THE LEVEL. 307. A level is an instrument used for ascertaining whether a given straight line is or is not horizontal. F K B C G The essential part of it consists of a glass tube ABC, in the form of the arc of a circle, which is closed at both ends and is nearly full of water. The tube, being not quite full of water, will have a bubble D in it. This bubble, when the tube is at rest, will only rest at the highest point of the tube. The tube is fixed in a case of wood or metal which is so made that when the base of it FG is horizontal the highest point K of the tube is visible, and the bubble can be seen at rest in it at the highest point of the arc of the tube. This highest point is carefully marked on the tube. To ascertain whether any given line is horizontal it is only necessary to put the base FG of the case of the 'level' in the position of that line and watch the position which the bubble takes up when the tube is kept at rest in that position. If the bubble rests at the position marked on the tube the line is horizontal and not otherwise. 308. The student can easily purchase for himself an ordinary carpenter's level and can make experiments with it. THE THEODOLITE. 309. A Theodolite is an instrument for measuring the horizontal angle subtended at the position of observation. by two distant visible objects. M IN Let P, Q be two visible distant objects seen from a place of observation O. Let PM, QN perpendiculars be let fall from P and Q respectively to the horizontal plane passing through 0. Then the horizontal angle subtended at O by P and Q is the angle MON [See Examples LXXVI. (16)]. [The angle subtended at O by P and Q is the angle POQ.] 310. The essential part of a Theodolite may be described as follows. Suppose two circular brass plates to be laid one on the other so that they are concentric and both are free to turn about an axis through their centre. Let the rim of the lower plate be graduated. That is on the rim will be marked 360 lines at equal distances indicating degrees subtended at the centre. Each degree will be subdivided into minutes etc. according to the size of the circle and the degree of accuracy to which the instrument is to be read. Let the rim of the upper plate have inscribed on it a vernier suitable for reading the graduations of the other rim. Now suppose the lower plate can be fixed in a horizontal position and that a telescope or other means of pointing at a distant object is mounted centrally on the upper plate. Then by first turning the upper plate till the telescope points to one distant object and reading the vernier; and again by turning the upper plate till the telescope points to another distant object and again reading the vernier, we shall obtain from the difference of these readings, the horizontal angle between the two distant objects. 311. The following figure is a picture of a part of a theodolite, shewing the arrangements usually made for fixing the lower plate in a horizontal position. EFD is the upper plate on which is engraved a vernier at E. AB is a portion of the rim of the lower plate. IHK are the upper parts of a tripod stand whose feet are placed on the ground. LM are two of the three screws which connect the head of the tripod stand with the axis round which the plates can turn. These screws are fastened to the tripod head by a clip which is indicated near M. When the tripod stand has been firmly placed on the ground so that the tripod head is fairly horizontal the plates can be made accurately horizontal by judicious turning of the three screws L, M, N. The screw at C allows the lower plate to be slightly turned with reference to the axis and tripod head. The arrangement FGH is a 'clamp' and a 'tangent screw.' When the screw head F is loosened, the upper plate can be turned quite freely round its centre; so that the telescope which is mounted on it, can be turned freely through any angle. When the screw F is tightened, the upper plate can only be turned with reference to the lower plate very slightly, by turning the screw head at B which is a tangent screw. 312. On the following page is a picture of a complete 'Transit' Theodolite. The upper plate is here shewn carrying a telescope TT" which is fixed to an axle of which one end R is seen. This axle is kept fixed parallel to the plate by the two pairs of upright legs which are firmly screwed to the upper plate. The graduated circle XYZ is fixed to the axis of the telescope and turns with it. The verniers b and c are fixed to the upright legs. a is a small magnifying glass for reading the verniers. d is a level fixed to the telescope and parallel to its axis. At f, e are the clamp and tangent screw which respectively fixes the graduated circle XYZ and slowly turns it. is the end of a level fixed parallel to the plane of the upper plate. On the top of the upper plate itself is seen a mariner's compass. 313. Suppose now that we are about to use the theodolite. We arrange the tripod; we loosen the clamp F; we turn the screws. L, M, N so that the plate ABC is horizontal; testing this by turning the upper plate into various positions and observing the level g in each position. The instrument is now ready to make an observation. 314. To make an observation. Suppose in the fig. on page v the observer is at 0. |