ment, of which the telescope may form a part, will only have reference to one particular point in this field of view, which particular point is considered as the center of this field of view. We must therefore place some fixed point in the field of view, and in the focus of the eye-piece, and the point to which the measurement will have reference will be that point of the object viewed, which appears to be coincident with this fixed point, or which, as the technical phrase is, is bisected by the fixed point.

The intersection of two fixed lines will furnish us with such a fixed point, and consequently two lines of spider's thread are fixed at right angles to each other in the focus of the eye-piece. They are attached by a little gum to a brass ring of smaller dimensions than the tube of the telescope, and which is fixed to the tube by four small screws, a, b, c, d. If the screw d be eased, while at the same time c is tightened, the ring will be moved to the right; but, if c be eased and d tightened, the ring will be moved to the left; and in a like manner it may be moved up or down by means of the screws a and b.

C

When the instrument is in adjustment, the axis of the tube of the telescope is set truly horizontal by means of the level beneath it, and the line of observation ought consequently to be parallel to this axis. Let A represent the proper position of the intersection of the cross

wires, and o A, the direction

of the axis of a pencil of light passing through the object

10

glass and coming to its focus at a. Then, the axis of the tube of the telescope being set truly horizontal, the line a o is also truly horizontal, and every point bisected by the intersection of the cross wires will be situated on the prolongation of the horizontal line A o.

Suppose now the position of the diaphragm carrying the cross wires to have become deranged. so that the point of intersection is moved to B, then every point bisected by the intersection of the cross wires will be on the prolongation of the line B O, and will consequently be below the true level point on the line a 0.

Let now the telescope be turned half round in the Ys, and

let the annexed figure represent it in its new position; then, in this new position of the telescope, the prolongation of the line B O will rise above the prolongation of the level

line A o, and, at the same distance from the telescope, the point now bisected by the intersection of the cross wires will be as much above the true level point on the line A o as the point before bisected by them was below it. The true level point is therefore midway between the two points observed in the two positions of the telescope, and the diaphragm carrying the cross wires is to be moved by means of the screws a, b, c, d, till their point of intersection coincides with that true level point. The telescope is then to be again turned round upon the Ys, and, if the same point be still bisected by the intersection of the cross wires, they are in their proper position; but, if not, the same method of adjustment must be repeated till the same point is bisected by the intersection of the cross wires in every position of the telescope.

This error of derangement has a technical denomination. The line o A, or o B, from o to the point of intersection of the cross wires, is called the line of collimation, and the error arising from their derangement, which we have shown the method of detecting and correcting, is called the error of collimation.

When the image of the object viewed, formed by the objectglass, either falls short of, or beyond the place of the cross wires, the error arising from this cause is called parallax. The existence of parallax is determined by moving the eye about when looking through the telescope, observing whether the cross wires change their position, and are flittering and undefined.

To correct this error, first adjust the eye-piece, by means of the moveable eye-piece tube, till you can perceive the cross wire clearly defined, and sharply marked against any white object.

Then by moving the milled-headed screwa, at the side of the telescope, the internal tube a is thrust outwards or drawn inwards, until you obtain the proper focus, according to the distance of the object, and you are enabled at once to see clearly the object, and the intersection of the wires, clearly and sharply defined, before it. The existence of parallax is very inconvenient, and, where disregarded, has frequently been productive of serious error. It will not always be found sufficient to set

ADJUSTMENTS OF BUBBLE-TUBE, AND OF AXIS. 101

the eye-glass first, and the object-glass afterwards. The setting of the object-glass, by introducing more distant rays of light, will affect the focus of the eye-glass, and produce parallax or indistinctness of the wires, when there was none before; the eye-piece must, in this case, be adjusted again.

Generally, when once set for the day, there is no occasion for altering the eye-glass, but the object-glass will of course have to be altered at every change of distance of the object.

In adjusting the instrument, the parallax should be first corrected, and then the error of collimation. The line of collimation being thus brought to coincide with the axis of the tube of the telescope, two further adjustments are necessary: the first to adjust the bubble-tube, so that it may truly indicate when the axis of the telescope is horizontal; and the second to set the axis of the telescope perpendicular to the vertical axis round which the instrument turns.

To adjust the Bubble-Tube.-Move the telescope till it lies in the direction of two of the parallel plate screws, and by giving motion to these screws bring the air bubble to the center of its run. Now reverse the telescope carefully in the Ys, that is, turn it end for end; and, should the bubble not settle at the same point of the tube as before, it shows that the bubble-tube is out of adjustment, and requires correcting. The end to which the bubble retires must then be noticed, and the bubble made to return one-half the distance by turning the parallel plate screws, and the other half by turning the capstan-headed screw at the end of the bubble-tube. The telescope must now again be reversed, and the operation be repeated, until the bubble settles at the same point of the tube, in the center of its run, in both positions of the instrument. The adjustment is then perfect, and the clips which serve to confine the telescope in the Ys should be made fast.

Lastly, to set the Axis of the Telescope perpendicular to the Vertical Axis round which the Instrument turns.-Place the telescope over two of the parallel plate screws, and move them, unscrewing one while screwing up the other, until the bubble of the level settles in the center of its run; then turn the instrument half round upon the vertical axis, so that the contrary ends of the telescope may be over the same two screws, and, if the bubble does not again settle at the same point as before, half the error must be corrected by turning the screw B, and the other half by turning the two parallel plate screws, over which the telescope is placed. Next turn the telescope a quarter round, that it may lie over the other two screws,

and repeat the process to bring these two screws also into adjustment; and when, after a few trials, the bubble maintains exactly the same position in the center of its run, while the telescope is turned all round upon the axis, this axis will be truly vertical, and the axis of the telescope, being horizontal by reason of the previous adjustment of the bubbletube, will be perpendicular to that vertical axis, and remain. truly horizontal, while the telescope is turned completely round upon the staves. The adjustment is therefore perfect.

The object of the above adjustments is to make the line of collimation move round in a horizontal plane, when the instrument is turned round its vertical axis, and the methods above explained suppose that the telescope itself is constructed with the utmost perfection, so that the axis of the tube carry ing the object-glass is always in the same straight line with the axis of the main tube, which carries the diaphragm with the cross wires. If this perfection in the construction of the instrument does not exist, the line of collimation will vary, as the tube carrying the object-glass is thrust out, and drawn in, to adjust the focus for objects of different distances. What is really required, then, is that the cross wires be so adjusted that the line of collimation may be in the same straight line with the line in which the center of the object-glass is moved, and that the bubble of the level be at the center of its run, when this line of collimation is directed to view objects, at the same level, or at the same distance from the center of the earth

We are indebted to Mr. Gravatt, of whose level we shall hereafter speak, for a method of collimating, which satisfies the above requirements, and removes any error arising from imperfection in the slide of the telescope, while at the same time the line of collimation is set with the end at the objectglass, slightly depressed, instead of exactly horizontal, so as to remove, or nearly so, the errors arising from the curvature of the earth, and the horizontal refraction.

To examine and correct the Collimation by Mr. Gravatt's Method.—" On a tolerably level piece of ground drive in three stakes at intervals of about four or five chains, calling the first stake a, the second b, and the third c.

"Place the instrument half way between the stakes a and b, and read the staff A, placed on the stake a, and also the staff B, placed on the stake b; call the two readings, Aʼand B′; then, although the instrument be out of adjustment *,

* The axis of the instrument is to be set vertical by means of the parallel plate screws, by placing the telescope over each pair alternately, and moving them, until the air bubble remains in the same position, when the instru ment is turned half round upon its axis.

yet the points read off will be equidistant from the earth's center, and consequently level.

"Now remove the instrument to a point half way between b and c. Again read off the staff B, and read also a staff placed on the stake c, which call staff o (the one before called a being removed into that situation). Now, by adding the difference of the readings on B (with its proper sign) to the reading on o, we get three points, say A', B', and c', equidistant from the earth's center, or in the same true level.

"Place the instrument at any short distance, say half a chain beyond it, and, using the bubble merely to see that you do not disturb the instrument, read all three staffs, or, to speak more correctly, get a reading from each of the stakes, a, b, c; call these three readings A", B", d'. Now, if the stake b be half way between a and c *, then ought o'"-d′-(A′′-A') to be equal to 2 [B"-B'-(A"-A)]; but if not, alter the screws which adjust the diaphragm, and consequently the horizontal spider line, or wire, until such be the case; and then the instrument will be adjusted for collimation.

"To adjust the spirit bubble without removing the instrument, read the staff A, say it reads A", then adding (A”—A) with its proper sign to B we get a value, say B'".

66 Adjust the instrument by means of the parallel plate screwst, to read B'" on the staff B.

Now, by the screws attached to the bubble-tube, bring the bubble into the center of its run.

"The instrument will now be in complete practical adjustment for level, curvature, and horizontal refraction, for any distance not exceeding ten chains, the maximum error being only 10th of a foot."

Before making observations with this instrument, the adjustments should be carefully examined and rectified, after which the screw B should never be touched; but at each station the parallel plate screws alone should be used for setting the axis round which the instrument turns truly vertical, when, in consequence of the adjustments previously made, the line of collimation will be truly level. For this purpose the telescope must be placed over each pair of the parallel plate screws alternately, and they must be moved till the air bubble settles in the middle of the level, and the operation being repeated till the telescope can be turned quite round upon the staff-head, without any change taking place in the position of the bubble, the instrument will be ready to read off the graduations upon the levelling staves, which we proceed to describe.

* Whatever be the distances between the stakes a, b, and C, the following proportions ought to hold, viz. :

·

The distance from ab: the distance a to c:: B"--B′ — (A′′ —A′): 0′′-d —(A”—A').

If this adjustment be made by the screw B, instead of the parallel plate screws, the line of collimation will be brought into its proper position with respect to the vertical axis.