Mathematical Instruments
Book IV. Ch. VII.

# Of the Construction and Uses of the Compass.

Instrument is made of Brass, Ivory, Wood, or any other solid Matter, from 2 to 6 Inches in Diameter, being in figure of a Parallelopipedon, in the Middle of which is a round Box, at the Bottom of which is described a Card (of which more in the Construction of the Sea-Compass) whose Circumference is divided into 360 Degrees. In the Center of this Card is fixed a well-pointed Brass or Steel Pivot, whose Use is to carry the touched Needle placed upon it, in Equilibrio, so that it may freely turn. This Box is covered with a round Glass, for hindring left the Air should any wise agitate the Needle.

One of the Ends of the Needle always turns towards the North Part of the World, but not exactly, it declining therefrom, and the other towards the South.

According to Observations made in October, in the Year 1715, in the Royal Observatory, the Needle declined 2 Deg. 5 Min. Westwardly.

Needles are made of Pieces of Steel, the Length of the Diameter of the Box, having little Brass Caps soldered to their Middle, hollowed into a conical Figure so, that the Needle being put upon the Pivot, may move very freely upon it, and not fall off; they are nicely filed into different Figures, those which are large being like a Dart, and small ones have Rings towards one End, for knowing that End which respects the North, as may be seen in the little Figures nigh the Compass.

To touch a Needle well, having first got a good Stone, begin your Touch near the Middle of the Needle, and pressing it pretty hard upon the Pole of the Stone, draw it slowly along to the End of the Needle, and lifting your Hand a good Distance from the Stone, while you put the Needle forward again, begin a second Touch in the same manner, and after that a third, which is enough, only take Care not to rub the Needle to and fro on the Stone, whereby the backward Rubs take away what Virtue the forward ones gave; but lift it out of the Sphere of the Stone’s Virtue, when you carry it forward again to begin a new Touch.

This admirable Property, by help of which great Sea-Voyages were first undertaken, and vast Nations both in the East and West discovered, was not known in Europe ’till about the Year 1260.

A Man by means of this Instrument, and a Map, may likewise go to any proposed Place, at Land, without enquiring of any body the way; for he need but set the Center of the Compass, upon the Place of Departure, on the Map, and afterwards cause the Needle to agree with the Meridian of this Place upon the Map: then if he notes the Angle that the Line leading to the Place makes with the Meridian, he need but in travelling keep that Angle with the Meridian, and that will direct him to the Place desired.

This Instrument is also very useful to People working in Quarries, and Mines under Ground; for having noted upon the Ground the Point directly over that you have a mind to go to, you must place the Compass at the Entrance into the Quarry or Mine, and observe the Angle made by the Needle with the Line of Direction: then when you are under Ground, you must make a Trench, making an Angle with the Needle equal to the aforesaid Angle; by means of which you may come to the proposed Place under Ground. There are several other Uses of this Instrument, the principal of which we are now going to speak.

## Use I.To take the Declination of a Wall with the Compass.

You must remember that there are 4 Points, called Cardinal ones, viz. North, South, East, and West, dividing the Horizon into 4 equal Parts, and when one of these Points are found, all the others may likewise: for if you have North before you, South will be behind, East on the right-hand, and West on the left.

A Wall built upon a Line tending from North to South, will be in the Plane of the Meridian; so that one Side thereof will face the East, and the other the West.

Another Wall, at right Angles with the former, that is, one built upon the Line of East and West, will be parallel to the Prime Vertical, and will not decline at all, and one of it’s Sides will, be directly South, and the other North.

But if a Wall is supposed to be built upon the Line DE, it is said to decline as many Degrees as is contained in the Arc F; therefore if, for Example, that Arc be 40 Degrees, the Side of the Wall facing towards the South, declines from the South towards the East 40 Degrees, and the opposite Side of the Wall will decline from the North towards the West 40 Degrees: so that the Declination of a Wall, is no more than the Angle made by the Wall and the Prime Vertical. Another Wall parallel to the Line GH, will decline as many Degrees as is contained in the Arc C; therefore if that Arc be 30 Degrees, the Side of the Wall respecting the South, will decline 30 Degrees from the South towards the West, and the other Side will decline 30 Degrees from the North to the East.

In all Operations made with a Compass, you must take care of bringing it nigh Iron or Steel, and that there be none concealed; for Iron or Steel entirely changes the Direction of the Needle.

I suppose here that the Pivot, upon which the Cap of the Needle is put, is in the Center of a Circle divided into 360 Degrees, or four Nineties, whose first Degree begins from the Meridian Line, and also that the Compass be square, as that which is represented in the Figure.

Apply the Side of the Compass where the North is marked, to the Side of the Wall; then the Number of Degrees over which the Needle fixes, will be the Wall’s Declination, and on that Side. If, for Example, the North Point of the Needle tends towards the Wall, it is a sign that that Side of the Wall may be shone on by the Sun at Noon; and if the Needle fixes over 30 Degrees, counting from the North towards the East, the Declination is so many Degrees from South towards the East. If it fixes over 30 Degrees from the North towards the West, the Declination of the Needle will be so many Degrees from the South towards the West.

But since the Declination of the Needle is at Paris 12 Deg. 15 Min. N. W. for correcting that Defect, 12 Deg. 15 Min. must always be added to the Degrees shown by the Needle, when the Declination of the Wall is towards the East; and, on the contrary, when the Declination is towards the West, the Declination of the Needle must be substracted.

As supposing, as we have already done, that the Needle fixes over the 30th Degree towards the East, the Declination of the Wall will be 42 Deg. 15 Min. from the South towards the East; but if the Needle fixes on the West-side of the Wall, over the 30th Degree, the Declination will be 17 Deg. 45 Min. from the South towards the West.

If the South Point of the Needle tends towards the Wall, it is a Sign that the South is on the other Side of the Wall, and consequently that Side of the Wall, whose Declination is to be found, will not be shone upon by the Sun at Noon; whence it’s Declination will be from the North towards the East: or West, according as it faces towards those Parts of the World. This will be more fully explained in the Treatise of Dialling.

## Use II.To take an Angle with the Compass.

Let the Angle DAE be proposed to be measured; apply that Side of the Compass, where the North is marked, to one of the Lines forming the Angle, as AD: so that the Needle may freely turn upon it’s Pivot, and when it rests, observe what Number the North Point of the Needle stands over; and finding it, for Example, 80 Degrees, the Declination of the said Line will be so many Degrees. Afterwards take, in the same manner, the Declination of the Line AE, which suppose 215 Degrees: substract 80 Degrees from 215 Degrees, there will remain 135, which substract from 180, and there will remain 45 Degrees, the Quantity of the Angle proposed to be measured.

But if the Declination of the Line AD had been, for example, but 30 Degrees, and the Line AE 265 Degrees, the Difference of those two Declinations, which would be 235 Degrees, would be too great to substract from 180 Degrees; whence in this Case 180 Degrees must be taken from 235 Degrees, and the Remainder 55 Degrees, will be the Angle proposed.

When Angles are measured with the Compass, there need not any regard be had to the Variation of the Needle, because the Variation will always be the same in all the different Positions of the Needle, provided at all times there be no Iron near it: and when the Compass cannot be put nigh the Plane, by means of some Impediment, it is sufficient to place it parallel, as the Figure shews, and the Effect will be the same.

## Use III.To take the Plot of a Forest, or Morass.

Let it be required to take the Plot of the Morass ABCDE, in which one may enter. To make these kinds of Operations, there must be fastened two Sights to the Meridian Line of the Compass; now plant long Staffs upright, so that they may be in Lines parallel to the Sides encompassing the Morass, and place the Compass upon it’s Foot in a horizontal Position: then look at two of the Staffs thro’ the Sights, putting always the Eye to that which is on the South Side of the Compass; and having drawn a Figure upon Paper something representing the Plot of the Morass, write upon the correspondent Line the Number of Degrees which the Needle, when fixed shews. At the same time measure the Length of each Side of the Morass, and set down their Lengths upon the correspondent Lines of your Memorial. When you have gone round the Morass, the Degrees denoted by the Needle, will serve to form the Angles of the Figure, and the Length of each Line will determine the Plot of the Morass proposed.

Let us suppose, for Example, that having placed the Compass along the Side AB, or which is all one, along a Line parallel to that Side, and placing the Eye next to the South Sight of the two Sights, two Staffs set up in that Line are espied. If the Needle fixes on the 30th Degree towards the East, set down the Number 30 upon the Line AB in the Memorial, and also 50 Toises, the Length of the Side AB: afterwards set the Compass, with it's Foot, along the Side BC, or in the Direction of the Staffs, putting always the Eye next the South Sight. If the Needle fixes on the 100th Degree, I write that Number on the Line BC, and at the same time 70 Toises, the Length of the Side BC: doing thus quite round the Morass, you may set down upon each correspondent Line of the Memorial, the Numbers of Degrees and Toises; by means of which, the Plot may be drawn in the following manner, by help of a Scale and Protractor.

Set down, one after the other, all the Angles observed with the Compass, and substract the least from it’s next great, as in this Table.

Angles observed Remaining Angles
30 Degrees
100 Degrees 70 Degrees
130 Degrees 30 Degrees
240 Degrees 110 Degrees
300 Degrees 60 Degrees

Draw the Indefinite Line AB, of 50 equal Parts, representing the 50 Toises measured; make the exterior Angle at the Point B 70 Degrees, and draw the indefinite Line BC, on which lay off 70 Toises from B to C. Make at the Point C an exterior Angle of 30 Degrees, and draw the indefinite Line CD, whose Length let be 65 Toises, conformable to the Length measured. Make likewise at the Point D an exterior Angle of no Degrees, and draw the Line DE of 70 Toises. Lastly, Make an exterior Angle of 60 Degrees at the Point E, draw the Line AE of 94 Toises, and the Plot will be compleated.

Note, All the Angles of the Figure taken together, ought to make twice as many right Angles, wanting 2, as the Figure has Sides: As, for Example, the Figure of this Use, having 5 Sides, all the Angles added together make 540 Degrees, or 6 times 90, which may serve to prove Operations.

This Manner of taking Plots is expeditious enough, but it is very difficult to make Operations exact with a Compass, because there may be Iron concealed nigh the Places whereat a body is obliged to place the Instrument.