Range Finders: The Labbez Telemeter.-Various small hand instruments called range finders have been devised to give approximate distances. Fig. 67 shows the Labbez telemeter, which gives without calculation distances from 250 to 3,000 yds. To use the instrument, select an object B, Fig. 68, at a considerable distance, and as nearly as possible at right angles to the line AC whose distance is required, and fix a point D in line with B at a distance of 30 yds. from A. Having set the zero of the revolving cylinder to the zero mark on the fixed cylinder, and also the toothed wheel at the end of the cylinder to zero, standing at A, look through the instrument at B, and revolve the toothed wheel with the forefinger until the reflection of c coincides with B. Now go to D, and again looking at B, revolve the toothed wheel until the reflection of c again coincides with B. The distance AC is then that indicated on the revolving cylinder opposite the zero mark on the fixed cylinder. B D 30 yds Fig. 68. Use of the Labbez Telemeter. The Weldon Range Finder.-The Weldon range finder is the patent of Colonel Weldon, R.A. It consists of three prisms of crystal ground to 90°, 88° 51' 15", and 74° 53' 15". In Fig. 69, let the distance AB be required. With the 90° prism, standing at A, set off the point c by making it coincide with the reflected image of B. AC is then perpendicular to AB. Now walk backwards from a, keeping in the line AC until the point D is reached, where the reflected image of B as seen in the 88° 51′ 15′′ prism coincides with the point A. The angle ADB is then 88° 51′ 15′′, and the distance AB is equal to 50 times the distance AD, which has to be measured. Somewhat greater accuracy is attained by using the 88° 51′ 15′′ prism only with a base twice the length of AD in Fig. 69 (see Fig. 70). Here CD = 2AD, and AB = 25 times CD. When the length of the base AD or CD is considerable, in order to save time in measurement retreat along the line DB until the point E is reached, where the reflected image of D as seen in the 74° 53′ 15′′ prism coincides with a or c. The length of the base AD or CD is then 4 times DE, and AD is equal to 200 times DE in Fig. 69, and in Fig. 70, AB = 100 times DE. In the official trials at Aldershot the mean error of the Weldon range finder was 34 yds. for each distance, and in India the average error was found to be 35 yds. for each distance. The Bate Range Finder.-The Bate range finder consists of a binocular field glass with two graduated limbs for measuring the angles. It is used in the same way as the Weldon and similar instruments. The angle subtended by the base is measured by putting in a gauge between the two graduated limbs, and the distance is expressed as a multiple of the base. The distance is equal to the measured base multiplied by the number indicated by the gauge. F Care of Instruments.-All instruments should be protected from rain, dust, and damp as much as possible. A waterproof bag should be used to cover the theodolite, level, or compass, &c., when mounted on the tripod and not in use. No part open to dust should be oiled, as this keeps all the dust that falls on it. The axes should be cleaned occasionally with chamois leather and a very little pure watch oil. Plumbago may be used instead of oil, as a soft lead pencil cut and a little put on the axis with the finger. The verniers and glasses should be cleaned with a soft camel's hair brush. Very dirty glasses may be cleaned with alcohol. If dust lies on the cross hairs, it may be removed by taking off both eyepiece and object glass and blowing through. Unless the cross hairs are wire, this is apt to break them if great care is not taken. If moisture gets inside the telescope tube, take off the eyepiece and let it evaporate. If moisture gets in between the two parts of the object glass (if composed of two glasses), remove the object glass and dry it by gentle heat at a fire or lamp, but do not take the glasses apart. Trigonometrical Formulæ for the Solution of Plane Triangles:-Right-angled Triangles.-In Fig. 70A, let ABC be a right-angled triangle, right-angled at c. Then sin A If s=(a+b+c), areas (s-a) (s-b) (sc) Fig. 70A.-Right-angled Triangles. b Fig. 70B.-Oblique Triangles. Sin2 A - sin2 B = COS2 B - COS2 A = sin (a + B) sin (A – B) Cos2 Asin2 B = COS (A + B) COS (A – B) Sin 2 A= 2 sin a cos A Cos 2 A = cos2 A − sin2 A = I - 2 sin2 A sin B2 COS = - 2 COS2 A - I (A+B) Cos 1⁄2 (A – B) (A + B) Sin ↓ (A – B) C Measuring Angles with the Theodolite.-Suppose the angle BAC, Fig. 71, is to be measured. Set up the theodolite exactly over the station at A (see page 202), and level up the instrument by means of the levels v on the upper plate t, Fig. 52. Set one of the verniers to zero or 360° by means of the clamp a' and tangent screw b'. Unclamp the screw ' and direct the telescope approximately on to the point в by hand. Then clamp and direct the cross hairs exactly on B by the tangent screw d'. Now unclamp a', and direct the telescope approximately on to the point c by hand. Clamp a' again, and adjust the cross hairs exactly on c by the tangent screw b'. The number of degrees, minutes, and seconds as now read on the vernier is then the required angle BAC. By |