A treatise on gyrostatics and rotational motion . /)(+(O, (4) where E and a are constants. This gives also 02=E sin (pt+a) (5) \ THE FREE EULERIAN PRECESSION 213 [f O — A is small bhe differentia] equations show thai (>,, 02 alter A=B very nearly, a resultant of AM, and \\ of magnitude AlE, inclined nearly at 45 to either component in the plane of th [uator, and revolving in the body in that plane with angular speed n(C — A) invariable line oil Mrs in the plane of this constant resultant and C,about which the Cn is also constant. After any disturbance OH remainsinclined at a c
A treatise on gyrostatics and rotational motion . /)(+(O, (4) where E and a are constants. This gives also 02=E sin (pt+a) (5) \ THE FREE EULERIAN PRECESSION 213 [f O — A is small bhe differentia] equations show thai (>,, 02 alter A=B very nearly, a resultant of AM, and \\ of magnitude AlE, inclined nearly at 45 to either component in the plane of th [uator, and revolving in the body in that plane with angular speed n(C — A) invariable line oil Mrs in the plane of this constant resultant and C,about which the Cn is also constant. After any disturbance OH remainsinclined at a constant angle toOC, and, as the plane HOC revolves in spacedescribes a cone in the body about OC as axis, and makes one revolutionin the period 2-A fn(C — A). But 2tt n is one day and A/(C — A) = 30(5nearly. Hence the invariable line, which is fixed in space, describes the cone ,1891 03 02 0-1 00 -01 -0-2-0-3 1892 1893 Berlin. HonoluluFig. 5S. just specified in 30(i days ; in other words, the axis of figure revolves roundthe invariable line in a cone of semi-vertical angle COH in that angle tan-1(AE/Ol) is small, and is not to be confounded with thevery much smaller mean angle [about 0-00867], between I, of rotation, which causes the slow continuous precession. If the magnitude of E is sensible this revolution of 00 should show avariation of latitude of places on the earths surface, the more considerablethe greater the value of E, since tanC0I = E/n. But determinations oflatitude by observations of the altitude of stars show only a very slightvariation, and therefore we must conclude that E is small. Observationsmade at Berlin, Potsdam, and Prague in L889-JK) to detect this effect showedchanges of only about half a second of angle. Though small, this variationwas no doubt real, as the latitude of a place can be determined to I l of asecond, whic
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