. The encyclopædia of geography: comprising a complete description of the earth, physical, statistical, civil, and political. let O be thecentre of the circles; arcs of which are to represent the parallels. By the nature of the projection, O C must be taken equal to the cotangent of 52° 30;this, to radius = 1, is .76733, and to a radius expressed by minutes, we haveO C = .76733 X = found O C, the radius of the middle parallel, the radius of any other parallel maybe found by adding or subtracting its distance in minutes of the meridian from the middleparallel. Thus we find
. The encyclopædia of geography: comprising a complete description of the earth, physical, statistical, civil, and political. let O be thecentre of the circles; arcs of which are to represent the parallels. By the nature of the projection, O C must be taken equal to the cotangent of 52° 30;this, to radius = 1, is .76733, and to a radius expressed by minutes, we haveO C = .76733 X = found O C, the radius of the middle parallel, the radius of any other parallel maybe found by adding or subtracting its distance in minutes of the meridian from the middleparallel. Thus we find the radii of parallels differing by 5°, as in the annexed table:— Next, we must find tlie points in which some one meri-dian cuts all the parallels. We shall suppose it to be 30°of longitude from O C, the axis of the map. From the nature of the developement, the arc of longi-tude on any parallel in the map is equal to the arc of theparallel on the sphere which it represents. This has to an arc of the same number ofdegrees of the meridian the proportion of the cosine of the latitude of the parallel to 14* V. Parallel. Radius. Parallel. Radius. 350 55 40 (iO 45 (15 50 70 ! 162 PRINCIPLES OF GEOGRAPHY. Part II. radius. Therefore, an arc of 30° = 1800 on a parallel whose latitude is L will be in minutes, 1800 X cosine this formula, the lengths of the arcs may be easily computed by a table of logarithmicBines; but, for a practical construction, it will be more convenient to have the chords of thearcs. Now, in arcs not exceeding 30°, the arc diminished by a fraction whose numerator isthe cube of the arc, and denominator 24 times the square of the radius, is very near equalto the chord; that is, a being put for any arc, and r its radius, chord a^a—^^a nearly. From this formula, the chords may easily be deduced from the an example, let the arc of 30° of longitude, and its chord on the parallel 35°
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