Mathematical Instruments

# Of the Theodolite.

This Theodolite consists of a Brass Circle, cut in form of the Figure B, usually about 12 or 14 Inches in Diameter, whose Limb is divided into 360 Degrees, and each Degree into as many Minutes, either Diagonally, or otherwise, as the largeness of the Instrument will admit.

Underneath, at the Places cc of this Circle, are fixed two little Pillars dd, for supporting an Axis, upon which is fixed a Telescope, with a square Brass Tube, having two Glasses therein, for better perceiving Objects at a great distance; whence this Telescope may be raised or lowered, according as Objects be Horizontal or not. The Ends of the aforesaid Pillars are joined by the Piece gg, upon the Middle of which is soldered a Socket with it’s Screw, for receiving the Top of the Ball and Socket E. Upon and about the Center of the Circle B, must the Index C move, which is a Circular Brass Plate, having upon the Middle thereof a Box and Needle, or Compass, whose Meridian Line answers to the Fiducial Line aa. At the Places bb of the Index are fixed two little Pillars for supporting an Axis, carrying a Telescope in the Middle thereof, whose Line of Collimation must be answerable to the Fiducial Line aa of the Index. This Telescope hath a square Brass Tube, and two Glasses therein, and may be raised or lowered, like that beforementioned. At each End of one of the perpendicular Sides of each Tube of the Telescopes, are fixed four small Sights for viewing nigh Objects thorough them.

The Ends of the Index aa are cut Circular, so as to fit the Divisions upon the Limb of the Circle B, and when the said Limb B is Diagonally divided, the Fiducial Line at one End of the Index shews the Degrees and Minutes upon the Limb. But when the Limb is only divided into Degrees, and every 30th Minute, we have a much better Contrivance for finding, the Degrees, and every 2 Minutes upon the Limb, which is thus: Let the half Arc pa of one End of the Index contain exactly 8 Degrees of the Limb; then divide the said half Arc into 15 equal Parts, at every five of which set the Numbers 10, 20, 30, beginning from the Fiducial Line or middle of the Index. Now each of these equal Parts will be 32 Minutes: Therefore if you have a mind to set the Fiducial Line of the Index to any Number of Degrees, and every 2 Minutes upon the Limb; for Example, to 40 Degrees 10 Minutes; move the Index so, the Fiducial Line being between the 40th Degree, and the 40th Degree and 30 Minutes, that the Line of Division, numbered 10 upon the Index, may exactly fall upon some Line of Division of the Limb; and then the Fiducial Line will shew 40 Degrees, 10 Minutes.

Again: Suppose the Fiducial Line being between the 50th Degree and 30 Minutes, and the 51st, then that Line of Division, of equal Parts on the Index, exactly falling upon some Line of the Divisions of the Limb, will give the even Minutes above 50 Degrees 30 Minutes the Fiducial Line stands at. As suppose the 4th Line of Division of the Index Hands exactly against some Line of Division of the Limb; then the Minutes above 40 Degrees 30 Minutes will be 8, that the Fiducial Line stands at: Understand the same of others.

Fig. D. is the Brass Ball and Socket, in which goes the Head of the three-legged Staff E, for supporting the Instrument when using: These three Legs are moveable by means of Joints, and may be taken shorter by half at the Places aaa, by means of Screws, for better conveniency of Carriage.

Thus have you the best Theodolite, as now made in England, briefly described. The Use thereof will be sufficiently understood by what our Author says of the Use of the Semi-Circle (which is but half a Theodolite), and I in the Use of the Plain-Table, and Circumferentor.

Note, There are some Theodolites that have no Telescopes, but only 4 Perpendicular Sights; two being fastened upon the Limb, and two upon the Ends of the Index. Note likewise, That the Index, and Box and Needle, or Compass of the Theodolite, will serve for a Circumferentor.