of the switch, and c the tangential abscissa to the given radius of curve due to an ordinate a; d be the distance for setting back the tangent point along a straight line, in order to make the curve tangential at the heel;

then d= b2-a2-c; where c= √ R2 − (R − a)2.

In case the curvature is such that c is greater than ba2, it is better to put the switch-point at the exact tangent point of design, and to adjust the closure or last fixed rail by cambering so as to fit up to the switch-heel, thus allowing the error in flatness to remain.

Corresponding adjustments in setting-out can be made for turnouts from curved main tracks, setting back for errors of sharpness, and cambering closures for those of flatness.

Radii of centre-lines of constructed railways.

It having been suggested that formulæ for the purpose of finding the radius of the centre-line of an actual railway-curve would be useful both to surveyors and engineers in the field, the following is appended to this part of the book.

Let C be the chord of the outer rail, measured tangential to the inner rail, to the middle of the metals everywhere.

R, the radius of the centre line in any case, whether the line be of single or of double track.

g, the gauge of the track, and s the six-foot interval between tracks, which frequently varies, and requires measurement.

The formulæ, when symmetrically arranged for purposes of calculation, direct and converse, are (1) for the

chord of a single track, (2) for that of the inner track of a double line, (3) for that of the outer track of a double

line.

R=1 x C

or, C=2 √g.√2R

(1)

2 48

R=

248

+s+g or, C=2√g.√2R-s+g (2)

s+gor, C=2 √g. √2R +5 +8 (3)

The first set of formulæ is applicable to any single case required in the field, and the second set to the tabulation of chords corresponding to given radii in round numbers; the same unit of measurement, whether feet or chains, being adhered to throughout.

Section I.

PART IV.

ROUTE-SURVEYS.

TRAVERSES OF ROUTES BY LAND
AND SEA.

ROUTE-SURVEYING may be divided into two classes; the one being exploration or itinerary surveys on comparatively unknown routes by land, the other being what is familiarly called Navigation, which deals in corresponding manner with the course of vessels at sea. They both follow the principles of a large Compass Traverse, already explained and exemplified (see pages 105 to 110 and Record No. III.), and vary from it mostly in that the distances from station to station are much greater, and more coarsely measured or estimated.

The portions of traverse in route-surveys are generally divided into journeys of one day, or of a day's run at sea; the traverse-stations have their distances apart fixed by local considerations on land, such as bends of valleys, ascents, passes, positions of villages, while at sea these distances depend on the times, or periods between changes of course arbitrarily adopted by the sailing-master. The final closing of such surveys, or traverse-work, depends on such previously well-known, or predetermined points, as towns, villages, etc., or at sea, rocks, ports, harbours and islands, whose positions are accurately known, and laid down on trustworthy

U

maps or charts, or recorded authentically. Some such points also serve for checking intermediate places in the route; but the principal means of daily verification. in all such work is direct astronomical observation aided by good chronometers for giving differences of longitude. Hence the necessity in route-surveys of having men capable of taking such observations, of having portable instruments for that purpose, and of also taking copies of the Nautical Almanac for the current and the following year, as these give the positions of all the principal celestial bodies for Greenwich mean time. In route-surveys the necessary astronomical observations, for the determination of latitude, longitude, and the direction of the meridian, are made at least once, or twice, a day; the intervening traverse-work is calculated and reduced to a single meridian, and the errors determined; the traverse-work can then be plotted on a plan, to some convenient scale, with names of places, dates, times, and everything desirable or suitable for record.

Such surveys are not generally the principal object of an exploration, but are more frequently subservient to obtaining knowledge on other points; such as for military purposes, in which case the gradients of the country or of the roads must be noted as suited to artillery or not; the condition of the country as suited for cavalry to act, passes, fords, and strong positions, places suited for ambuscade or cover for troops, have to be noted; the amount of shelter, food, fuel, and forage that might be obtained; the amount and quality of the water all along the route, the times and seasons of crops, their preparation and harvesting; the amount of timber and stone available for hutting and bridges;

and the number and disposition of the inhabitants, their arms, resources, and modes of organisation, attack, and defence. Information on most of these points is generally useful under any circumstances, apart from purely military considerations; and although it is essential to a military route-report, it is also of service in the event of any engineering or mining works being contemplated. In drawing up such reports of supplies, shelter, and accommodation, care should be taken to distinguish between the amount available on an emergency, or for a permanence, also to note whether the people are disposed to trade or otherwise, and whether they have been spoilt by gratuitous gifts, or deceived by false promises or inducements.

Sometimes route-surveys form part of a scientific exploration, in which case the geological features, the mineral resources, the fauna and flora, the climate and meteorological conditions of the country are sometimes the most important subjects of observation; while in others the anthropological data, the personal peculiarities of the people, their habits, history, customs, superstitions, traditions, ideas, cleanliness, prevalent diseases, virtues and vices, are the main points of interest. Under such circumstances the duties of the expedition generally fall rather heavily on the members composing it, especially as those in connection with the mere transit and arrangements for passage through the country and intercourse with the natives form serious part of them.

It frequently happens too that the mere sight of surveying instruments exercises a most irritating effect on the inhabitants, who may look on them as forerunners of annexation, loss of independence, or religious interference. Under these circumstances the survey-work