Vertical Arc.-Proceeding with the consideration of the component parts of the theodolite, we now come to the vertical arc or circle, which in the former case consists of a semicircle of metal, divided on one side each way from 0 deg. to 90 deg., and subdivisions, whilst the other side is divided to show the hypotenusal allowance in links per chain. Connected with this semicircle are trunnions, which work in journals in the head of the bearers or " A frames E E (Figs. 89, 90, and 94); and on the top is a strong bar, carrying the supports or Y's, R' R', in which rests the telescope G.. It is to these supports, from their resemblance to the letter Y, that this particular type of instrument is so called. The telescope G is held in the Y's (Fig. 95) by clips, working upon a hinge on one side, and fastened on the other by a pin passing through eyes in

the jaw of the Y and the clip. This arrangement has been superseded in the most modern theodolite by a spring, which prevents any possibility of the telescope falling out of the supports by neglecting to fasten the pin in the clips.

Compass.-Beneath the telescope and between the "A" frames a compass-box D is fixed upon the vernier plate, containing a silver ring, graduated from 0 deg. to 360 deg. The needle is supported upon an agate centre, and has a lever connected with it, by which, when not in use, it may be thrown off its centre, and thus save undue wear. Attached to the compass-box is a vernier for reading the minute subdivisions on the vertical arc, which is clamped by the screw T on the top of the "A" frame, whilst slow motion is effected by the tangent screw u.

Telescope. The telescope & consists of two tubes, one sliding within the other. The outer tube has at its further end J (Fig. 96) the" object-glass," which forms at its focus an inverted image of the object looked at. This is protected by a sliding cylinder J, which pulls out to shield the object-glass from the sun and weather, at the end of which is a movable disc to close it up when not in use (see sketch, Fig. 97. The inner tube has at its nearer end

Ha combination of glasses called the eye-piece, which magnifies the inverted image. By moving the inner tube inwards and out

wards, with the rack and pinion contained within it, the milledhead 0 working a screw through a collar on the larger tube, the foci of the object-glass and eye-piece are adjusted till they coincide, which is known by the distinct and steady

appearance of the image.

Upon the outer tube are also collars a a, very accurately turned, to fit into the Y's of the "A" frame.

O

DISC

The Diaphragm.-At the common focus of the object-glass and eye-piece where the inverted image is seen is the diaphragm or partition at G G G. The diaphragm consists of a ring of metal (Fig. 98) held within the telescope by means of four capstan screws placed at right angles to each other. The screws work easily through holes in the telescope, but the threads actuate the diaphragm ring, so that it may be brought vertically or horizontally nearer the sides of the telescope, by screwing or unscrewing. Across this diaphragm or partition are usually three spider's webs, or equally very fine platinum wires. (see Fig. 99), one horizontal, A B, and the other two, c D, E F,

Fig. 97.

deviating slightly to opposite sides of a vertical plane. The point G, where these wires intersect, should be exactly in the axis or

line of collimation of the telescope. In some theodolites there are only two wires, one vertical and the other horizontal.

Attached to the telescope underneath (in some cases above) is a spirit-level K (Fig. 96), which by screws may be set exactly parallel to the line of collimation; so that when the air bubble is in the centre of the level the telescope is horizontal.

The Vernier.-The vernier, in its ordinary sense, is a contrivance wherewith the intervals between the divisions on the primary scale may be accurately measured. It is a scale whose length is generally one less than a certain number on the primary scale, so that, supposing the lower plate is divided into degrees and half-degrees, if we take 29 of the subdivisions (or 14 deg. 30 min.*) and divide this length into one more or less parts than those of the primary scale, whose length regulates that of the vernier, we shall have a means of determining the actual number of minutes which intervene between the subdivisions.

It is customary to divide the vernier into thirty equal parts, so that it has thirty spaces to the twenty-nine subdivisions on the limb.

For greater minuteness of observation some modern theodolites are divided into thirds and fourths as well as into half degrees, in which cases the verniers are divided into twenty and fifteen parts respectively, so as to accurately record the intervals between the subdivisions.

In consequence of the limb and vernier being circular in shape, it is found more easy to illustrate the relationship of the latter to the former by straight line, and Figs. 100, 101, 102 will serve to do so.

Fig. 100 shows a portion of the primary scale drawn straight from 45 deg. to 72 deg., and from 50 deg. to 64 deg. 30 min. I have marked the 29 half-degrees as the length of the vernier. Now, taking this length and dividing it afresh into thirty equal parts, it will be seen by Fig. 101 that, whereas the vernier scale commences at 50 deg. and terminates exactly at 64 deg. 30 min., so that the commencement and termination are coincident with the division 50 deg. and 64 deg. 30 min. on the lower scale, yet not one of the divisions of the vernier intermediate between its commencement and termination will cut any one of the points in the lower scale between 50 deg. and 64 deg. 30 min. If the student can once grasp this fact, then the difficulty of the vernier is simplified.

Now, if the foregoing argument be proven, it is easy to understand that once the vernier moves from 50 deg. it is possible for

66739

*The degree is shown by a circle thus "," minutes by one dash thus ""',' and seconds by two dashes, thus ""."

15°00′ 00′′ or 30 Half s
LENGTH OF VERNIER 14°30'.00'

50

any one of its divisions to intersect any one of the divisions and subdivisions of the lower scale, but only one at a time.

As an illustration, the first division of the vernier may be in line with 50 deg. 30 min., and such being the case, the other twenty-nine divisions would not be coincident. This then would show the angle to be 50 deg. 1 min. Again, the tenth division

may be coincident with 45 deg. This shows that ten minutes more than the 50 deg. or commencement have been recorded, in other words, 50 deg. 10 min. Further, if the twentieth division or the upper scale is coincident with any division or subdivision on the lower one, it must of necessity be at 60 deg., consequently the reading of the vernier is 50 deg. 20 min. And lastly, if the thirtieth division or end of the upper scale is coincident with one

069

Fig. 102.

790

of the divisions or subdivisions of the lower one, it must be at 65 deg., and thus, thirty of the divisions in the upper scale having traversed from left to right, the arrow a (Fig. 101) will be coincident with the subdivisions between 50 deg. and 51 deg., or at 50 deg. 30 min. So we see, that even if each of the thirty divisions of the upper scale are consecutively coincident with any division or subdivision of the lower one, at the end we have only moved one half degree in a direction towards the right.

Now, supposing it is discovered by aid of the microscope that the arrow A (Fig. 102) has passed 50 deg. 30 min., common sense will tell that the first half-degree in the lower plate has been passed, and it is desired to ascertain how many of the minutes in the second half-degree are recorded by the vernier.

In this case (Fig. 102) it will be seen that the seventh division of the upper scale is coincident with 54 deg., and seeing that the arrow a has passed the first half-degree beyond 50 deg., then the reading will be 50 deg. 30 min. + 7 sec. 50 deg. 37 min., and supposing the thirtieth division of the vernier was coincident with any in the lower scale, it must be that at 65 deg. 30 min. when the arrow a will have reached the full length of the first degree past 50 deg. or 51 deg.

At the risk of being thought verbose upon this subject, I have endeavoured to make the vernier appear as clear as possible. The foregoing remarks apply to those theodolites whose limbs are only divided into degrees and half-degrees; but in the larger instruments the degrees are divided into third parts of twenty minutes each. "Suppose, for example, the limb is so divided, and that it is to be subdivided by a vernier to third parts of a degree or 20 min., each subdivision being one-sixtieth part of the primary division, the length of the vernier will be 60 — 1 = 59 divisions of the primary scale; and it will be divided into sixty equal parts, each equal to 59-60ths of a division of the primary scale.' Το make this more simple, if we take twenty of the divisions and subdivisions of the lower scale and deduct one from that length, then by dividing this length of nineteen parts of the lower scale into twenty we shall have a vernier which will exceed each single minute of the first third of a degree, as each one becomes coincident with one of the divisions or subdivisions of the primary scale.

The cost of "Y" theodolites is as follows: four-inch, £21; fiveinch, £25; six-inch, £30.

Transit Theodolite. This is unquestionably a more reliable instrument (Fig. 103) than the cradle, although objections against it have been raised, principally on account of the increased height of the standards or a frames. I can only say that I would never use any other where accuracy and facility of work are important. One of its greatest advantages is that by reason of the standards