260 ON A DYNAMICAL TOP. 



axis disturbed in any way, its subsequent motion would be that of the top 

 when the bob is a little below the critical position. 



The axis of angular momentum would have an invariable position in space, 

 and would travel with respect to the earth round the axis of figure with a velo- 



CA 



city = D -'j where at is the sidereal angular velocity of the earth. The apparent 

 A 



pole of the earth would travel (with respect to the earth) from west to east 



A 



round the true pole, completing its circuit in -^ -j sidereal days, which appears 



O A 



to be about 325*6 solar days. 



The instantaneous axis would revolve about this axis in space in about 

 a day, and would always be in a plane with the true axis of the earth and 

 the axis of angular momentum. The effect of such a motion on the apparent 

 position of a star would be, that its zenith distance would be increased and 

 diminished during a period of 325 '6 days. This alteration of zenith distance 

 is the same above and below the pole, so that the polar distance of the star 

 is unaltered. In fact the method of finding the pole of the heavens by obser- 

 vations of stars, gives the pole of the invariable axis, which is altered only by 

 external forces, such as those of the sun and moon. 



There is therefore no change in the apparent polar distance of stars due to 

 this cause. It is the latitude which varies. The magnitude of this variation 

 cannot be determined by theory. The periodic time of the variation may be 

 found approximately from the known dynamical properties of the earth. The 

 epoch of maximum latitude cannot be found except by observation, but it must 

 be later in proportion to the east longitude of the observatory. 



In order to determine the existence of such a variation of latitude, I have 

 examined the observations of Polaris with the Greenwich Transit Circle in the 

 years 1851-2-3-4. The observations of the upper transit during each month were 

 collected, and the mean of each month found. The same was done for the lower 

 transits. The difference of zenith distance of upper and lower transit is twice 

 the polar distance of Polaris, and half the sum gives the co-latitude of Greenwich. 



In this way I found the apparent co-latitude of Greenwich for each month 

 of the four years specified. 



There appeared a very slight indication of a maximum belonging to the set 

 of months, 



March^ 51. Feb. 52. Dec. 52. Nov. 53. Sept. 54. 



