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across the interior of the telescope very fine wires, or threads from a spider's web, so that their intersection may not only coincide with the axis CE, but cross it precisely at W, the common focus of the two glasses, where the image of the staff (or distant object) is formed, and therefore the wires and the staff will appear to an observer as one object, or, at least, equally distant from him. The following diagram shows the appearance of the wires and the staff as seen through an inverting telescope; where a b represents the horizontal wire, c and d two

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wires placed at right angles to it, and separated so as to admit, at usual distances, the staff e to appear between them, by which the observer can always tell if the staff-man holds it erect in a lateral direction, as before explained. The staff is represented as seen at the moment of completing an observation; the horizontal cross wire coinciding with the division .20 above 16 feet, the staff being read downwards in consequence of its apparent inversion; the reading, therefore, of such an

observation, to be entered in the field-book, would be 16.20 feet.

The adjustment of the line of collimation consists in making the centre of the horizontal wire (or intersection of the wires in instruments intended for measuring angles) coincide with the optical axis of the telescope ; this, when once accomplished, will, with care, keep correct for a long time, but the placing it in the common focus of the two glasses requires attention at every observation. For detailed instructions upon the former, we refer to the treatise on Mathematical Instruments, &c. ; but as the latter forms part of every observation, and is the source of the perplexing parallax, we shall speak of it in this place.

The cross wires are fixed to a plate, called a diaphragm, attachedby screws to the slide G H, which also carries the slide D F of the eye-piece. The point W, or focus of the object glass, does not remain constant for terrestrial objects, but varies with every change in the distance of the staff; if it be brought closer to the instrument, the image, or focal point, will recede further from the glass, and vice versa; therefore, the wirest and the focus of the eye-piece must be brought to coincide with that of the object glass by their respective slides; and first, the eye-piece should be moved in its slide till its focus coincides with the wires in the tube GH; when this is accomplished, the observer will see the wires perfectly sharp and well-defined ; next, motion must be given to the slide G H, by turn

ing a milled head attached to the telescope, which gives motion to the slide by rack work; this will carry both the wires and the focus of the already adjusted eyepiece to coinc de with the focus of the object glass, on whatever part of the optical axis of the instrument it may be situated. When this is done, the adjustment of the telescope for observation will be complete, and its proof consists in the observer having at the same time a clear and well-defined image both of the staff and the cross wires, which will be the case if they seem to be attached to each other, or, in other words, appear equally distant from him; and the moving about of the observer's eye does not detect any apparent displacement of the staff, with respect to the wires. Such a displacement, or relative motion, is what is meant by parallax; and when it exists, it must be got rid of by a repetition of the adjustment of the glasses as above described, till the motion of the eye will no longer detect the least apparent movement, or passing and repassing of the wires and the staff; till this is done, no correct observation can be made.

From what has been advanced on the subject of the corrections for curvature and refraction, it may be necessary, before entering upon any practical examples, to remark, that such corrections are very seldom applied in practice, the observer, by the arrangements of

his operations, doing away in a great degree their injurious effects, which we will endeavor to explain.

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Suppose it were required to find the difference of level between any two points G and H in the preceding figure; let A B represent a portion of the earth's surface, let C represent the centre, and C G, CI and

Now a spirit-level being

CH the radii of the earth. set up and adjusted at I, an observer looking through the telescope would see objects in the direction of the horizontal line D E only, and a staff held upright at I would be read off in the point E on the horizontal line; but this point is higher than the true level by the distance H E, which is the correction for curvature due to the distance I H (see page 9); and if that quantity be subtracted from the reading of the staff, the remainder will show the difference of level between the points I and H. If the same process be gone through by holding a staff at G, then the difference of level between G and I will also be ascertained, which being compared with the former difference, will show how much higher one of the points G or H is above the other; but it must be evident, that if G and H be equally distant

from I, the horizontal line D E, being a tangent to the surface at the middle point I, must cut the staff at D on the same level with the point E; that is, C D is equal to C E, therefore D and E are level points, being equidistant from the centre of the earth; and if the reading of one staff above the ground is greater than the reading of the other, the difference will at once show the variation of level between the points where the staves were held, viz., G and H; the effect of curvature is thus removed by simply placing the instrument midway between the station staves. The effects of the atmospheric refraction will likewise be done away with in the same process, because it will affect both observations alike, unless under peculiar circumstances of the weather, &c., over which the observer has no control.

The above method of finding differences of level, by placing the instrument as near as possible midway between the two staves, and noting their readings, is the one adopted in practice; but as it can scarcely ever happen, on account of the extent of the work, that one placing of the instrument will complete it, a succession. of similar operations must be performed, as shown in the annexed engraving.

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Suppose it were required to find the difference of

level between the points A and G; a staff is erected at

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