. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. the circumfer-ence of the equator. Since the circumference of any parallel u * This formula may be obtained by the principles of the resolution of i o-4tation, given in treatises on Mechanics. Thus, inthe figure, the rotation of the point L about the axisof the earth, PO, may be resolved into two rota-tions, one about the radius LO, and the other aboutthe radius MO, drawn perpendicular to LO. If vrepresents the angular velocity of L about the axisPO (or 15° in one hour), and v and v the angular velociti
. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. the circumfer-ence of the equator. Since the circumference of any parallel u * This formula may be obtained by the principles of the resolution of i o-4tation, given in treatises on Mechanics. Thus, inthe figure, the rotation of the point L about the axisof the earth, PO, may be resolved into two rota-tions, one about the radius LO, and the other aboutthe radius MO, drawn perpendicular to LO. If vrepresents the angular velocity of L about the axisPO (or 15° in one hour), and v and v the angular velocities about theaxes LO and MO, we have, from Mechanics, v = v cos LOP, and v = v cos POM,Now, the rotation about the axis OM will have no effect in changing theapparent position of the plane of vibration of the pendulum, since it isanalogous to the case at the equator considered in the text; while therotation about the axis LO, being analogous to the case at the pole, willproduce a similar effect. The apparent angular motion, then, of theplane of vibration will be v cos LOP, or v sin LINEAR VELOCITY OF ROTATION. 7C to that of the equator as the radius of the parallel is u> theradius of the equator, the linear velocity will diminish as weleave the equator in the same ratio that the radii of the successive parallels diminish: in the ratio, that is, of the cosine of thelatitude, as was proved in Art. 69. For instance, the cosine of60° being J, the linear velocity at that latitude is only 8i milesa minute. Note.— According to Clarkes Spheroid of 1866 (which is adopted byour Coast and Geodetic Survey as the basis of all calculations) the dimensionsof the earth are as follows :— Equatorial radius 6,378, metres = Polar 6,356, = These numbers are likely to be in error as much, perhaps, as 100 metres, pos-sibly more; they can hardly be 300 metres wrong. (Young.) In ClarkesSpheroid of 1878 the equatorial radius is given as 6,378,190 metres; th
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