577.—The general appearance of the instrument resembles the transit theodolite, already described [art. 368], in every way except for the addition of the microscope and scale, shown in perspective in Fig. 250. The details of construction of the microscopic apparatus may be followed in Fig. 251. T telescope with sensitive level B mounted upon it; R body of microscope connected solidly upon the same axis as the telescope, shown in half section. The eye-piece is placed at right angles to the microscope and telescope, and reads through the reflection of a prism P to the face of the instrument. The details of the eye-piece are shown in section Fig. 252. The tangential scale is shown in section Fig. 251 S with the micrometer with edge reading vernier at M. The compass of the instrument C is of the trough form, and placed on the opposite side to the level to be used after transitting the telescope from the position in which it is shown in the figure. The axis of the connected telescope and microscope is exactly 6 inches above the surface of the tangential scale S.
Fig. 253.—Omnimeter webs; a telescope, b microscope.
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578.—The telescope diaphragm is generally webbed with one horizontal and two vertical webs, Fig. 253 a, the altitude reading being taken from the top of the horizontal web, and the horizontal angular position from the centre of the interval between the vertical webs. The microscope diaphragm b has two horizontal webs, and reads from the centre of the interval, which is judged by the eye. Observed in this manner, there is no error due to covering angle subtended by the webs themselves. The most exact reading is obtained with a fine point.
579.—Reading of the Tangent Scale.—As the micrometer divides half a principal division into 500, the complete figured divisions are therefore divided into 1000. This is done for the sake of decimal notation. In reading it is only necessary to observe that the shorter or half division is 500, which must be added to the micrometer reading when it is past this division; as for instance 65½ reading is 65,500, and say the micrometer reads 234 past this, the reading is then clearly 65,500 + 234 = 65,734, just as before described for reading half degrees with the vernier.
580.—Value of the Scale taken in Rectangular Coordinates.—The radius from the transverse axis of the telescope to the tangent surface of the scale is exactly 6 inches. The scale is 4 inches divided into 100,000 parts, as it is read with the aid of the micrometer and vernier. The radius therefore in terms of the scale would be at 6 to 4, that is 150,000. By this we see that the divisions of the scale by the angle subtended give tangents, the value of each division of which is the reciprocal of this on 150,000 of the radius or base to any unit we may select. If we make the unit 1 foot, then one division represented by a unit of change of position of the vernier reading, and consequently of equal angular change in the direction of the axis of the telescope, would give a tangent of 1 foot upon a stadium placed at 150,000 feet distance. If the stadium were made 10 feet, as is usual, the same angular magnitude would be traversed in ten times this distance, or over 280 miles, making the value of the units of the vernier 1,500,000. This will give a general idea of the delicacy of the instrument so far as constructive principles are concerned, and not its performance.
581.—The Stadium is marked off in a number of feet, links, or metres, according to the unit taken for measurement of the surface of the land. The English stadium is generally formed of a 14-feet levelling staff, with the surface painted with a ground of plain white. At 10 feet apart two black bands about 2 inches wide are painted in, leaving in the centre of each band a clear white line of about one-tenth of an inch in width. These white lines are carefully set to 10-feet standard centre to centre. But a better plan is to have two equilateral triangles painted, with their apices meeting to the centre. An intermediate 5-feet line is drawn in black, which is found convenient for near measurements, to avoid too great angular displacement of the telescope. When the measurement is in chains, 15 links or 20 links may be taken for the distance of the lines apart to give the tangent. For metre measurement 3 metres are commonly taken for the stadium division. These are in each case subdivided. The lowest stadium reading should be 1 foot at least from the ground to avoid grass and other obstructions.
