to the south, and each of the remaining points to its respective position in the horizon; in the centre of the card underneath, is fixed a finely polished conical brass socket, about one third of an inch deep.

The e compass box is a basin of brass or wood, having a fine pointed steel needle fixed perpendicularly in its bottom: on the point of this, the above-mentioned socket in the bottom of the card being placed, the card is balanced and turns freely as impelled by the attractive force of the magnet. The box is suspended within a brass hoop or ring, by means of two gimbols placed on opposite sides, which serve as an axis, and admit free motion; and this hoop is in like manner suspended on the opposite sides of a square wooden box by gimbols, at 90° distance from the former, a contrivance intended to secure the horizontal position of the inner box and card, whatever may be the motion of the ship in which the compass is placed'.

iThose who cross forests, deserts, and uninhabited countries, find this instrument a necessary companion to direct them; they keep the compass always before them, and follow the direction of that point which indicates the situation of the place they wish to arrive at. The like method is employed in steering a ship, which is kept in such a position, that the proposed point may, of its own accord, stand in a direction towards the head of the ship. Note, N b E means north by east; NNE, north north-east; NE bN, north-east by north; NE, north east, &c. &c. which will be easily understood.

87. A table shewing the degrees and minutes that every point of the compass makes with the meridian *.

In the preceding figure the line NS is called the meridian line; the two first columns of the table extend from north both ways to east and west, as the two last do from south; the two first points in the first and second columns make the same angle with the meridian line NS (11°

15') reckoning from the north point, that the two first in the 5th and 6th columns do, reckoning from the south, and the like is evidently true of the points in any horizontal line of the table. The angles made by the points in the first and second columns with the meridian are therefore measured by the arcs intercepted between them and the north point, viz. the first column, on the east side of north; and the second on the west in like manner the angles made by the points in the 5th and 6th columns with the meridian are measured by the respective arcs intercepted between them and the south point, those in the 5th column being on the east of south, and those in the sixth on the west: for example, N NE is 22° 30′ to the east of north, N N W is the same distance west of north; SSE is the same distance east of south, and S SW is the same distance west of south. . In the third column each number denotes the distance from north or south of the points against which it stands; and the numbers in the fourth column shew the degrees and minutes of the arc intercepted between the north or south, and the points against which they stand.

88. The use of the above Table.

When a question is proposed in which the conditions require that lines should be drawn in given positions with the meridian expressed in points of the compass, the construction may be made with the greatest facility, by means of this table; to effect which this is the

RULE.-1. Describe a circle and draw the diameter NS for the meridian, N being the north point, S the south.

2. Take the degrees and minutes from the table which correspond with the points mentioned in the question, and measure arcs from the meridian equal to them.

The table is thus constructed: divide 360 (= the number of degrees in the circumference of a circle) by 32 (= the number of points in the compass,) and the quotient is part of the circumference =11° 15', or 1 point of the compass; this doubled is 22o 30' for two points; its triple is 33° 45′ for three points, and so on.

3. Draw lines through the centre to the points thus measured, and construct your figure by drawing its sides respectively parallel to these, and each of its proper length taken from a scale of equal parts.

4. If the position of one of the lines be required, draw a line parallel to it through the centre of the circle, measure the angle this line makes with the meridian, then the point of the compass which stands opposite this measure will give the bearings or position required'; and its length, taken in the compasses, and applied to a scale of equal parts, will give its

measure.

EXAMPLES.-1. A man intends to travel from C to Z which lies N N W from C 6 miles, but he must first call at D, which lies NE 3 miles, then at H, N b W from D 5 miles, and lastly at K, which is SW from H 4 miles; at H how far is he distant from Z, and what course must he travel to arrive there?

Here I first draw cCZ through the point d, distant 22° 30' from N (answering to NNW); next I draw ab at 45° distance from N (answering to N E); next I draw rn at 11° 15' distance on the left of N (answering to N b W); and since aS=Nb=45°, it is plain K that ab will be the SW as well as the NE line. I then take CD=3, draw DH parallel to rn and make it=5, whence I draw HK parallel to ab and make it= 4, I then join KZ and find its measure to be 24 miles nearly, and its bearings (shewn by the parallel rv, the position of which is measured by the arc No)

d

N

H

บ

The position, or bearings of a line may likewise be known by simply drawing a meridian from the given point, and measuring the angle which that line makes with it; the degrees contained in it being found in the table will shew the point of the compass required.

N 18° E, that is, Nb E 7o E, or 74 degrees to the eastward of north by east.

2. B is 8 miles NW from C, and 4 4 miles N from B; required the course and distance from A to C ? Ans. course S

31o E. Distance 11 miles.

3. A ship sailed SE 12 leagues, NNE 20 leagues, and NNW 30 leagues; required her distance from the point sailed from, and her course back?

89. THE PERAMBULATOR ", called also a pedometer, waywiser, and surveying wheel, is an instrument for measuring large distances on ground nearly level; it consists of a wheel 84 feet in circumference, which the measurer drives before him, by means of two handles, fixed at the end of a hollow shaft, terminating in two cheeks to receive the wheel, and in which its axis turns. The wheel goes over one pole of ground in every two revolutions, and its motion is communicated by the intervention of various clock-work movements within the shaft, to a dial, fixed near the handles, the index of which points out the distance passed over.

THE GUNTER'S CHAIN • is used to measure smaller distances than those to which the perambulator is applied; its length is 66 feet 22 yards =:4 poles, and is divided into 100 links, each 7,92 inches in length. This is the most convenient instrument of any that has been contrived for measuring land, because 10

m The bearings of two objects from each other may be estimated either in degrees, or points; degrees may be turned into points, or points into degrees, by referring to the table; thus, if an object bear 33° 45′ to the east of south, by turning to the table I find that the exact point of bearing is SEbS; if it bear 25° to the west of north, the bearing in points is NNW 2° 30′ W, that is, 2o 30' west of NNW. Or the reckoning may be made to the nearest quarter point, thus N 14° 4' W is NbWW; S 28° 7' E is SSE E; in like manner N 64° 41′ E is NE bE E, &c. &c.

"The price of this instrument is from five to ten guineas. The name Pedometer is likewise applied to an instrument of a watch size for the pocket, for ascertaining distances, either walking or riding, and costs from three to fifteen guineas. The perambulator, Gunter's chain, and tapes, will measure with sufficient exactness for most purposes where the ground is level, but where it is not, distances should be found by trigonometrical calculation.

• The Gunter's chain will cost from five to fourteen shillings, according to its strength, and the perfection of its workmanship.

chains in length, and one in breadth, (=100000 square links) make just an acre.

91. THE MEASURING TAPES P are of one, two, three, or four poles in length; they are applied to the same purposes as the chain, and, if kept dry, will measure with tolerable exactness.

92. THE MEASURING ROD may be of six, eight, or ten feet in length; it is divided into single feet, which are subdivided into halves and quarters, or into tenths of a foot, for the convenience of measuring small distances.

93. STATION STAVES or prickets, are staves of about five or six feet in length, having a small flag fixed at one end, the other end being sharpened to a point for fixing in the ground; these staves are used in measuring, for marking stations, which are required to be seen and distinguished at a distance.

94. THE ARROWs are of wood or iron, pointed at one end, and their use is to stick in the ground as a mark, at the end of every chain or other measure.

95. PROBLEMS.

Prob. 1. An observer at 113 feet distance from the foot of an obelisk, finds its angular altitude to be 40°; required its height, that of the observer's eye above the plane of the horizon being 5 feet?

These tapes are sold at the shops of the mathematical instrument makers, and cost from five to twelve shillings, according to their length.

The above instruments, at the prices we have mentioned, will perhaps be found too expensive for the student's pocket; in that case his own ingenuity may supply him with all that is necessary for measuring vertical and horizontal angles and distances. A theodolite may be made with a circular piece of stiff pasteboard, graduated and nailed (through its centre) on the top of a piece of mop-stick, the other end of the stick being sharpened to a point for fixing it in the ground. A quadrant likewise may be made of pasteboard, in like manner graduated, and having a piece of lead, or a stone, hung from its centre by a string. The chain or tapes may have their place supplied by a string previously measured, divided, and subdivided, according to the mind of the operator. The measuring rod may be made of any stick, of a proper length and thickness. The station staves may be made of sticks having one end pointed and the other split, for the purpose of holding a piece of white paper, and the arrows may be cut out of any hedge.

With apparatus of this kind, I have frequently known altitudes and distances determined, with sufficient exactness for any common purpose.