tude, either by zenith distances or meridional transits, the two additional wires, which may be used in either position, afford increased accuracy of result.'

7. Reflecting Telemeters.-While in the adoption of either of the two former principles, a known distant height is required for observation, in the one case taking the form of a level staff graduated to hundredths of a foot, and in the other case a simple vertical rod with two marks on it exactly ten feet apart, a further simplification in this respect is effected by the adoption. of the horizontal or reflecting telemeter, when a simple unmarked vertical staff, or vertical line or edge of a building, becomes sufficient to observe on. The constant quantity in this case is the length of the hori zontal hollow bar or tube constituting the telemeter, and the angle observed in operation being that subtended by this constant length at the distant point or staff, the distance is a trigonometrical function of this angle and is obtained from inspecting a table con

The principle of the eyepiece micrometer is very simple, its manipulation easy, and it is free from the difficulties involved in using microscopes. In applying it to the measurement of the horizontal angle subtended by a marked length on a bar held up horizontally at an unknown distance, the micrometer is set horizontal by means of the collar. The field of view then shows two parallel vertical threads, a horizontal serration, and the object with its two marks: the fixed thread is first set exactly to one of the object marks by motion around the axis of the instrument, through its clamping and tangent screws, and the moveable vertical thread is set to the other object-mark by turning the micrometer screw. The reading is effected by counting the number of intercepted teeth in the serration for units, and reading the number of divisions on the micrometer screw opposite its index for tenths and hundredths, the sum being an angular measure of the length observed. The total value of the reading is then reduced to seconds, in accordance with the known sum of the micrometer, and from this subtended angle the distance of the object can be calculated, or obtained from a table. In vertical measurement the mode is the same. (The chaining of long, and even moderate distances, can thus be entirely superseded.)

structed to suit the constant length of the instrument used.

The instruments of Professor Piazzi Smyth, Lieut.Colonel Clerk, Otto Struve, and the optician Adie were respectively 60, 72, 735, and 36 inches long; there is also a small 18-inch instrument made by the latter suited to range-finding, military surveys, and rough purposes generally, but Adie's 36-inch instrument is perhaps that best known to the general public.

Its principle of operation is that of taking two simultaneous observations on the distant vertical line or object from the two extremities of the instrument where there are two object-glasses and two reflecting prisms, the one fixed so as to reflect the object in the direction of the tube, the other moveable about its vertical axis by a tangent screw, so that its reflected ray may be transmitted along the axis of the tube in a reverse direction the reflected rays from these end prisms are received by a pair of central prisms in the field of the telescope which are reversed in position and divert the rays into the line of vision of the single eyepiece used. A horizontal separation in the field of view, similar to that in other reflecting instruments, in conjunction with the movement of the tangent screw, enables the two reflections of the vertical line or distant object to be superimposed, so as to form one continuous vertical line, when the scale-reading will give the required angle. Each division on the fixed scale is two minutes, and each one on the vernier is two seconds, the intermediate minute, if odd, being shown by the coincidence of the verniers. The index error requires occasional verification, as in the case of all reflecting instruments (see Section on Angular Measurement), and if it should be required to

effect an index adjustment, the screws under the endprisms may be very slightly moved with a screw-driver until it is correct; this is necessary after cleaning the instrument. The eye and object glasses, and the end and central prisms, can all be easily got at for purposes of wiping and cleaning. Any distance may be once measured with this instrument in about half a minute, but a mean of several readings is to be preferred. The maximum error in distance with the 36-inch instrument, is 3 inches at 300 feet, 7 feet at 1500 feet, and 30 feet at 3000 feet.

The advantages of instruments of this type are, the doing away with the necessity of any graduated or marked distant staff of vertical position; and that in long sights the effect of varied refraction is annihilated in results. The defects of telemeters based on this principle are―That the twice reflected images in long sights lose their sharpness of outline, and that the two images being in very close proximity, if not overlapping, excessive nicety of management is required to measure the required interval. That any unequal expansion of the tube, arising from alteration of temperature, by direct solar heat, causes curvature and alters the angles of reflection, thus producing considerable error.

It seems hence to be a reasonable conclusion that such instruments become practically useless for very accurate survey work, both in hot climates and in very hot weather anywhere, although outer cases and sunshades may be used to mitigate ill effects; and that even in temperate climates the amount of accuracy in result with instruments as short as 36 inches is insufficient; although longer instruments of 60 inches

might answer all practical purposes for distances up to about 700 feet or even more.

While instruments of this type might certainly be used in conjuction with reflecting instruments for angular measurement, it must be remembered that when telemetry is accurate, rapid, and easy, triangulation can be carried on without the need of any angular measurement; while if triangulation is required simultaneously with levelling operations, telemeters on the vertical refracting principle before mentioned are much to be preferred.

The means, appliances, and instruments more specially used in levelling will be treated in the chapter devoted to that subject.

Section 3.

INSTRUMENTS AND APPLIANCES COMMONLY USED IN ANGULAR MEASUREMENT.

As the object of a survey is to produce a delineation of the country, district, town, route, or piece of land on a horizontal plane, the angles mostly required in surveying are horizontal angles; vertical angles are less required, from the fact that elevations on the earth's surface being comparatively small, the angles commonly subtended by them are also small, vitiated by atmospheric refraction, and hence less capable of direct observation with sufficient minuteness; while levelling operations for the determination of direct height or depth can be carried out with greater accuracy of result.

Surveying instruments for angular measurement generally fall under one or other, or some modification or combination, of the three following types.

I. The Altitude and Azimuth, or Theodolite type; for measuring horizontal and vertical angles.

2. Repeating Circles and Reflecting Instruments for measuring angles in any desired single plane.

3. Magnetic Instruments, for obtaining magnetic bearings, or angles dependent on them.

I. Instruments of the first type are made in many sizes and of various patterns, from the 3-feet theodolite, reading to fractions of seconds and weighing about two hundredweight, of the Great Trigonometrical Survey, down to the 4-inch theodolite reading to one minute which is used by surveyors that prefer a light instrument. The most common size used in England is the 5-inch theodolite, which, with the aid of a vernier, gives horizontal angles correct within half a minute; the 6-inch theodolite reading to a third of a minute is also very common; while the 8-inch theodolite reading to 10" is used only on very extended or extremely accurate work, in which case it is generally of the transit-theodolite pattern, and fitted for rough astronomical purposes. The patterns in most common use are the Y theodolite, having a semicircular vertical arc; the Everest, having two small portions of vertical arc; and the Transittheodolite, which has the advantage of the reversibility of the telescope in a vertical plane, and is made either with or without any vertical arc: the first pattern being the most common, the second the lightest, the third the most preferable in some respects. In important subterraneous surveys and tunnel work, transit-theodolites, with a hollow bearing-axis, are generally considered necessary in order to obtain sufficient light from a lamp on the cross-wires. They are generally set up over any required point or spot simply by the help of a plummet hanging from a hook below the axis of the instrument, and by moving the legs of the tripod until exactly in