c, the centre of anallatism, or unchangeableness, are proportional to their distance from c. The point c being then set in the exact vertical axis of the instrument, the required objects were attained, besides the additional advantage in observations having the line of sight inclined to the horizon, that the requisite correction on this account is exactly effected simply by multiplying the observed distance by the square of the cosine of the inclination. The compound telescope above described was only 2 inches in diameter, with a focal length of 15 inches, but had a magnifying power of from 60 to 80 times. Porro also used 5, or 7, horizontal hairs or threads in some instances instead of three, in order to check errors in reading the graduations on the staff, and to help in their subdivision by the eye, as well as to assist in cases where some readings were obscured by casual obstruction.

The maximum error with such an instrument was

2000

000

both in distances less than 660 feet, and 10th in distances more than 660 feet up to 1320 feet, beyond which distance the sights become useless for practical work on account of increased error. The instrument admitted of testing in all its parts, but the threads were permanently fixed; it is evident that such an instrument would require a good maker, and perhaps be expensive.

The further employment of the telemeter on the Schuykill topographical survey resulted in the following practical conclusions, indicated by Mr. Lyman in a paper read before the Franklin Institute in 1868.

Ist. That the additional lenses and complications adopted by Porro, to cause the centre of anallatism to

fall in the exact vertical axis of the instrument, were needless, as the inconvenience from adding to every distance observed a constant quantity, equal to the sum of the focal distance of the object-glass and the distance of that glass in front of the vertical axis, rarely exceeding one foot, is comparatively trifling.

2nd. That three horizontal hairs or wires are sufficient for all purposes, as the reading of the middle wire affords sufficient check on the other two; that fixed are preferable to moveable wires with protected adjusting screws; and that the fixed wires should be so set that the visible height on the staff intercepted between the middle and either outer wire should bear some exact ratio to the distance, such as I foot to 100, thus avoiding calculation.

3rd. That the staff should be graduated to hundredths of a foot.

4th. That, in combination with the above arrangements, a telescope magnifying only 20 times, and reading to the 200th of a foot at a distance of 660 feet, will produce results as correct as those of Porro's larger and more complicated instrument.

5th. That the errors arising from spherical aberration may under these circumstances be neglected in angles of less than 10° on either side of the focal axis.

Distance-wires. From these conclusions, it appears that a good level-telescope with three distance wires. and a 16-feet level-staff are sufficient for all ordinary purposes, in distances limited to 660 feet if the telescope will read correctly to one graduation or th of a foot at that distance. The length of staff utilised would beth of the distance, or 132 feet, and the error in reading, lying within a half of a graduation or th

1

100

00

cause an error in th of the distance.

of a foot at this range, would thus distance of three inches, or about Using the same telescope, which would give readings at increased distances up to 1320 feet with half of the exactitude before mentioned, the maximum error in sights between 660 and 1320 feet would then be double the former. If however a telescope of superior power be used, capable of reading to hundredths of a foot at a distance of 1000 feet, which every superior 18-inch level telescope should do in clear weather, the maximum error in distance, about 5 inches, will as before be only up to that distance. The same ratio of maximum error to distance could be attained up to 1320 feet distances with a still more powerful telescope, magnifying about 25 times.

Under these circumstances it seems surprising that everyone possessing a level with a good telescope does not have distance wires added to the diaphragm by a good maker, which can be done at the small cost of halfa-guinea, and that anyone should buy a new level without such distance wires. It would, however, be very much preferable to have the distance lines marked on a lens, if this could be done without destroying several in the attempt and thus causing much expense. Before applying distance wires to a telescope for telemetrical purposes it is as well to ascertain its magnifying power; this can be best effected by direct practical observation on a graduated staff with the aid of Pouillet's reflecting tube. This tube being fitted and clamped on to the eyepiece of a telescope enables the reflected real image. of the staff to be seen in coincidence with its direct magnified image, and by a comparison of the two apparent sets of graduations, the magnifying power of the

с

telescope is simply and correctly determined. It then becomes a mere matter of calculation, as before shown, to ascertain within what limits of distance the telescope is correctly suitable to purposes of telemetry under a favourable condition of the atmosphere. The constant error for any such instrument can be determined by a series of observations combined with accurate measurements to various distances.

Telemetrical observation on staves of known length.— The next development of the principle of telemetrical observation was carried out in Eckhold's Omnimeter (which like Porro's Omnimeter also serves as a theodolite), having for result that graduations on the staff

FIGURE 3. ECKHOLD'S TELEMETRY,

become needless, two correct marks being alone necessary. In this instrument a telescope and a microscope are permanently attached to each other at right angles, both turning together in the same vertical plane, and have their common turning axis at a known fixed height above a horizontal scale, placed parallel to the telescope, on which the microscope reads. When the telescope is directed first to the top or upper mark of the distant staff, a reading is taken on the scale with the microscope, a second reading is taken in the same way when the telescope is directed to the bottom or lower mark of the distant staff; the difference of these two readings made with the help of a micrometer is the measure of the required distance.

Thus if S the height observed on the staff, which is generally fixed at 10 feet,

D=the distance of the staff from the instru

ment,

h=the height of the telescope axis above the

scale,

l=the length or difference of readings on the

scale,

it is evident that the two triangles described through the motions of the telescopic and of the microscopic lines of sight are similar; hence if the distance is required,

Sh Ioh

D= or

generally, and if the distance be known, any unknown height (s) observed at that distance, is

Also the height of any point at that distance, either above or below the level of the axis of the instrument, can be obtained; for when the telescope is set truly level, the microscope reads exactly on a zero or point of departure on the scale; thus this instrument acts as a level as well as a telemeter, in the same operation. The readings on the scale, which is only about four inches in length may be made to six figures, of which two are read with the microscope and four with the aid of the micrometer disc. The mode of operating with this instrument is thus described by Mr. Eckhold in an article in Spon's 'Dictionary of Engineering.'

1. Place the staff vertically at one end of the distance to be measured, and the instrument properly