It is also desirable that a plan of the station of observation be made, marking the position of the axis of the instrument, with written dimensions of its distance by ordinates from some marked and fixed points. These data are useful to identify the station for future observations, and serve also when reducing angles to the centre.

to the centre of the face exposed to the light. For example, let a b c d be the base of the signal observed from O. If, on account of the dis

tance, the illuminated face a b can alone be seen, the telescope will be directed to the point A, a middle point in a b instead of the point C the centre of the signal, the amount of error being equal to the angle A O C. The value for this error is

A

A O

and the shorter the distance A O, provided it be great enough to prevent the sides in the shade from being seen, the greater will be the error. In very accurate trigonometrical operations, this correction is not to be neglected, as the error due to this cause has been known in cases of truncated pyramids with broad bases to amount to 15" or 20"*.

DELAMBRE, Base du Système Métrique, vol. i., page 221.

PRACTICAL DIRECTIONS ON THE CONSTRUCTION OF SIGNALS.

Permanent objects are, as before observed, to be chosen in preference for signals: their advantages are solidity and consequent steadiness and durability; they also economize time and money otherwise expended in the special erection of signals. But such permanent objects do not always exist in localities best suited for stations, and they perhaps would form ill-conditioned triangles. They are in those cases to be determined in position by intersections, but especial signals must be used for the summits of the triangles. Even when permanent objects are applicable, they do not always dispense from the necessity or expediency of placing temporary signals on their summits, in order to render their intersection by the cross wires more precise.

To the variety of form and character of signals there is, of course, no limit; they depend on the nature of the country, its capabilities, the distances between the stations, the importance of the work, the outlay contemplated, &c. A few details, however, on signals adapted to different circumstances, may be given at this stage of

our course.

In common surveys, embracing from several parishes to a whole country, as also in surveys for railroads, canals, and similar works, sides of triangles or connected bases have to be measured from 2 or 3, to 6 or 8 miles in length. For the purpose of ranging such lines, signals may be made by firmly fastening straight poles in the tops of high isolated trees, if their position gives the direction required.

An economical signal, suitable for lines of 8 or 10

miles in length, is represented in the annexed sketch, in which a long pole or mast, forming the signal, is held in a vertical position by a strong post, the lower part of which

is firmly fixed in the ground to a depth of 6 or 8 feet. A collar, towards the upper part of the post, confines the mast in its place, its lower end being fastened by a pin, round which it freely revoles as on a centre in a vertical

plane, when the collar is unclapsed or unlocked. If the pole be very high and made of two pieces, or placed in an exposed situation, it is strengthened and kept upright by means of guys and stays. Such a signal admits of the instrument being placed in the axis of the signal, which is for that purpose let down temporarily by being made to revolve on the pin that supports its base.

All posts or masts erected for signals are usually made to bear bunting flags; these should be of at least two colours,―red and white, when they are to be seen projected against trees or dark ground,—green and red, when they are to be relieved against the sky.

But as flags are useless in calm weather, a state of the atmosphere selected by preference for observations, they may be advantageously replaced by a small cone or barrel fastened towards the top of the pole. This may be painted red, if relieved against trees or ground; black, if relieved against the sky.

A good and easily recognised signal is also made by fixing at the top of the pole or mast a circular disk of sheet iron 2 or 3 feet in diameter, and a rectangular plate 4 or 5 feet long by 14 broad; they are placed at right angles, one above the other. On their faces circular openings are cut, to diminish the surface of resistance offered to the air. The diagram represents this form of signal viewed obliquely to both planes. It is much used on railways, and found well adapted to be seen at considerable distances *.

* "The reflection of the sun from a plane mirror, as affording a point of observation that might be seen at remote distances, was employed by General Roy in 1782, and in 1822 by Professor Gauss, while engaged in a trigonometrical measurement in Hanover; and the principle was adopted in this country by Colonel Colby and Captain Kater, when verifying General Roy's triangulation connecting the meridians of the Greenwich and Paris observatories. At their concluding station on Shooter's Hill, seven or eight days elapsed, during which Hanger Hill tower, though only 10 miles distant, remained completely obscured by the dense smoke of London*." To overcome this cause of delay, several flat plates of polished tin were attached one below the other to the signal post at angles calculated to reflect the sun's rays in the required direction, the inclination of the plates being so computed in reference to the relative position of the two stations and the sun that

*Philosophical Transactions, 1826.

TO DISCOVER LOST STATIONS.

In the progress of the triangulation carried on in 1821 by Colonel Colby and Captain Kater, for the purpose of

they should keep up a tolerably continuous reflection for a considerable time, the rays being caught and thrown from each plate nearly as soon as by the motion of the sun they had left the plate above it*. This plan was successful, and in subsequent operations in 1823 in was again resorted to, and with equal success.

"General Roy had, on several occasions, but especially in carrying his triangles across the channel to the French coast, made use of Bengal and white lights; for these, parabolic mirrors, similar to those with which our light-houses are supplied, and illuminated by argand burners, were afterwards substituted," as the short duration of the first rendered them inconvenient. This power again proving inadequate to the purposes of subsequent operations, in 1822, Colonel Colby and Captain Kater, conjointly with MM. Arago and Mathieu, employed, for the first time, an apparatus of a different kind. A large plano-convex lens, 0·76 metre in diameter, was substituted for a parabolic reflector, and the illuminating body used was an argand lamp with four concentric wicks. The lens was composed of a series of concentric rings reduced in thickness, and cemented together at the edges. The light which this gave is stated to have been 3 times the intensity of that given by a reflector, appearing at the distance of 48 miles like a star of the first magnitude t.

1

"But valuable as this apparatus may be when employed in a lighthouse (the purpose for which it was invented and constructed by M. Fresnel), the properties of the parabolic reflector appeared still to give it a preference for the service of the trigonometrical survey, provided a more powerful light could be substituted in its focus, instead of the common argand lamp." This object was accomplished by Lieutenant Drummond, by submitting a ball of chalk-lime to a stream of oxygen directed through the flame of alcohol. The size to be given to the ball of lime is regulated by the amount of divergence required to be given to the light, the rays only that proceed from the focus being reflected in a direction parallel to the axis of the parabola. The diameter generally used by Lieutenant Drummond was inch, as it proved quite sufficient to make the requisite allowance for aberration in the reflector from its true figure, as well as uncertainty of direction arising from

66

* Memoir of the Professional Life of Captain Drummond, by CAPTAIN LARCOM, R.E., vol. iv., Roy. Eng. Papers.

+ Philosophical Transactions, 1826, p. 328; and 1828, p. 154.