagues, from the Latitude of 36 deg. from A to M, and by Dead Reckoning should be in the Latitude of 35 deg. If the Observed Latitude be 35 deg. 20 min. which is at S; In this Case, if the Error be wholly imputed to the Distance, the Line SX being drawn parallel to NA, would cut off or shorten the Distance as much as the Measure MX, which is 26 Leagues; which because it seems absurd and improbable, is not to be admitted of: Wherefore imputing the Error to the Rhomb only, place one Foot of the Extent AM in S, and with the other cross the Line NA at L; and so is AL the Departure from the Meri∣dian required; whereby the Rhomb-line, if it were drawn, will be ordered to pass through F the Cross.

By the Traverse-Scale.

IF you extend the Compasses from 100, to 72 the Distance; the same Extent will reach from the Difference of Latitude by Observation, to the true Rhomb, which is almost East by South: and if you apply that Distance to one Point on the Line N. S. of the Scale, the other will reach to the Departure required 70 6/10 Leagues.— Which is far better than the other way.

The Fourth PRECEPT, CASE, or EXAMPLE.

IF a Ship sail East or West, and the Dead and Observed Latitude doth agree, the Reckoning cannot be corrected; but if they differ, the Error will be partly in the Rhomb, and partly in the Distance: In such a Case keep the Meridian-distance, and the Difference of Latitude is the Distance you are gone to the Northward or South∣ward of the East and West.

By the Traverse-Scale.

EXtend the Compasses from 100, to the Distance sailed; the same Extent will reach from the Difference of Latitude by Observation, to the true Course: So that you may in a moment do all these Questions and Cases by the Traverse-Scale, and Line of Numbers and Artificial Points and Quarters thereon. If you have but the perfect Use of it, I know there is no Instrument whatsoever more ready to resolve any useful Question, and correct your Reckoning.

Lastly, If by frequent Observation you find the Ship is still carried from the East or West, either Northward or Southward, you may conclude some Current to be the cause thereof: Keep the Distance by Dead Reckoning and Observation, and the Diffe∣rence is the Distance from the Parallel.

We will not multiply too many Examples, but rather advise the Ingenious to make use of such as his need shall require; for understanding what hath been said, will be advantageous to the Practitioner.