ARBOR VILE is the familiar name given to a tree, the botanical name of which is Thuja or Thitya. There are many species. The American Arbor Vitae is a large shrub or small tree, sometimes called while cedar ; the wood is very durable, but is difficult to obtain except in small pieces ; it makes excellent posts and rails, and the branches are used for making brooms. The Chinese and theWeeping Arbor Vitae are not much employed in the arts. The Callitris Arbor Vita is said by Broquiart and other authorities to yield the useful substance Gum Sandarac [Sesmatao]; and the wood of this tree, under the name of alerce, is in great repute in the east for build ing religious edifices ; the roof of the cele brated cathedral of Cordova is built of this wood, and exemplifies the fitness of the ma terial for such purposes.
ARC, a bow, signifies any part of a curve line. The straight line which joins the extra mities of the arc is called its chord.
The practical method of finding the length of an are is as follows :—Divide the arc into a number of smaller arcs, making the number large in proportion to the degree of accuracy required, and add together the chords of the smaller arcs. The sum of the chords will
differ very little from the are, even when the number of subdivisions is not very large. For instance, the arc of the quadrant of a circle, whose diameter is ten million of inches, is 7,853,982 inches, within half an inch. Divide this quadrant into ten equal parts, and the sum of the chotds is 7,845,010 inches : divide the quadrant into fifty parts, and the same sum is 7,853,659 inches, which is not wrong by more than one part out of 24,316. For only twenty sub-divisions the sum of the chords is 7,851,063 inches, wrong only by one part out of 3890. Therefore, for every prac tical purpose, an arc of a circle (and the same may be said of every other curve) is the poly gon made by the chords of a moderate number of sub-divisions of the arc.