before; turn the Index about with the North End, or Flower-de-Luce, next your Eye, and count the Degree to the oppofite, or South End of the Index, and this will correspond with the Degree cut by the South End of the Needle.

At the Second, or next Station, unscrew the Inftrument, and set the South of the Index to the Degree of the laft Station; turn the whole about, with the South of the Index to you, and cut the Object at the foregoing Station; fcrew the Inftrument fast, and with the North of the Index, to you, cut the Object at the next following Station, the Degree then cut by the South of the Index will correfpond with the Degree cut by the South End of the Needle, and fo through the whole.

Some Theodolites have a ftanding Pair of Sights fixed at 360 and 180, befides thofe on the moveable Index: If you would use both, look thro' the ftanding Sights, with the 180 next you, to an Object at the foregoing Station; fcrew the Inftrument faft, and direct the upper Sights on the moveable Index, to the Object at the following Station, and the Degree cut by the oppofite End of the Index, will give you the Quantity of the Angle of the Field.

Two Pair of Sights can be of no Ufe in finding the Angles from the Meridian: and inafmuch as one Pair is fufficient to find the Angles of the Field, the fecond can be of no Ufe: Befides, they obftruct the free Motion of the moveable Index, and therefore are rather an Incumbrance than of any real Ufe. Some will have it, that they are useful with the others, for fetting off a right Angle, in taking an Off-fet; and furely this is as easily performed by

the

the one Pair on the moveable Index; Thus, if you lay the Index to 360, and 180, and cut the Object either in the laft or following Station, fcrew the Inftrument faft, and turn the Index to 90 and 270, and then it will be at Right Angles with the Line. So that the fmall Sights, or thofe to the Circle, can be of no additional Ufe to the Inftrument, and therefore fhould be laid afide as ufelefs.

This Inftrument may be used in windy and rainy Weather, as well as in mountainous and hilly Grounds; for it does not require an horizontal Pofi- . tion to find the Bearing, or Angle, as the Needle doth; and therefore is preferable to any Inftrument that is governed by the Needle.

Mr. Gabriel Stokes, formerly Mathematical Inftrument-Maker, and Surveyor of Land, in Effex-Street, Dublin, has contrived a fmall Inftrument of this Nature, about fix or seven Inches Diameter, which is accurately divided, and is much more portable than a Theodolite, which he calls a Pantometron: Which may be had upon Application to Mr. Thos. Reading, Mathematical Inftrument-maker and Surveyor of Land, who ferved his Time to the faid Mr. Stokes, at prefent dwelling in George's-Lane, near Stephen's-Street, Dublin.

OF

OF THE

SEMICIRCLE.

TH

HIS Inftrument, as its Name imports, is a half Circle, divided from its Diameter into 180 Degrees, and from thence again, that is, from o, to 360: It is generally made of Brass, and is from 8 to 16 Inches Diameter.

On the Center there is a moveable Index with Sights, on which is placed a Circumferentor-Box, as in the Theodolite.

This Inftrument may be used as the Theodolite in all Refpects, but with this Difference, when you are to reckon the Degree to that End of the Index which is off of the Semicircle, you may find it at the other End, reckoning the Degree from 180 forwards,

OF

PLANE TABLE.

A

PLANE TABLE is an Oblong of Oak, or other Wood, about 15 Inches long, and 12 broad; they are generally compofed of 3 Boards, which are eafily taken afunder, or put together, for the Conveniency of Carriage.

There is a Box Frame, with 6 Joints in it, to take off and put on as Occafion ferves: it keeps the Table together, and is likewife of Ufe to keep down a Sheet of Paper which is put thereon.

The Outfide of the Frame is divided into Inches and Tenths, which ferve for ruling Parallels or Squares on the Paper, or for fhifting it, when Occafion ferves.

The Infide of the Frame is divided into 360 Degrees, which, tho' unequal on it, yet are the Degrees of a Circle produced from its Center, or Center of the Table, where there is a small Hole.

The Degrees are fubdivided as fmall as their Distance will admit; at every tenth Degree are two Numbers, one the Number of Degrees, the other its Complement to 360.

There is another Center Hole, about of the Table's Breadth from one Edge, and is in the Middle between the two Ends. To this Center Hole on the other Side of the Frame, there are the Divifions of a Semicircle, or 180 Degrees; and these again are fubdivided into Halfs, or Quarters, as the Size of the Inftrument will admit.

That

That Side of the Frame on which the 360 Degrees are, fupplies the Place of a Theodolite, the other that of a Semicircle.

There is a Circumferentor Box of Wood, with a Paper Chart at the Bottom, applied to one Side of the Table by a Dove-tail Joint, faftened by a Screw. This Box (befides its rendering the Plane Table capable of answering the End of a Circumferentor) is very useful for placing the Inftrument in the fame Position every Remove.

There is a Brass Ruler or Index, of about two Inches broad, with a sharp or fiducial Edge, at each End of which is a Sight: On the Ruler are Scales of equal Parts, with and without Diagonals, and a Scale of Chords; the whole is fixed on a Ball and Socket, and set on the three legged Staff.

1. To take the Angles of the Field by the Table.

Having placed the Inftrument at the first Station, turn it about till the North End of the Needle be over the Meridian, or Flower-de-Luce of the Eox, and there fcrew it faft. Affign any convenient Point, to which apply the Edge of the Index, so as thro' the Sights you may fee the Object in the laft Station, and by the Edge of the Index, from the Point draw a Line. Again, turn about the Index with its Edge to the fame Point, and thro' the Sights obferve the Object in the fecond Station, and from the Point, by the Edge of the Index, draw another Line; fo is the Angle laid down: On that laft Line fet off the Diftance to the fecond Station, in Chains and Links: Apply your Inftrument to the fecond Station, taking the Angle as before; and after the like Manner proceed till the whole is finished.