748
THEORY AND PRACTICE OF ENGINEERING. Rook II.
Circles of all sues are divided into 360 degrees, as Fis the centre of the circle BCD, to which they allradiate.
Degrees are divisions which may be shown by rightor curved lines, and are here drawn on the circum-ference of the circle E D C, as well as on the parallelogram,A DLC11K.
By geometricians degrees are understood to be the 360thpart of the circumference of a circle, or of four right angles:each of these degrees is divided into 60 minutes, and eachminute into 60 seconds, and we find such a division re-cognised by the ancients. The Chinese divide the circleinto 365|j parts, so that the sun daily describes one ofthese degrees.
The French mathematicians in some instances dividethe quadrant or right angle into 100 degrees, and eachdegree into an hundred minutes, which suits better theirdecimal method of computation. A degree of latitude isunderstood to be that distance an observer must advancealong the meridian on the surface of the earth to the northor south, in order to produce a variation of one degree inthe altitude of the pole ; the exact measurement of one ofthese degrees has been a study of the greatest interest, asby it is ascertained the dimensions of the globe itselfAt the present day this problem has acquired greaterimportance, in consequence of the discovery of the earth’sellipticitv ; for it is by the comparison of the lengths ofthe meridional degrees at different latitudes, that we areenabled to ascertain accurately its true figure.
The great irregularities of the surface of the earth renderit difficult, but as the length of a degree depends on theradius of the circle on which it is measured, it will readilyappear that the terrestrial degrees at different places, ifmeasured on the external surface, must be unequal. Toobviate this, and to reduce all the degrees to the sameradius, the surface of the sea is supposed to be continuedall round under the continents, and to this surface orlevel all the measurements are made to refer. The prin-ciple adopted is the following: two stations being as-sumed on the same or nearly the same meridian, thedistance between them must be found with great exact-ness in feet or yards ; this being done, the latitude of eachof the stations is then determined, the difference of the twolatitudes being the length of the celestial arc interceptedbetween the two stations, and by comparing this with theterrestrial measure, the number of yards or feet corre-sponding to a degree is known.
An error of a second made in the measurement of thecelestial arc corresponds to 100 feet on the ground, so thatgreat nicety of observation is required before it can be as-certained with precision.
From measurements made at various stations, the di-mensions and ellipticity of the earth are found to be,
Equatorial diameter - - 41,813,330 = 7924*87
Polar ditto - - 41,704,788 = 7898*63
Difference of diameters - 138,542 = 26*24
A Circle is a plane bounded by a single line, calledits circumference: the area dotted is a plane so cir-cumscribed by a line A B C D struck from the centreE, and equal circles are those struck from similar radii,as II NI and FLG.
A Semicircle always contains 180 degrees, and is divided,as OPQ.
A Protractor is such a figure, and used to set out de-grees : its simplest form is a semicircular limb of metal
its j.
Fig.707.
Fig 709.
Fig. 710.