SECTION XX. 297 theworld, A B the semidiameter at the equator, and N c the semi - diameter of the parallel of latitude for London. Then arith- metically, if the line A a (suppose 1000 equal parts) allow 70 miles for a degree, what will n C {i. e. about 621 equal parts) allow ? Ans, 43f. Or trigonometrically thus.: A E is the whole sine of 90e, or radius. N C. is the sine of the colatitude 38d1. Then say, As A a or the sine 90d is to 70 miles, so is N e or A n the sine of 38d1 to 432 miles. Note, This diagram or figure will shew the value of a de- gree oflongitude in any parallel of latitude, if from every degree in the arch E c E. a perpendicular were drawn to the line A B. Therefore a whole line of sines if numbered backward, and applied to a scale of 70 equal parts, will shew the Miles con- tained in one degree of longitude under any parallel of latitude whatsoever. Having shown in former problems how to take the meridian altitude of the sun, and thereby to find the latitude of any place on the earth, .I think it may be proper now to shew how to pro- ject the sphere for any latitude upon the plane of the meridian, and represent it in straight lines, which is called the analemma ; because the erection of this scheme (and sometimes of ,a little part of it) will solve a variety of astronomical problems, as will appear hereafter. Problem XV, " To erect the analemma, or represent the sphere in straight lines for the latitude of London 511 degrees." First, It is supposed you have a scale of chords at hand, or a quadrant ready divided into 90 degrees. 'rake the extent of 60 degrees of the line of chords in your compasses, (or which is all one) the radius of your quadrant, and describe the circle a z E x s o, for a meridian both north and south as in figure xxiii. viz. N E s, which represents 12 o'clock at noon; and N o s, which represents the hour of midnight. Through ç the centre draw the line x o for the horizon. At 90 degrees distance from n and o mark the point z and n for the zenith and nadir ; then draw the line z D which will cross s o at right angles, and will represent the azimuth of east and west ; as the semicircle z o n represents the north azimuth, and z it n ,the south. Above the horizon o mark N for the north pole elevated 314, degrees ; through the centre c draw the line N s for the axis of the world; which line will also represent the hour circle of six o'clock, being at 90 degrees distance from noon and midnight ; s will stand for the south pole, depressed as much below n the south side of the horizon, as x the north pole is raised above o on the north side of it.
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