802

THEORY AND PRACTICE OF ENGINEERING.

Rook II.

Small spirit levels arc also used, which arc made ofglass, and mounted on brass tubes; M and V are smallbrass plates which have an upright and horizontal cutmade through them, so that the eye can see from one tothe other, and when the bottom O K P is placed uponany surface, by looking through M N a level may be ob-tained : sometimes a glass tube F is placed on the top ofa box II, which is furnished with an eye-hole at O.

The earth’s diameter being nearly 41,79G,4S0 feet, or791G miles, it has been estimated that the height of theapparent above the true level for every mile is a littlemore than 8 inches. To find the difference between the true and apparent level, the dis-tance levelled should be squared, and its product then divided by the mean diameter of theearth, when its quotient will be the difference required: for the differences of the heightsof the apparent levels at different distances are as the squares of those distances; in shortlengths the differences are small, but they increase rapidly as the distances increase; in tenchains it is *12 of an inch; in twenty chains '5; in thirty 1T2; in forty' 2; in fifty 3*12;and in 100, 12 - 50 inches.

Compound Levelling is usually adopted where great accuracy is required, and this is per-formed by taking back and forward sights; by this means errors are easily corrected ; theheight obtained at a back or forward observation is deducted from the other, so that whenthese heights are compared together, the result may be depended upon, it being obtainedupon the spot, sufficient correctness is arrived at: in setting out a canal or railroad,it is usual to go over the same ground a second time in an opposite direction, beginningthe first operation where the latter ended; and if the results turn out the same inboth cases the correctness is sufficiently ascertained. It is, however, necessary to measureand set off the distances with the chain, and to reduee all the sloping measures to theirhorizontal value: the distance between the sights ought to be short, and the piquet-bearershould be careful to hold his staff upright, and to place it on the same spot for a forwardor back observation.

Drawing a Section or Profile of a Country after it has been levelled, to enable an estimateof tlie expense to be made, for the construction of a canal, railroad, or other work,is the next point to be considered. This drawing, to be useful, should be on a largescale, that is to say, from 8 to 16 inches to a mile : in the first instance an inch represents afurlong, and each chain the tenth of an inch ; when this scale is doubled, it is usually called5 chains to an inch. A straight line representing the base or level is first drawn, whichmay represent the horizon; on this is set out the several distances that have beenmeasured upon the ground ; the profile lines are then laid down, and after the heights areaccurately set out, the surface of the country may be traced through them : by such asection a sufficient knowledge of the expense may be acquired for the formation of any en-gineering work that may be constructed.

In the year 1742 it was proposed to the Academy of Sciences at Paris, to show on allmaps by the means of contour lines the respective levels of the districts surveyed. The ideaseems to have been suggested by the marks left around a hill after the waters on an inun-dation had been drawn off; supposing the valleys around a number of hills were to beinundated, and the water suffered for a sufficient length of time to stand at one level, thenif piquets or stumps were driven around the margin, to mark the extent of the surfaceof the water, and their position mapped and a line traced through them, then such a contourline would show the various spots which were at the same level, and if it were possibleto lower the surface by degrees, and draw off a foot of its depth at each time, and mark itsvarious boundaries in a similar manner and map them as before, such a series of contourlines would accurately express the height of the ground, and show where the relative levelswere to be found : we can imagine Shooter’s Hill, which is 400 feet in height, immersedin water, and that it could be lowered or drawn off a yard in depth each time ; thenif stumps could be driven to mark the water’s edge, as this was done, and these stumpsor the figure they comprised mapped, we should then have expressed by contour linesthe extent of the level planes at every* yard of elevation.

In public surveys where three chains are used to an inch, such a scries of lines laid downwould be found of the greatest possible service to the engineer about to cut a roador canal through the country so mapped, as he would at once see all the points whichwere upon the same level: for the supply of a town with water such a survey would beof the greatest importance, and facilitate the operations of the engineer.

The engineer, when surveying a country through which a railroad or canal is to pass,must not only pay the greatest attention to the levels of the several districts, but also noticethe manner in which the earth’s strata are disposed ; if he has an eye to judge accurately, hemay, like Brindley, perform much of his task by walking over the intended line, and get athorough knowledge of the difficulties be has to overcome : general ideas are too frequently

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Fig. 939.