. Elements of precise surveying and geodesy. ix kilometers greater than the true ellipticalquadrant. In certain cases it might be more logical to usethe radius of a circle whose quadrant is equal to the truequadrant; this requires the equation ^ttR = 10001997meters, from which R = 6 369 kilometers = 3 957 statute miles,and this is less by two miles than the mean radius of thesphere. This discrepancy is unavoidable, since the proper- 54- LINES ON A SPHERE. 149 ties of a sphere and a spheroid are not the same. Thus it isimpossible, when precision is demanded, to regard the earthas a sphere. Prob
. Elements of precise surveying and geodesy. ix kilometers greater than the true ellipticalquadrant. In certain cases it might be more logical to usethe radius of a circle whose quadrant is equal to the truequadrant; this requires the equation ^ttR = 10001997meters, from which R = 6 369 kilometers = 3 957 statute miles,and this is less by two miles than the mean radius of thesphere. This discrepancy is unavoidable, since the proper- 54- LINES ON A SPHERE. 149 ties of a sphere and a spheroid are not the same. Thus it isimpossible, when precision is demanded, to regard the earthas a sphere. Prob. 53. Taking the area of the earths spheroidal surface as196 940 400 square miles, find the radius of a sphere having thesame area. 54. Lines on a Sphere. The intersection of a plane and a sphere is always a the plane passes through the center of the sphere thecircle is called a great circle, its radius p being R and its circumference the plane does not pass through the ^Z center the radius of the circle is less than 9. R, say r, and its circumference is 27rr. All great circles cut out by planes passing through the axis of the earth are called meridians and these, of course, converge and meet at the poles. All small circles cut out by planes perpendicular to the axis are called parallels. Latitude is measured north and south on the meridians from the equator toward the poles, while longitude is measured east and west on the parallels from the meridian of Greenwich. Using the mean figures of the last Article, one minute oflatitude corresponds to i 852 meters or 6077 feet. Oneminute of longitude on the equator has the same value, butone minute of longitude on any parallel circle is smaller thenearer the circle is to the pole. Thus if y^ be a point on aparallel whose radius AC is r, and whose latitude AOQ is 0,and if R be the radius of the sphere, then r ^ R coscp, andaccordingly 2 7rr — 2 7rRCos(f), that is, the length of theparallel circle is equal to the
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