Mathematical Instruments
Book VII. Ch. I.

# Of the Construction and Use of the Sea-Compass, and Azimuth Compass.

## Section I.

The first Figure shews the Compass Card, whose Limb represents the Horizon of the World. It is divided into four times 90 Degrees, and very often but into 32 equal Parts; for the 32 Points, whereof the four principal Points, which are called Cardinal ones, cross each other at Right Angles, viz. the North, distinguished by the Flower-de-Luce, the South opposite thereto, and the East and West. Now if each of these Quarters be bisected, we shall have the eight Rhumbs. Again, Bisecting each of these last Spaces, we shall have the eight Semi-Rhumbs. And lastly, Bisecting each of these last Parts, we shall have the sixteen Quarter-Rhumbs. The four Collateral Rhumbs take their Name from the four Principal Rhumbs, each assuming the two Names of those that are nighest them: as, the Rhumb in the Middle, between the North and the East, is called North-East; that between the South and the East, is called South-East; that between the South and the West, is called South-West; and that in the Middle between the North and the West, is called North-West.

Also every of the eight Semi-Rhumbs assumes it’s Name from the two Rhumbs that be nighest it; as that between the North and North-East, is called North North-East; that between the East and North-East, is called East North-East; that between the East and South-East, is called East South-East, and so of others.

Finally, Each of the Quarter-Rhumbs has it’s Name composed of the Rhumbs or Semi-Rhumbs which are nighest to it, in adding the Word one-fourth after the Name of the Rhumb nearest to it. For Example; The Quarter-Rhumb nearest to the North, and next to the North-East, is called North one-fourth North-East; that which is nearest the North-East towards the North, is called North-East, one-fourth North; and so of others, as they appear abbreviated round the Card. Each Quarter-Rhumb contains 11 Deg. 15 Min. the Semi-Rhumbs 22 Deg. 30 Min. and the whole Rhumbs 45 Deg.

The Inside of this Card, which is supposed double, is likewise divided into 32 equal Parts, by a like Number of Radii, denoting the 32 Points, and the Middle thereof, which is glewed upon a Pasteboard, hath a free Motion upon it’s Pivot, that so it may be used when the Declination or Variation of the Needle is found. Note, The Outside of this Card is placed upon the Limb of the Box.

The second Figure represents a piece of Steel in form of a Rhumbus, which serves for the Needle, and is fastened under the moveable Card with two little Pins, so that one of the ends of the longest Diameter of the said Rhumbs be precisely under the Flower-de-luce. This piece of Steel must be touched by a good Load-stone; so that one end may direct itself towards the North part of the World. The manner of doing which, we have already shewn in speaking of the Load-stone, and the Compass. Note, It is not so well to glew the said Needle under the Card, as some do, as otherwise to fasten it; because that causes a Rust very contrary to the magnetick Virtue.

The little Figure B, in the middle of the Rhumbus, which is called the Cap of the Needle, is made of Brass, and hollowed into a Conical Form. This Cap is applied to the Center of the Card, and is fastened thereto with Glew.

The third Figure represents the whole Compass, whereof A is a round wooden Box, about six or seven Inches Diameter, and four deep; (we sometimes make these Boxes square) bb and cc are two Brass Hoops, the greater of which being bb, is fastened to the Sides of the Box at the opposite Places BB. The other Hoop cC is fastened by two other Pivots, at the Places CC, diametrically opposite to the Hoop bb; and these two Pivots go into Holes made towards the top of another kind of wooden Box, in which the Card is put. And by this means, this last Box, and the two Hoops will, have a very free Motion; so that when the great Box A is placed flat in a Ship, the letter Box will be always horizontal, and in equilibrio, notwithstanding the Motion of the Ship. In the middle of the Bottom of this last Box, is placed a very strait and well pointed brass Pivot, on which is placed the Cap B of the Card, which Card having a very free Motion, the Flower-de-luce will turn towards the North, and all the other Points towards the other correspondent Parts of the World. Finally, the Card is covered with a Glass, that so the Wind may have no power on it.

### Use of the Sea-Compass.

The Course that a Ship must take to fall to a proposed Place, being known by a Sea-Chart, and the Compass placed in the Pilot’s Room, so as the two parallel Sides of the square Box to be fixed according to the length of the Ship, that is, parallel to a Line drawn from the Poop to the Prow; make a Cross, or other Mark, upon the middle of that Side of the square Box perpendicular to the Ship’s length, and the most distant from the Poop, that so the Stern of the Ship by this means may be directed accordingly.

Example. Departing from the Island of Ushant, upon the Confines of Britany, we desire to fall towards Cape Finisterre in Galicia. Now in order to do this, we must first seek (according to the manner hereafter directed) in a Mercator’s Chart, the Direction or Course of the Ship leading to that Place; and this we find is between the South-West and the South South-West; that is, the Ship’s Course must be South-West, one-fourth to the South. Therefore having a fair Wind, turn the Stern of the Ship, so that a Line tending from the South-West, one-fourth South, exactly answers to the Cross marked upon the middle of the Side of the square Box; and then we shall have our Desire. And by this means, which is really admirable, we may direct a Ship’s Course as well in the Night as in the Day, as well being shut up in a Room in the Ship, as in the open Air, and as well in cloudy Weather as fair; so that we may always know whether the Ship goes out of her proper Direction.

### Of the Variation or Declination of the Needle.

It is found by experience, that the touched Needle varies from the true North, that is, the Flower-de-luce does not exactly tend to the North part of the World, but varies therefrom, sometimes towards the East, sometimes towards the West, more or less, according to different Times, and at different Places.

About the Year 1665, the Needle at Paris did not decline or vary at all; whereas now its Variation is there above 12 Degrees North-westwardly, Therefore every time a favourable Opportunity offers, you must endeavour to observe carefully the Variation of the Needle, that so respect thereto may be had in the steering of Ships. If, for example, the Variation of the Needle in the Island of Ushant, which was the supposed Place of Departure in the abovementioned Example, was 10 Degrees; and if the Ship should exactly keep the Course of South-West, one-fourth to the South, instead of arriving at the Cape Finisterre, it would to another Country 10 Degrees more to the East.

Now to remedy this, you need only remove the Cross, upon the Side of the Box, shewing the Rhumb of Direction, more easterly by the Quantity of the Degrees of the Needle’s Variation westwardly; and so as often as a new Declination or Variation of the Needle be found, the place of the said Cross must be altered. Note, When the Box is quite round, a Mark must be made against the North and South on the Body of the said Box.

If likewise a Vessel departs from the Sorlings in England, in order to fall to the Island of Madeira, you will find by a Sea-Chart that her Course must be South South-West; but if at the same time the Variation of the Needle be six Degrees North Easterly, the Cross denoted upon the Edge of the Compass must be removed six Degrees towards the West, in order to direct the Ship according to her true Course found in the Chart.

But if a Sea-Compass be used, wherein the Position of the Needle may be altered, as that which hath a double Card, the Flower-de-luce of the Card must be fixed, so that its Point may shew the true North; and then you will have it to alter every time there is a new Variation observed. Now in this Case the Cross upon the Edge of the Compass must not be altered.

It is very necessary, and principally in long Courses, for Seamen to make Celestial Observations often, in order to have the Variation of the Needle exactly, that the Direction of the Vessel may thereby be truly had, as likewise that they may know where they are, after having escaped a great Storm, during which they were obliged to leave the true Course, and let the Vessel run according as the Wind or Currents drove her.

## Section II. Of the Azimuth Compass.

This Compass is something different from the common Sea-Compass before spoken of. For upon the round Box, wherein is the Card, is fastened a broad brass Circle AB, one Semi-circle whereof is divided into 90 equal Parts or Degrees, numbered from the middle of the said Divisions both ways, with 10, 20, &c. to 45 Degrees; which Degrees are also divided into Minutes by Diagonal Lines and Circles: But these graduating Lines are drawn from the opposite part of the Circle, viz. from the Point b, wherein the Index turns in time of Observation.

bc is that Index moveable about the Point b, having a Sight ba erected thereon, which moves with a Hinge, that so it may be raised or laid down, according to necessity. From the upper part of this Sight, down to the middle of the Index, is fastened a fine Hypothenusal Lute-string, or Thread de, to give a Shadow upon a Line that is in the middle of the said Index.

Note, The reason of making the Index move on a Pin fastened in b, is, that the Degrees and Divisions may be larger; for now they are as large again as they would have been, if they had been divided from the Center, and the Index made to move thereon.

The abovenamed broad brass Circle AB, is crossed at Right Angles with two Threads, and from the ends of these Threads are drawn four small black Lines on the In side of the round Box; also there are four Right Lines drawn at Right Angles to each other on the Card.

This round Box, thus fitted with its Card, graduated Circle, and Index, &c. is to be hung in the brass Hoops BB; and these Hoops are fastened to the great square wooden Box CC.

### The Use of the Azimuth Compass in finding the Sun’s Magnetical Azimuth or Amplitude, and from thence the Variation of the Compass.

There are several ways of finding the Variation of the Needle, as by the rising and setting of the same Star, or by the Observation of two equal Altitudes of the Star above the Horizon, since the said Star, at each of those Times, will be equally distant from the true Meridian of the World; or else by a Star’s passage over the Meridian.

But these Methods are not much used at Sea: First, because the Time wherein the Sun, or a Star, passes over the Meridian, cannot be known precisely enough; for there is a great deal of Time taken in making Observations of the Sun’s Altitudes, ’till he is found to have the greatest, that is, his Meridian Altitude.

Secondly, Because the Sun’s Declination may be considerably altered, and also the Ship’s Latitude between the Times of the two Observations of his equal Altitudes above the Horizon, Morning and Evening, or of his Rising and Setting.

Therefore the Variation of the Compass may much better be found by one Observation of the Sun’s magnetical Amplitude, or Azimuth. But the Sun’s Declination, and the Latitude of the Place the Ship is in, must be known, that so his true Amplitude may be had; his Altitude must also be given, when the magnetick Azimuth is taken, that so his true Azimuth may be had at that Time also.

Now if the Observation be for an Amplitude at Sun-rising, or an Azimuth before Noon, you must put the Center of the Index be upon the West Point of the Card within the Box, so that the four Lines on the Edge of the Card, and the four Lines on the Inside of the Box, may agree or come together. But if the Observation be for the Sun’s Amplitude, Setting, or an Azimuth in the Afternoon, then you must turn the Center of the Index right-against the East Point of the Card, and make the Lines within the Box concur with these on the Card. Having thus fitted the Instrument for Observation, turn the Index be towards the Sun, ’till the Shadow of the Thread de falls directly upon the Hit of the Sight, and upon the Line that is along the middle of the Index; then will the inner Edge of the Index cut the Degree and Minute of the Sun’s magnetical Azimuth, from the North or South.

But note, that if the Compass being thus placed, the Azimuth be less than 45 Deg. from the South, and the Index be turned towards the Sun, it will then pass off the Divisions of the Limb, and so they become useless as it now Hands: therefore you must turn the Instrument just a Quarter of the Compass, that is, place the Center of the Index on the North or South Point of the Card, according as the Sun is from you, and then the Edge thereof will cut the Degree of the Magnetick Azimuth, or Sun’s Azimuth from the North, as before.

The Sun’s Magnetical Amplitude (that is, the Distance from the East or West Points of the Compass, to that Point in the Horizon whereat the Sun rises or sets), being observed by this Instrument, the Variation of the Compass may be thus found.

Example. Being out at Sea the 15th Day of May, in the Year 1715, in 45 Degrees of North Latitude, I find from Tables that the Sun’s Declination is 19 Deg. North, and his East Amplitude 27 Deg. 25 Min. North. Now I observe by the Azimuth Compass, the Sun’s Magnetical Amplitude at his rising and setting, and find that he rises between the 62d and 63d Deg. reckoning from the North towards the East part of the Compass, that is, between the 27th and 28th Degrees from the East; and since in this Case the magnetical Amplitude is equal to the true Amplitude, I conclude that at this Place and Time, the Needle has no Variation.

But if the Sun at his rising should have appeared between the 52d and 53d Degrees from the North towards the East, his magnetical Amplitude would then be between 37 and 38 Degrees, that is, about 10 Degrees greater than the true Amplitude: and therefore the Needle would vary about 10 Degrees North-Easterly. If, on the contrary, the magnetical East Amplitude found by the Instrument should be less than the true Amplitude, their Difference would shew that the Variation of the Needle is North-Easterly. For if the magnetical Amplitude be greater than the true Amplitude, this proceeds from hence, that the East part of the Compass is drawn back from the Sun towards the South, and the Flower-de-luce of the Card approaches to the East, and so gives the Variation North-Easterly. The reason for the contrary of this is equally evident.

If the true East Amplitude be Southwardly, as likewise the magnetical Amplitude, and this last be the greater; then the Variation of the Needle will be worth West; and if, on the contrary, the magnetical Amplitude be less than the true Amplitude, the Variation of the Needle will be North-Easterly, as many Degrees as ate contained in their Difference.

What we have said concerning North-East Amplitudes, must be understood of South-West Amplitudes, and what we have said of South-East Amplitudes, must be understood of North-West Amplitudes.

Finally, If Amplitudes are found of different Denominations; for Example, when Amplitudes are East, if the true Amplitude be 6 Deg. North, and the magnetical Amplitude 5 Deg. South; then the Variation, which in this Case is North-West, will be greater than the true Amplitude, it being equal to the Sum of the magnetical and true Amplitudes: and so adding them together, we shall have 11 Degrees of North-West Variation. Understand the same for West Amplitudes.

The Variation of the Compass may likewise be found by the Azimuth; but then the Sun’s Declination, the Latitude of the Place, and his Altitude must be had, that so his true Azimuth may be found.