Arc
Collier's New Encyclopedia (1921)
in geometry, a portion of the circumference of a circle, cut off by two lines which meet or intersect it. Its magnitude is stated in degrees, minutes, and seconds, which are equal to those of the angle which it subtends. Hence, counted by degrees, minutes, and seconds, the arc of elevation and the angle of elevation of a heavenly body are the same, and the two terms may be used in most cases indifferently. The straight line uniting the two extremities of an arc is called its chord. Equal arcs must come from circles of equal magnitude, and each must contain the same number of degrees, minutes, and seconds as the others. Similar arcs must also each have the same number of degrees, minutes, and seconds, but they belong to circles of unequal magnitude. Concentric arcs are arcs having the same center. In mathematical geography, an arc of the earth's meridian, or a meridional arc, is an arc partly measured on the surface of the earth from N. to S., partly calculated by trigonometry. Such arcs have been measured in Lapland; in Peru; from Dunkirk, in France, to Barcelona, in Spain; at the Cape of Good Hope, and from Shanklin Down, in the Isle of Wight, to Balta, in Shetland. It was by these measurements that the earth was discovered to be an oblate spheroid. In electricity, a voltaic arc is a luminous are, which extends from one pencil of charcoal to another when these are
Collier's New Encyclopedia (1921)
JOAN OF fixed to the terminals of a battery in such a position that their extremities are one-tenth of an inch apart.
Collier's New Encyclopedia (1921)
JOAN OF. See JOAN OF ARC.
What Has Changed in the Last Century
The geometry in Collier's 1921 entry is still exactly what a student learns today: arcs measured in degrees, minutes and seconds, chords, concentric arcs. What has dated is everything applied. Earth's figure is no longer pinned down by painstaking meridian arcs surveyed from Lapland to Peru but by satellites: the WGS 84 reference ellipsoid, adopted in 1984 and now the basis of GPS, gives the equatorial radius as 6,378,137 metres and a flattening of about 1/298.257. And the "voltaic arc" between two charcoal pencils, the standard electric light of the 1880s and 1890s, had already been beaten by the tungsten filament by 1921; carbon arc lamps survive today only in a few niches, while the arc itself lives on in welding and xenon lamps.
Written for this edition, 2026.