526 Transactions. — Miscellaneous. 



segment of a circle are equal to one another. He described 

 the circle from the centre found as above, and saw that it 

 passed through several well-known stars (Plate XLV., fig. 2). 



Let a and b represent two such stars ; P 1 , P 2 , P 3 , successive 

 positions of the pole of daily rotation at intervals of, say, 

 1,000 years. If, then, Vab be the true circle described by 

 the pole the angles a~P l b, «P 2 6, a~P 3 b, must be equal to one 

 another, but if the stars a and b are not in the circumference 

 of the true circle the angles will not be equal. We are not 

 told how many trials were made, and errors found and cor- 

 rected ; but at length the true centre was accurately deter- 

 mined, and it w T as found to be in the position above stated. 

 It followed, therefore, that each of the poles of daily rotation 

 was slowly tracing a circle in the heavens round the axis of 

 second rotation. The time occupied in describing this arc 

 of the circle fixed the time required for a complete -second 

 rotation, and the diameter of the circle passing through the 

 pole of the elliptic gave the dates of the maximum and mini- 

 mum obliquity and their amounts. 



I will not attempt to indicate the astronomical conse- 

 quences, beyond observing that they reduce to geometric and 

 mathematical certainty what was before vague, and only 

 defined as a conical motion of the earth's axis ; the preces- 

 sion of the equinoxes and the obliquity of the ecliptic, which 

 vary in their rates and amounts continually, are determined 

 with perfect precision hundreds of years in advance ; so also 

 are the positions of stars for each zenith, for, as he shows, 

 the zenith of each observatory moves by the second rotation 

 in a special direction and at a special rate ; and it is proved 

 that in many cases, though probably not in all, the supposed 

 proper motions of the stars are a result of the proper motions 

 of the zeniths of the observatories, caused by the second rota- 

 tion of the earth, and that the speculations about our system 

 rushing through space towards the constellation Hercules have 

 a doubtful foundation in facts. As General Drayson well puts 

 it, however accurate and powerful our telescopes and observ- 

 ing-instruments may be, the real instrument with which we 

 make our astronomical observations is the earth itself, which 

 by its motions gives us our only means of measurement, and 

 until we know precisely what its motions are we cannot make 

 any really accurate observations. 



Enough has been said on the astronomical aspect of the 

 discovery. From our present point of view it is chiefly im- 

 portant from the fact that the most rigid scrutiny has hitheito 

 failed to detect a flaw in the process of reasoning which has 

 led to the discovery of the earth's second rotation, and tl.e 

 geometrical consequences of the discovery have been proved 

 to correspond exactly with recorded astronomical observations 



