. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. f thearc. and therefore all that is needed to satisfy this conditionis that the latitude of each extremity shall be determined byappropriate observations. Instead of determining the latitude of each place indepen-dently of the other, we may, if we choose, obtain the difference oflatitude directly, by observing at each place the meridian zenithdistance of the same celestial body. In Fig. 25, let A and G bethe two extremities of the arc, 0 the centreof the earth, and 8 the celestial body onthe meridian. I
. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. f thearc. and therefore all that is needed to satisfy this conditionis that the latitude of each extremity shall be determined byappropriate observations. Instead of determining the latitude of each place indepen-dently of the other, we may, if we choose, obtain the difference oflatitude directly, by observing at each place the meridian zenithdistance of the same celestial body. In Fig. 25, let A and G bethe two extremities of the arc, 0 the centreof the earth, and 8 the celestial body onthe meridian. If Z is the zenith of thepoint A, the meridian zenith distance of Sat A, reduced to the centre of the earth, isthe angle ZCS. In the same manner thetrue meridian zenith distance of S at G isthe angle ZCS. The difference of these twozenith distances, or the angle ZCZ, is evi-dently the difference of latitude of G and A. Fig. 25. If the celestial body crosses the meridian between the twozeniths, as at S, the difference of latitude is numerically thesum of the two meridian zenith 62 FORM OF THE EARTH. 63. Results,—By the process above described, or by proc«esses of a similar character, arcs of different meridians, andin different latitudes, have been carefully measured. The sumof the arcs thus measured is more than 60°, and the length ofa degree of the meridian has been found to be, on the average, miles. Multiplying this by 360, we obtain 24,858 milesfor the circumference of a meridian, and dividing this cir-cumference by n, () we find the length of the earthsdiameter to be 7912 miles. 64. Spheroidal Form of the Earth.—One remarkable fact isnoticed when we compare the lengths of the degrees of the meii-dian,measured indifferent latitudes; and that is, that the lengthof the degree is not the same at all parts of the meridian^but sen-sibly increases as we leave the equator. The length of a degreeat the equator is found to be miles, whilst at the pol
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