The-od′o-lite.
An instrument for measuring horizontal and vertical angles, but particularly adapted for accurately measuring the former.
Its principle is identical with that of the altitude and azimuth instrument; the construction and purpose of the two, however, differ, the latter being employed for astronomical purposes, while the theodolite is used for land surveying; but the better instruments of this class may be employed for observing the altitudes of celestial bodies.
The vertical circle is not generally, however, of sufficient size, nor so graduated as to be available for very accurate astronomical observations.
This instrument has been used in extensive geodetical operations in
England and in this country, such as the
British Ordnance Survey and the United States Coast Survey, while in
France the repeating circle of Borda has been preferred.
The telescope has a motion on a horizontal axis, and has a vertical graduated circle, which has also a horizontal.
See under telescope for notice of the first use of telescopes in triangulation or measuring angles.
The first survey made by an instrument with a perfect circle is said to be that of Zealand, by Bugge, in 1762-68.
Ramsden's theodolite had a circle 3 feet in diameter, and was completed in 1787.
It had two telescopes of 36 inches focal length.
It was used for a triangulation to connect the observatories of
Greenwich and
Paris, and also in the
English, Irish, and Indian trigonometric surveys.
The telescope circle and stand are capable of motion round a vertical axis.
The altazimuth may be considered a modification of the transit instrument, and has been called a transit theodolite, being adapted for meridional or extra-meridional observations indifferently.
Everest's theodolite is so called from its designer,
Sir G. Everest, late of the
East Indian Survey, and is among the best of its class.
The
Wurdemann's theodolite, used by the Coast Survey, is mounted upon a repeating stand, that is, one which has an axis of its own, having a clamp and tangent so as to read any angle on any part of the limb.
This stand has adjusting feet for leveling, so as to bring the axis vertical on uneven ground.
The base of the instrument proper consists of a leveling tripod, from which rises a central column forming the barrel of the axis; on the outside of the column the main
limb of the instrument is fastened.
The central column is of cast-iron, and the principal vertical axis of steel plays within the column.
The upper or large end of the axis has attached to it a plate carrying, firstly, three reading micrometer microscopes, 120° apart; secondly, two columns with Y's for receiving the pivots of the telescope axis.
The pivots rest with one half of the diameter in the Y's, the other half projecting for the legs of the striding level to rest upon.
The telescope is 38 inches focal length, the object-glass 2 9/10 inches aperture, provided with a 4-inch vertical finder-circle for use in taking solar or star azimuths, and on the right-hand side of the telescope is the usual clamp and tangent for vertical fixture and movement.
A small central reflector of 1/10 inch diameter throws the light from a lamp attached outside to the cross lines of the eye-piece.
The light from the lamp, passing through the telescope axis to the center of the tube, is reflected upon the wires by the reflector.
The wires are contained in a micrometer eye-piece.
The clamp and tangent for the horizontal movement of the alidade is not, as usual, attached to the horizontal circle, but on a collar immediately underneath the alidade on a separate disk.
The clamp arm fitting on this disk contains a piece of steel which is pressed against the disk by means of the clampscrew, which fixes the arm, a small portion of the clamp-ring being cut out opposite to the screw, so that there are but three points of contact in clamping.
To the outer end of this clamparm is attached one portion of the tangent screw, whilst the other holds to a projecting part of the alidade plate.
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2544]
Two cross levels on the alidade plate afford means for perfectly leveling the instrument.
The micrometer microscopes read to one minute of arc to one revolution of the screw.
The drum of the screw is divided into 60 divisions, each having the value of 1″, of which tenths are generally estimated, and are quite perceptible.
The peculiar features of the instrument are, —
1. The circle is freed from the clamp and tangent, being independent.
2. The optical power is high.
Without this, mere size of the instrument is of little advantage.
For instance, the microscopic readings on the limits may be read to as great accuracy, 10‴, as the five-foot mural circle of the
Naval Observatory,
Washington.
Lengths of a Degree of Longitude on the Parallels of Latitude, for each Degree of Latitude from the Equator to the Pole.
| Lat. | Miles. | Lat. | Miles. | Lat. | Miles. | Lat. | Miles. | Lat. | Miles. |
| 1° | 59.99 | 19° | 56.73 | 37° | 47.92 | 55° | 34.41 | 73° | 17.54 |
| 2 | 59.96 | 20 | 56.38 | 38 | 47.28 | 56 | 33.45 | 74 | 16.54 |
| 3 | 59.92 | 21 | 56.01 | 39 | 46.63 | 57 | 32.68 | 75 | 15.53 |
| 4 | 59.85 | 22 | 55.63 | 40 | 45.96 | 58 | 31.79 | 76 | 14.52 |
| 5 | 59.77 | 23 | 55.23 | 41 | 45.28 | 59 | 30.9 | 77 | 13.5 |
| 6 | 59.67 | 24 | 54.81 | 42 | 44.59 | 60 | 30. | 78 | 12.48 |
| 7 | 59.55 | 25 | 54.38 | 43 | 43.88 | 61 | 29.09 | 79 | 11.45 |
| 8 | 59.42 | 26 | 53.93 | 44 | 43.16 | 62 | 28.17 | 80 | 10.42 |
| 9 | 59.26 | 27 | 53.46 | 45 | 42.43 | 63 | 27.74 | 81 | 9.38 |
| 10 | 59.09 | 28 | 52.97 | 46 | 41.68 | 64 | 26.3 | 82 | 8.35 |
| 11 | 58.89 | 29 | 52.48 | 47 | 40.92 | 65 | 25.36 | 83 | 7.31 |
| 12 | 58.69 | 30 | 51.96 | 48 | 40.15 | 66 | 24.4 | 84 | 6.27 |
| 13 | 58.46 | 31 | 51.43 | 49 | 39.36 | 67 | 23.44 | 85 | 5.23 |
| 14 | 58.22 | 32 | 50.88 | 50 | 38.57 | 68 | 22.48 | 86 | 4.18 |
| 15 | 57.95 | 33 | 50.32 | 51 | 37.76 | 69 | 21.5 | 87 | 3.14 |
| 16 | 57.67 | 34 | 49.74 | 52 | 36.94 | 70 | 20.52 | 88 | 2. |
| 17 | 57.38 | 35 | 49.15 | 53 | 36.11 | 71 | 19.53 | 89 | 1.05 |
| 18 | 57.06 | 36 | 48.54 | 54 | 35.27 | 72 | 18.54 | 90 | .00 |
note. — Degrees of longitude are to each other in length as the cosines of their latitudes.
