then, although the instrument be out of adjustment,* yet the points read off will be equi-distant from the earth's centre, 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 c (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 c, we get three points, say A', B', and c', equidistant from the earth's centre, 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", c". Now, if the stake b be half way between a and c,† then ought d'-c' — (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 (À”” —▲ ́) with its proper sign to B' we get a value, say B ́”.

"Adjust the instrument by means of the parallel plate screws, to read в"" on the staff B.

"Now, by the screws attached to the bubble-tube, bring the bubble into the centre 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 onlyth of a foot."

Gravatt's method of collimating is objectionable from its

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

† Whatever be the distances between the stakes a, b, c, the following proportions ought to hold, viz. :—

The distance from a b: the distance a to c :: B"- B′ — (A′′ — A′) : c′′ — α′ — (A′′—A'): if not the diaphragm does not move in a straight line.

‡ 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.

needless complexity in the case of a good instrument, and from its failing to correct a bad one, since the curvilinear motion of the diaphragm, if any, which it indicated, can only be set right by the instrument maker.

To test and adjust, if necessary, the Collimation of a Level, the following simple method is the best:-If a pool of water large enough be at hand, drive in two stakes, three or four chains apart, exactly level with the surface of the water. If no such pool of water be convenient, select a piece of ground as nearly level as possible, and drive in two stakes, three or four chains apart, until the readings obtained from a point midway between them be exactly the same for each: then, if the instrument have been set up with its axis truly vertical, the tops of the two stakes will be exactly on the same level, as is the case with the stakes in the pool of water.

Set up the instrument in the line of the stakes, about half a chain beyond one of them; then if the readings of the staff, placed alternately on each of the stakes, be the same, the line of collimation is correct; but if not, alter the position of the diaphragm, until exactly the same reading is obtained from both stakes, and the collimation will be adjusted.

The instrument having been carefully examined and rectified, in using the instrument the screw в 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 stand, 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.

GRAVATT'S DUMPY LEVEL.

To Mr. Gravatt is undoubtedly due the credit of having, in the construction of the Dumpy level, led the way to all the improvements which have recently been made in this instrument, terminating in the improved Y level, than which we

can imagine nothing better adapted to satisfy all the requisites of a perfect instrument.

We shall here merely mention the characteristic points of Gravatt's level; and its construction, and mode of adjustment by the maker, as well as the method of using it, will be fully understood from the detailed description of the Y level (p. 12).

This instrument is furnished with an object-glass of large aperture and short focal length; and, sufficient light being thus obtained to admit of a high magnifying power in the eye-piece, the advantages of a much larger instrument are

secured, without the inconvenience of its length: hence has arisen the name of Dumpy, given to the instrument. The diaphragm is carried by the internal tube, a a, which is nearly equal in length to the external tube. The external tube, TT, is sprung at its aperture, and gives a steady and even motion to the internal tube, a, a, which is thrust out, and drawn in, to adjust the focus for objects at different distances, by means of the milled-headed screw A. The spirit level is placed above the telescope, and attached to it by capstan-headed screws, one at either end, by means of which the bubble can be brought to the centre of its run.

The telescope is attached to a horizontal bar, but room is just left between the telescope and the bar for the compassbox. By this means the instrument is rendered very firm and compact, in comparison with the old instrument, in which the level was placed below the telescope.

A cross level, k, is placed upon the telescope at right angles to the principal level, 7, 7, by which we are enabled to set the instrument up at once with the axis nearly vertical. This is intended to give the advantages of expedition in setting the instrument, and saving in the wear and tear of the parallel plate screws. From its extreme shortness, however, it does not perform its duty well, and to give it

greater length, to a sufficient extent to be really useful, would be very inconvenient, and it would be then very liable to disarrangement.

A mirror, m, mounted upon a hinge-joint, is placed at the end of the level 7, 7, so that the observer, while reading the staff, can at the same time see that the instrument retains its proper position-a precaution by no means unnecessary in windy weather, or on bad springy ground.

The telescope is attached to the horizontal bar by capstanheaded screws, B, B, by which the line of collimation is set perpendicular to the vertical axis; and the instrument is set up upon parallel plates, as will be understood from the description of the Y level.

ELLIOTT'S IMPROVED DUMPY LEVEL.

In Gravatt's, as in levels previously constructed, the level, telescope, and horizontal bar were made in one piece, and the parallel plate, with conical axis, formed a head-piece to which the former was screwed when in use. Now a tighter or slacker connection between the telescope and the parallel plate portion of the instrument would produce a disparagement, which would manifest itself in the impossibility of making the bubble maintain the centre of its run, whilst the instrument was turned completely round on its axis. For this reason it is imperative always, in levels so fixed to the parallel plates, to turn them constantly to the right, and never to the left, in adjusting them and pointing them for use. If they were often turned to the left, not only would their correctness be certainly injured, but they might even get screwed off, and fall.

In the level now under consideration, the horizontal bar and conical axis are in one piece, and cannot be disunited, so that the level, telescope, and parallel plates are not adapted for separation, or liable to the disarrangement which accompanies it. Secondly, the horizontal bar is made so as to have its principal thickness and strength in the vertical direction, and not in the horizontal, where there is neither any strain nor any material injury that could be produced by a strain. Thirdly, the cross-level k is removed, and a circular level is placed below the telescope instead of the compass box.