Chap. VIII.

GEOMETRY.

799

6r

thus it is apparent the true level is the earth's curvature: all bodies at an equal distancefrom its centre arc supposed to be level.

In levelling for a llailroad or a Canal., it is often necessary toplace the levelling staves 300 or 400 yards apart, and then it is |

important to make some allowance for the curvature of the earth, as weshall hereafter describe ; but before we proceed, it is necessary todescribe the staff or target made use of for determining the height ofthe several objects above or below the level line. The most commonform is that of a rod 1^ inches square, and 6 feet 6 inches long, made ofmahogany, and inlaid on its face with a white wood to receive thedivisions and figures : the staff consists of two pieces dovetailed intoeach other throughout their whole length, so that one half of the rodslides upon the other, in consequence of which the rod can be pulledout or extended to 12 feet long, and yet will leave a foot of the twohalves joined together for maintaining the straight line of the instru-ment : the divisions begin to count from the bottom of the staff.

The vane is a thin piece of mahogany 10 inches long and 3 wide,having projections behind, which form a socket for fitting the rod, !

and enable it to slide up and down ; this motion is rendered more j- gf}

certain by the addition of a flat spring placed in the socket. In thecentre of the vane is pierced a hole, through which may be read offthe figure on the staff, and the edges of this hole being chamfered,the horizontal wires which cross it can be distinctly perceived as theylie over the divisions of the scale beneath : when this staff is placedin a truly vertical position, its vane can be elevated or depressed, asthe signal is given by the engineer who is at the levelling instrument ;fof the teldSlupe Cannot be altered by elevation or depression, there-fore the vane is moved upon the staff until it is brought into exactcoincidence with the horizontal hair of the instrument : so that whenthe cross-wire of the vane is raised so high as to intersect 6 feet, thereis a stop to prevent its being pushed higher : when a greater height &t

is required, the vane is put to this height, and then it is raised by Fig. 925.

sliding up the front portion of the staff, which carries the vane with it.

Several methods of marking these rodsare adopted, but all begin to count fromthe bottom of the staff: some have a doublescale of divisions running up the middleof the front; on some the side consistsof feet and inches divided into tenths,and others of feet divided into hundredthparts, without regard to inches. When thelevels can be taken in inches and tenths, orin feet and hundredths, the calculations arerendered more easy and simple, and ithas been suggested that the decimal di-vision should be adopted for rules andscales generally.

The staves now in use are generallywithout vanes, having their graduationsdistinctly marked in feet, tenths, andhundredths; these were introduced byMr. William Gravatt, and are made ofthree pieces of mahogany with joints at theends, to enable them to be united in onelength of 17 feet or more; such stavescan be packed up with the stand ofthe instrument, and are more portable.

Mr. Sopwith of Newcastle has improvedupon these, by adding a spring catchto that which slides, so that it is moreeasily retained in its place ; but, howevercorrectly’ these may be graduated, if theattendant who holds them is not very careful, errors of great magnitude may result, forwhen the face is turned from the last forward station to become the next back, anerror of an eighth of an inch is sometimes the result of carelessly placing it on theground: to remedy this the greatest attention should be observed, and the stave should be