R=180° F and lies SE.; when F lies between 180° and 270° RF-180° and lies SW.; and when Flies between 270° and 360°, R= 360° – F, and lies NW.

The separate co-ordinates are thus obtained:

Each abscissa along the meridian

=corresponding distance x cosin R,

Each ordinate or departure

=corresponding distance x sine R;

these separate co-ordinates are added up or subtracted, in accordance with their signs being similar or different, from the starting point up to the point whose independent co-ordinates are required; that is to say, up to each one successively; and when the traverse is a closed one, round back to the starting point again where the final verification is shown by proving its co-ordinates through results of the summation to be equal to zero.

Compass traverses of large extent to be delineated on a very small scale, such as those of travellers and navigators, are to a certain extent based on the same principle or method of procedure. A chapter will subsequently be devoted to the special subject of route surveys.

Details of traverse work.—The above constitutes the skeleton of the traverse work; the adjacent details or filling in may be done by distances and offsets measured, or with the occasional aid of minor triangulation as before explained.

The verification of the compass.-The compass used in surveys of small extent requires merely rough verification; the magnetic meridian can only be indicated as accurately as the graduation of its circle will admit. The variation of the compass at Greenwich in 1879 is

18° 45′ W.; and the magnetic elements are given every year in Whitaker's Almanac. To determine the variation of any compass, used at any place and time, is practically to read the bearing when sighted in the direction of the true meridian. Various modes of finding the meridian are mentioned in the chapter on Astronomical Observations on route surveys; but the most simple and rough methods, not requiring the aid of a Nautical Almanac or of accurate instruments are the two following: Ist. Take the bearings of the sun at sunrise and at sunset, when its lower limb is a semidiameter above the horizon, the bisection of the angle formed will be the direction of the true meridian. 2nd. The direction of the polestar is that of the true meridian, when a plummet shows that a true line passing through it and the star Alioth, & Ursa Majoris (the fifth star of the Great Bear) is truly vertical. Having thus either plumbed down and picketed the true meridian from any spot, or determined the correct azimuth of any spire or mark from it, the marks should be made permanent for future purposes of verification.

A specimen of Compass-Survey is given in Plate IV. and Field-record No. III.

Section 6. SEXTANT SURVEYS.

The adjustments of the surveying sextant have been explained in the paragraph on Reflecting Instruments (page 40). In the abstract the instrument would appear most perfect for the purposes of the surveyor, being extremely portable and giving angular readings to 20 seconds, as well as being free from all the liability to error that is so inconvenient in magnetic instruments. In practice, however, it is not so much used as would other

wise be the case, chiefly for the following reasons. In the first place, as it does not give angles in the exact plane of the horizon, but in the plane of the eye of the observer and the two objects observed; it either becomes necessary to take two altitudes with each angle and to reduce it by calculation to a horizontal angle (the formulæ and examples for this are given at page 59 in the collection of formula), or it is necessary to set up a rod strictly vertical, or to hang a plumb-line in the exact direction from the observer of one of the objects, and then handle the instrument in an approximate horizontal plane, and observe a horizontal angle. Besides the inconvenience and tediousness of setting up additional rods or plumb-lines with accuracy for every set of angles, in windy weather it is impracticable to observe on them with precision; while permanent vertical lines, such as edges of buildings, are not always available, and anything approaching to the guesswork involved in dispensing with vertical lines may vitiate the whole of the angular observations. In the second place, the exact superposition of the direct and the reflected image is essential to a correct angular observation; in clear weather, and with well-defined objects not more than 90° apart, this is easy; but when the objects are ill-defined, the weather dull (as is frequent in Great Britain), and when the angle is between 90° and 120°, so that the mirror presents a narrow breadth to the observer's eye, the operation involves considerable doubt and has to be repeated. once or twice; this is both troublesome and tedious. These two objections render the instrument inconvenient in triangulation, while the difficulty in observing very obtuse angles with it, and, in fact, the impossibility without a supplementary arc, render it inconvenient in