PROFESSOR MAXWELL ON A DYNAMICAL TOP. 569 



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- 



C — A 

 city = w — £- where w is the sidereal angular velocity of the earth. The apparent 



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



the true pole, completing its circuit in ^-^ sidereal days, which appears 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 observations 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 ap- 

 proximately 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 7 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. 



This result, however, is to be regarded as very doubtful, as there did not ap- 

 pear to be evidence for any variation exceeding half a second of space, and more 

 observations would be required to establish the existence of so small a variation 

 at all. 



I therefore conclude that the earth has been for a long time revolving about 



