(Fig.249) and P' the pin; then the plane in which the telescope moves, seen edgewise, is SP'; and, after being turned around, the line of sight moves in the plane SP", as far to one side of the vertical plane SP, as SP' was on the other side of it.

Rectification. Since the second adjustment causes the line of sight to move in a plane perpendicular to the axis on which it turns, it will move in a vertical plane if that axis be horizontal. It may be made so by filing off the feet of the standards which support the higher end of the axis. This will be best done by the maker. In some instruments one end of the axis can be raised or lowered.

(364) Centring eye-piece.

In some in

A

struments, such as that of which a longitudinal
section is shown in the margin, the inner end
of the eye-piece may be moved so that the BE
cross-hairs shall be seen precisely in the cen-
tre of its field of view. This is done by means
of four screws, arranged in pairs, like those of
the cross-hair-ring screws, and capable of mov-
ing the eye-piece up and down, and to right
or left, by loosening one and tightening the
opposite one. Two of them are shown at A, A,
in the figure; in which B, B, are two of the
cross-hair screws.

In some

(365) Centring object-glass. instruments four screws, similarly arranged, two of which are shown at C, C, can move, in any direction, the inner end of the slide which carries the object-glass. The necessity for such an arrangement arises from the impossi

Fig. 250.

bility of drawing a tube perfectly straight. Consequently, the line of collimation, when the tube is drawn in, will not coincide with the same line when the tube is pushed out. If adjusted for one position, it will therefore be wrong for the other. These screws, however, can make it right in both positions. They are used as follows.

Sight to some well defined point as far off as it can be distinctly seen. Then revolve the telescope half around in its supports; i. e. turn it upside down.* If the line of collimation was not in the imaginary axis of the rings or collars on which the telescope rests, it will now no longer bisect the object sighted to. Thus, if the horizontal hair was too high, as in Fig. 251, thus line of Fig. 251.

A

с

B

collimation would point at first to A, and after being turned over, it would point to B. The error is doubled by the reversion, and it should point to C, midway between A and B. Make it do so, by unscrewing the upper capstan-headed screw, and screwing in the lower one, till the horizontal hair is brought half way back to the point. Remember that in an erecting telescope, the cross-hairs are reversed, and vice versa. Bring it the rest of the way by means of the parallel plate screws. Then revolve it in the Ys back to its original position, and see if the intersection of the cross-hairs now bisects the point, as it should. If not, again revolve, and repeat the operation till it is perfected. If the vertical hair passes to the right or to the left of the point when the telescope is turned half around, it must be adjusted in the same manner by the other pair of cross-hairs screws. One of these adjustments may disturb the other, and they should be repeated alternately. When they are perfected, the intersection of the cross-hairs, when once fixed on a point, will not move from it when the telescope is revolved in its

* In Theodolites, the Telescope is revolved in the Ys. I Transits, the maker, by whom this adjustment is usually performed, revolves the Telescope, in the same manner, before it is fixed in its cross-bar.

supports. This double operation is called adjusting the line of collimation."

To test this, Then turn the

This line is now adjusted for distant objects. It would be so for near ones also, if the tube were perfectly straight. sight to some point, as near as is distinctly visible. telescope half over. If the intersection does not now bisect the point, bring it half way there by the screws C, C, of Fig. 250, moving only one of the hairs at a time, as before. Then repeat the former adjustment on the distant object. If this is not quite perfect, repeat the operation.

This adjustment, in instruments thus arranged, should precede the first one which we have explained. It is usually performed by the maker, and its screws are not visible in the Transit, being enclosed in the ball seen where the telescope is connected with the cross-bar.†

All the adjustments should be meddled with as little as possible, lest the screws should get loose; and when once made right they should be kept so by careful usage.

This "adjustment of the line of collimation" has merely brought the intersection of the cross-hairs (which fixes the line of sight) into the line joining the centres of the collars on which the telescope turns in the Ys; but the maker is supposed to have originally fixed the optical axis of the telescope, (i. e. the line joining the optical centres of the glasses), in the same line.

+ The adjustment of "Centring the object-glass is the invention of Messrs. Gurley, of Troy.

CHAPTER IV.

THE FIELD-WORK.

Fig. 252.

LOC

(366) To measure a horizontal angle. Set up the instrument so that its centre shall be exactly over the angular point, or in the intersection of the two lines whose difference of

ᎪᏅ

direction is to be measured; as at B in the figure. A plumb line must be suspended from under the centre. Dropping a stone is an imperfect substitute for this. Set the instrument so that its lower parallel plate may be as nearly horizontal as possible. The levels will serve as guides, if the four parallel-plate screws be first so screwed up or down that equal lengths of them shall be above the upper plate. Then level the instrument carefully, as in Art. (338). Direct the telescope to a rod, stake, or other object, A in the figure, on one of the lines which form the angle. Tighten the clamps, and by the tangent-screw, (see Art. (336)), move the telescope so that the intersection of the crosshairs shall very precisely bisect this object. Note the reading of the vernier, as explained in the preceding chapter. Then loosen the clamp of the vernier, and direct the telescope on the other line (as to C) precisely as before, and again read. The difference of the two readings will be the desired angle, ABC. Thus, if the first reading had been 40° and the last 190°, the angle would be 150°. If the vernier had passed 360° in turning to the second object, 360° should be added to the last reading before subtracting. Thus, if the first reading had been 300°, and the last reading 90°, the angle would be found by calling the last reading, as it really is, 360° + 90° = 450°, and then subtracting 300°.

It is best to sight first to the left hand object and then to the right hand one, turning "with the sun," or like the hands of a watch, since the numbering of the degrees usually runs in that direction.

It is convenient, though not necessary, to begin by setting the vernier at zero, by the upper movement (that of the vernier plate on the circle) and then, by means of the lower motion, (that of the whole instrument on its axis), to direct the telescope to the first object. Then fasten the lower clamp, and sight to the second object as before. The reading will then be the angle desired. An objection to this is that the two verniers seldom read alike.*

After one or more angles have been observed from one point, the telescope must be directed back to the first object, and the reading to it noted, so as to make sure that it has not slipped. A watch-telescope (see Art. 339) renders this unnecessary.

The error arising from the instrument not being set precisely over the centre of the station, will be greater the nearer the object sighted to. Thus a difference of one inch would cause an error of only 3" in the apparent direction of an object a mile distant, but one of nearly 3' at a distance of a hundred feet.

(367) Reduction of high and low objects. When one of the objects sighted to is higher than the other, the "plunging telescope" of these instruments causes the angle measured to be the true horizontal angle desired; i. e. the same angle as if a point exactly under the high object and on a level with the low object (or vice versa) had been sighted to. For, the telescope has been caused to move in a vertical plane by the 3d adjustment of Chapter II, and the angle measured is therefore the angle between the vertical planes which pass through the two objects, and which "project" the two lines of sight on the same horizontal plane.

This constitutes the great practical advantage of these instruments over those which are held in the planes of the two objects observed, such as the sextant, and the "circle" much used by the French.

* The learner will do well to gauge his own precision and that of the instrument (and he may rest assured that his own will be the one chiefly in fault) by measur ing, from any station, the angles between successive points all around him, till he gets back to the first point, beginning at different parts of the circle for each angle. The sum of all these angles should exactly equal 360°. He will probably find quite a difference from that.