By this simple mode the level of any intended land, &c. may be correctly taken, observing to limit the sight as much as possible: indeed, it is always best to con fine theni to distances not exceeding three hundred yards ; because the differ ence between the rectilinear and the horizontal levels are then greatly dimin ished, and the whole survey will prove far more correct. This will be easily seen from the following sketch. (Plate VIII. Miscellanies, fig. 2). Let A B re present a sight taken at 2100 yards, and let A C be an equal distance measured on the surface of the segment A D, but brok en oft' at every three hundred yards, i. e. into seven portions : it must be obvious that the line B C will give a greater length than would result from the proportion al ready stated, the perpendicular falling so much beyond D ; and that such differ ence would increase in its disproportions according as the range of sight might be enlarged. To prove this still more clear ly, let us state that the quadrant 0 P (fig 3), of the earth's surface stands on a radius P S of four thousand miles. Now the first taken from the summit 0 of that quadrant would be a parallel to that hori zontal radius, and a tangent to the arc at its summit, as from 0 to X. It is evident that if a sight of four thousand and one miles could be taken in the direction 0 X, a perpendicular falling from X would not even touch the point P, from which it would be a mile distant. It is true, that our sights are not to be compared with the foregoing extents; but it is equally true, that we verge towards the error above shown when we take too long sights.
Perhaps nothing can be more decep tive than the common mode of estimating levels more than once we have witness ed the opinions of smatterers in this branch of surveying, who have levelled the instrument with great exactness, and directed the telescope to a very distant hill, on seeing the point of intersection cut near its summit, have concluded the spot so indicated to be on a level with that where the instrument stood. This mis conception arises purely from a long rec tilinear sight, without considering that the base of a remote hill is a plane, whose surface stands at a very great angle from that on which the level is placed ; as shown by the dotted lines representing a hill R intercepted by the line of sight A very good kind of level is made on a portable plan, by several mechanics in this branch. It consists of a small tube of glass let into a plate with which it is ex actly parallel. This is the surface, chew ing the bubble in the tube, as before de scribed : the under part of the box, which may be about eight inches long, two broad, and two deep, has a spring and screw that cause the box to change its direction from either above or below the horizon, to an exact rectilinear level, as indicated by the air left in the glass tube. At the centre of the bottom of the box is a brass stud, serving to fix into a hole made in the top of a walking-stick, &c. This kind of level, in the hands of a skilful surveyor, may be used to great advantage, where very great precision is not required ; but as the sight is taken only from the upper edges of the box's ends, it does not admit of that great nicety which is indispensable in many opera tions, and where the smallest deviation from a true level might occasion immense expense and inconvenience.
The level represented in Plate Level, was made by the justly celebrated Jesse Ramsden, F. R. S. and considered by him as the most complete. It stands on three legs, which fold up into the size and ap pearance of a moderately thick round stafli three sliding rings, or leather bands, suffice to keep them compact and firm. The upper parts of the legs fit into a brass plate, as in theodolites, on the sur face of which is a strong male screw, serving to fasten the working part of the instrument at pleasure, to its centre. The female screw is cut withinside a projec tion b b of a brass plate a a : this projec tion has a hole through its top, and con tains a brass ball d, screwed into an other similar plate e e ; by which means the two plates are connected together, and the upper one can be turned about in any direction, while the lower one re mains fixed. Four screws n passing through the lower plate, being worked in until they touch the bottom of the upper plate, serve either to fix the latter firmly; or, by unthreading one or two, and work ing in the opposite ones, to change the inclination of the upper plate, and to bring it to an exact level. 'These are called the parallel plates, though they often stand at an angle, the one with the other, when the direction of the upper one requires changing as above shown.
The ball d is perforated with a conical hole, to receive an axis 1, that is screwed to the bottom of the compass box, f, on which are two square brass arms FC, pro jetting from it diametrically opposite to each other. Il is a small brass angle, or frame, called a Y, screwed to the end of the arm C: it supports in its forked ter mination one end of the telescope K, of which the other end rests in a Y, (letter ed N), similar to H, but which can be raised or lowered, by means of a screw having a milled head ; as seen at y. The spirit level L is fixed to the telescope by two screws at its ends, whereby it can be brought into exact adjustment with the culmination of the telescope.
The level, which is the essential part of the instrument, has been already de scribed ; but it is proper to add, that the ends of the tube containing the alcohol, when made of glass, should be hermeti cally sealed at its ends, which should then be cased in brass. Mr. Itamsden prefer red a very slight convexity in the tube ; considering it best adapted for sheaving the most trifling deviation from a perfect level, and causing the bubble to become more accurately centrical. With respect to the telescope, it is similar to those ge nerally fitted to theodolites, &c. and has been described in the preceding part of this article. It is laid on in the two Y pieces, and kept in by two curved pieces of brass. In figure Ii is the achromatic object glass, fixed within the end of-a tube, sliding within the external cylinder of the telescope, and moved very gra dually by a rack and pinion on the mill. headed nut i: the distance of the glass 11 from the eye-piece, is thereby adjusted to a suitable focus.