This section is from "The American Cyclopaedia", by George Ripley And Charles A. Dana. Also available from Amazon: The New American Cyclopędia. 16 volumes complete..

In algebra, the number expressing the greatest number of times which an unknown quantity enters a term as a factor. Thus the term x2y3 is of the second degree with respect to x, of the third with respect to y, but is called a term of the fifth degree. The degree of an equation is that of its highest term. Thus, 4x3+7x2=8, is an equation of the third degree. II. In trigonometry, 1/90 part of a right angle, indicated by a small circle near the top of the figure; thus, 30° signifies one third of a right angle. Each degree is divided into 60 minutes, each minute into 60 seconds; thus, 31° 12' 15" is read 31 degrees, 12 minutes, 15 seconds. III. A degree of latitude is the distance N. or S. between two places on the same meridian at which plumb lines would make an angle of one degree with each other. Owing to the flattening of the earth toward the poles, this distance increases in length as the observer goes N. or S.; being about 2,740 ft. more at latitude 60° than at the equator. The length of the degree midway between the equator and the poles is about 69 1/10 statute miles.

Many careful measurements of a degree have been made by various European governments, not only in their own territories, but in South America, India, and Africa. The most northern accurate measurement was in Lapland, the most southern at the Cape of Good Hope; and measurements have also been taken both in India and South America, almost exactly upon the equator. The longest arcs measured are those in France by Mechain and Delambre, and that in India by Col. Lambton; the first being over 12°, the second nearly 16°. From a complete discussion of all the observations, Bessel deduces the following results: the diameter of the earth at the equator is 41,847,192 English feet; the diameter through the poles 41,707,314 English feet; so that the difference of the diameters, divided by the longest diameter, gives us almost exactly the quotient of 1 divided by 300 (1/300). These results of Bessel may be compared with those of other astronomers, for which see Earth. They all agree very nearly with each other and with the celestial phenomena that depend upon the ellip-ticity of the earth.

It is remarkable that this, the only way of determining the size of the earth, was invented and put in practice by Eratosthenes, in Egypt, in the 3d century B. C. IV. A degree of longitude is the distance between two places of the same latitude, the difference of whose clocks is exactly four minutes; in other words, the planes of whose meridians make an angle of 1° with each other. The length of a degree of longitude is at the equator 69.16 statute miles; at latitude 20° it is about 65.015 miles; at latitude 30° it is reduced to 59.944, at 40° to 53.053, and at 50° to 44.342.

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