covered with glass, to exclude dust and moisture. In the figure the hatchings are drawn in different directions on the parts which move with the Vernier, and on those which move only with the limb.

(329) The Telescope. This is a combination of lenses, placed in a tube, and so arranged, in accordance with the laws of optical science, that an image of any object to which the Telescope may be directed, is formed within the tube, (by the rays of light coming from the object and bent in passing through the object-glass) and there magnified by an Eye-glass, or Eye-piece, composed of several lenses. The arrangement of these lenses are very various. Those two combinations, which are preferred for surveying instruments, will be here explained.

Fig. 215 represents a Telescope which inverts objects. Any object is rendered visible by every point of it sending forth rays of light in every direction. In this figure, the highest and lowest points of the object, which here is an arrow, A, are alone considered. Those of the rays proceeding from them, which meet the object-glass, 0, form a cone. The centre line of each cone, and its extreme upper and lower lines are alone shown in the figure. It will be seen that these rays, after passing through the object-glass, are refracted, or bent, by it, so as to cross one another, and thus to form at B an inverted image of the object. This would be rendered visible, if a piece of ground glass, or other semi-transparent substance, was placed at the point B, which is called the focus of the object-glass. The rays which form this image continue onward and pass through the two lenses C and D, which act like one magnifying glass, so that the rays, after being refracted by them, enter the eye at such angles as to form there a magnified and inverted image of the object. This combination of the two plano-convex lenses, C and D, is known as "Ramsden's Eye-piece."

This Telescope, inverting objects, shows them upside down, and the right side on the left. They can be shown erect by adding one or two more lenses as in the marginal figure. But as these lenses absorb light and lessen the distinctness of vision, the former arrangement is preferable for the glasses of a Transit or a Theodolite. A little practice makes it equally convenient for the observer, who soon becomes accustomed to seeing his flagmen standing on their heads, and soon learns to motion them to the right when he wishes them to go to the left, and vice versa.

Figure 216 represents a Telescope which shows objects erect. Its eye-piece has four lenses. The eyepiece of the common terrestrial Telescope, or spy-glass, has three. Many other combinations may be used, all intended to show the object achromatically, or free from false coloring, but the one here shown is that most generally preferred at the present day. It will be seen that an inverted image of the object A, is formed at B, as before, but that the rays continuing onward are so refracted in passing through the lens C as to again cross, and thus, after farther refraction by the lenses D and E, to form, at F, an erect image, which is magnified by the lens G.

In both these figures, the limits of the page render it necessary to draw the angles of the rays very much out of proportion.

(330) Cross-hairs. Since a considerable field of view is seen in looking through the Telescope, it is necessary to provide means for directing the line of sight to the precise point which is to be observed. This could be effected by placing a very fine point, such as that of a needle, within the Telescope, at some place where it could be distinctly seen. In practice this fine point is obtained by the intersection of two very fine lines, placed in the common focus of the object-glass and

of the eye-piece. These lines are called the cross-hairs, or crosswires. Their intersection can be seen through the eye-piece, at the same time, and apparently at the same place, as the image of the distant object. The magnifying powers of the eye-piece will then detect the slightest deviation from perfect coincidence. "This application of the Telescope may be considered as completely annihilating that part of the error of observation which might otherwise arise from an erroneous estimation of the direction in which an object lies from the observer's eye, or from the centre of the instrument. It is, in fact, the grand source of all the precision of modern Astronomy, without which all other refinements in instrumental workmanship would be thrown away." What Sir John Herschel here says of its utility to Astronomy, is equally applicable to Surveying.

The imaginary line which passes through the intersection of the cross-hairs and the optical centre of the object-glass, is called the line of collimation of the Telescope.*

The cross-hairs are attached to a ring, or short thick tube of brass, placed within the Tele

scope tube, through holes in which pass loosely four screws, (their heads being seen at a, a, a, in Figs. 212 and 213), whose threads enter and take hold of the ring, behind or in front of the cross-hairs, as shown (in front view and in section) in the two figures in

Fig. 217.

Fig. 218.

the margin. Their movements will be explained in Chapter III. Usually, one cross-hair is horizontal, and the other vertical, as in Fig. 217, but sometimes they are arranged as in Fig. 218, which is thought to enable the object to be bisected with more precision. A horizontal hair is sometimes added.

The cross-hairs are best made of platinum wire, drawn out very fine by being previously enclosed

* From the Latin word Collimo, or Collineo, meaning to direct one thing towards another in a straight line, or to aim at. The line of aim would express the meaning.

in a larger wire of silver, and the silver then removed by nitric acid. Silk threads from a cocoon are sometimes used. Spiders' threads are, however, the most usual. If a cross-hair is broken, the ring must be taken out by removing two opposite screws, and inserting a wire with a screw cut on its end, or a stick of suitable size, into one of the holes thus left open in the ring, it being turned sideways for that purpose, and then removing the other screws. The spider's threads are then stretched across the notches seen in the end of the ring, and are fastened by gum, or varnish, or beesThe operation is a very delicate one. The following plan has been employed. A piece of wire is bent, as in the figure, so as to leave an opening a little wider than the

wax.

ring of the cross-hairs. A cobweb is cho

sen, at the end of which a spider is hanging, and it is wound around the bent wire, as in the figure, the weight of the insect

Fig. 219.

keeping it tight and stretching it ready for use, each part being made fast by gum, &c. When a cross-hair is wanted, one of these is laid across the ring and there attached. Another method is to draw the thread out of the spider, persuading him to spin, if he sulks, by tossing him from hand to hand. A stock of such threads must be obtained in warm weather for the winter's wants. A piece of thin glass, with a horizontal and a vertical line etched on it, may be made a substitute.

(331) Instrumental Parallax. This is an apparent movement of the cross-hairs about the object to which the line of sight is directed, taking place on any slight movement of the eye of the observer. It is caused by the image and the cross-hairs not being precisely in the common focus, or point of distinct vision of the eye-piece and the object glass. To correct it, move the eye-piece out or in till the cross-hairs are seen clearly and sharply defined against any white object. Then move the object glass in or out till the object is also distinctly seen. The cross-hairs will then seem to be fixed to the object, and no movement of the eye will cause them to appear to change their place.

Fig. 220.

EOS

(332) The milled-headed screw seen at M, passing into the telescope has a pinion at its other end entering a toothed rack, and is used to move the object glass, O, out and in, according as the object looked at is nearer or farther than the one last observed. require a long tube: long distances a short tube.

Short distances

The eye-piece, E, is usually moved in and out by hand, but a similar arrangement to the preceding is a great improvement. This movement is necessary in order to obtain a distinct view of the cross-hairs. Short-sighted persons require the eye-piece to be pushed farther in than persons of ordinary sight, and old or longsighted persons to have it drawn further out.

(333) Supports. The Telescope of the Transit is supported by a hollow axis at right angles to it, which itself rests at each end, on two upright pieces, or standards, spreading at their bases so as to increase their stability. In the Theodolite, the telescope rests at each end in forked supports, called Ys, from their shape. These Ys are themselves supported by a cross-bar, which is carried by an axis at right angles to it and to the telescope. This axis rests on standards similar to those of the Transit. The Telescope of the Theodolite can be taken out of the Ys, and turned "end for end." This is not usual in the Transit. Either of the above arrangements enables the Telescope to be raised or depressed so as to suit the height of the object to which it is directed. A telescope so disposed is called a "plunging telescope."

In some instruments there is an arrangement for raising or lowering one end of the axis. This is sometimes required for reasons to be given in connection with " Adjustments.'

(334) The Indexes. The supports, or standards, of the telescope just described are attached to the upper, or index-carrying circle.* This, as has been stated, can turn freely on the lower or graduated circle, by means of its conical axis moving in the hollow conical axis of the latter circle. This upper circle carries the index, V,

* In some instruments this circle is the under one. In our figures it is the upper one, and we will therefore always speak of it as such.