Chap. VIII.
GEOMETRY.
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so as to open and form at one time two angles of any given inclination; the middle ruler,which is double, has a fine wire or thread stretched in the opening, the others haveone similarly placed from end to end, so adjusted that the three tend to the centre of theinstrument : they can readily be directed towards an object, and their angles accuratelymeasured : such a station pointer may be made by graduating an arc of a circle on a sheetof glass ground on one side, upon which, with a pencil, all the angles may be marked; this,laid upon paper, may be easily set oft’and traced.
When the demicircle is to be used, it has its planeplaced horizontally for taking distances, and uprightfor heights; having a joint which works upon amovable socket, it can be easily adjusted ; a plumbline at once indicates whether it is truly vertical orhorizontal.
To take an angle with this instrument, we turnit in such a manner that the object A is seen throughthe sights on its diameter, and then, without movingthe demicircle, we look along the alhidade or mov-able rule, and when through its sights the object Cis seen, the angle ABC can be laid down. Thenumber of degrees contained in this angle may becounted off between H and I, which may then bewritten down.
The demicircle now yields to the azimuth instru-ment, which measures angles with greater facility,whether vertical or horizontal, serving also the pur-poses of the theodolite; it does not possess thepower of repetition, but should an error occur,it may be reduced or rectified by measuring thesame angle upon different parts of the arc, whichmay be accomplished by turning the instrumenton its stand, and adjusting it as required : such ob-servations frequently repeated, and a mean resulttaken, are free from any great error.
To take the height of an object the demicircle isturned or placed upright, and adjusted by the plumbpassing through its centre, when its base will be ho-rizontal and at right angles with the height to hetaken. The alhidade is then turned until throughits sights the object O is seen ; the angle M N Owill be ascertained, and the degrees may be countedoff.
Distatices between places inaccessible may be ascer-tained and measured in the following manner : whenthe angle A B C is taken, measure on the groundthe distance between BAandBC, and constructupon paper with a scale the angle taken, and pro-ceed as has been before described.
It will appear evident that if upon the angleG E F, the dimensions are set off from E to F andE to G that have been previously taken from Bto A and from B to C, by the scale the distancebetween the objects may be accurately measured.
We may infer that this instrument was used first bythe Arabians, from the index or ruler which carriedthe sights being called an alidade or alhidade,which, on the limb of the instrument, showed thenumber of degrees or minutes that the object wasabove the horizon.
Besides the altitude and azimuth circle, we havenow mural and reflecting circles for measuringthe altitudes and azimuths of stars: the muralis so called because it is supported by a longaxis passing into a wall, to which the plane of thecircle is parallel; the reflecting circle carries amirror, by which an object is seen by reflected
vision ; another object is viewed directly the two arc **
brought to coincide, and the angular distance be- Fig. 002.
tween them is measured by the inclination of the mirror to the axis of the telescope,
Fig. 961.