342 



SCIENCE 



[Vol. XXII. No. 568 



Pole was supposed to move it was imagined that the 

 course of the Pole of the Heavens was not a true circle. 



Now, as it has been jDroved that the movement of 

 the earth which causes the Pole of the Heavens to 

 move, is a second rotation, it follows, as a geometrical 

 law, that, as long as the Pole of this second rotation 

 remains fixed, the course of the Pole of the Heavens 

 must trace a circle, and no other curve than that of 

 a circle. It has also been asserted that the Pole of the 

 Heavens does trace a circle in the Heavens, but not 

 round the Pole of the Ecliptic as a centre, this centre 

 being somewhere very close to the Pole of the Ecliptic, but 

 the exact position of this centre was unknown. 



Hence, it is evident that the true curve traced by 

 the Pole of the Heavens, or the true radius of the cir- 

 cle traced by the Pole of the Heavens has, during the 

 past three hundred years, been undefined and unknown. 



The confusion in one branch of astronomy which has 

 prevailed in consequence will become evident by an ex- 

 amination of the following diagram : 



E is the centre of the circle of which bPa is the cir- 

 cumference, b, P and a being three points on the circum- 

 ference. 



Suppose the angle bPa to be 95°. If the point P be 

 moved to P' then it is a geometrical law that the angle 

 bP'a will also be 95'^. Also if the point P be moved 

 to P" then bP"a will be 95^. 



We can now apply this law to Astronomy. Suppose A 

 and B to be two stars, and P the Pole of the Heavens, at 

 any date, the stars being believed to be on the circumfer- 

 ence of the circle traced by the Pole. Suppose the stars 

 A and B to differ in Eight Ascension exactly 95°. Then, 

 as the Pole moved round the circumference to P', the two 

 stars A and B would always differ 95"^ in Right Ascen- 

 sion. 



If repeated observations showed that the difference in 

 Right Ascension between the stars A and B did not re- 

 main constant at 95°, but varied slightly from year to 

 year, then these stars would be assigned ''a proper motion" 

 in Right Ascension, whereas the real cause of the differ- 

 ence in Right Ascension of these two stars, not being a 

 constant quantity, may be due to the fact that the radius 

 of the circle which the Pole describes is not that which 

 it has been imagined to describe, and the two stars were 

 not, in consequence, on the circumference of the circle. 

 Some stars, on the other hand, are known to have a 

 proper motion. During very many years it was asserted 

 that the Pole of the Heavens traced a circle round the 

 Pole of the Ecliptic as a centre, and on this erroneous 

 assumption the theory of the proper motions of the stars 

 was based. (See pages 126 to 130 in "Untrodden Ground 

 in Astronomy and Geology.") Many earnest, hard-work- 



ing men have employed their time in making out lists of 

 the supposed proper motions of stars, and pages of astro- 

 nomical societies' volumes have been filled with these 

 lists. Medals have been given for this work, but what is 

 their value ? 



To assert that any star has a "proper motion" in Right 

 Ascension, in consequence of the Right Ascension vary- 

 ing, whilst the true course which the Pole of the Heavens 

 traces has been unknown; and the exact manner in which 

 each zenith is affected, has not even been considered yet, 

 is very remarkable. But during the last hundred years 

 astronomers have copiied each others' proceedings, with- 

 out apparently perceiving that to define the true circle 

 traced by the Pole of the Heavens was the first important 

 problem to be solved; and until this jaroblem was solved 

 auy assertions relative to the proper motion of the stars 

 were valueless. 



Instead of the Pole of the Heavens tracing a circle 

 round the Pole of the Ecliptic as a centre, and keeping 

 constantly 23° 28' from it, recorded observations prove 

 that the Pole is carried by the Second Rotation round a 

 circle, the radius of which is 29° 25' 47", the whole circle 

 being completed in a period of 31,682 years, the Pole of 

 Second Rotation being 6° from the Pole of the Ecliptic, 

 and so situated that at the date 2295.2 A.D. the Pole of 

 the Heavens, the Pole of the Ecliptic, and the Pole of 

 Second Rotation will be on the same great circle of the 

 sphere. 



The following diagram indicates the course of the Pole 

 of the Heavens during one entire Second Rotation of the 

 earth : 



\'S5"'M..BC. 



^-5616 B.C. 



2.a96"-2 A^•D. 



The circle represents the course traced by the Pole of 

 the Heavens, in consequence of the Second Rotation. 

 At the date 13544 B. C. the Pole was at N, at 5626 B. 0. 

 it was at O, and at 2295.2 it will be at Q. 



The distance of the Pole of the Heavens as it moves 

 round this circle from C, the Pole of Second Rotation, is 

 a constant quantity, viz.: 29° 25' 47". E, the Pole of the 

 Ecliptic, is 6° from C Hence, when the Pole of the 

 Heavens was at N, it was distant from E 29° 25' 47" -|- 6° 

 =35° 25' 47". 



'^ The rate of the Second Rotation, as indicated by the 

 length of arc over which the Pole is carried in a given 

 time, is 40.9" annually. Hence, we can easily calculate 

 .at what part of the circle the Pole was, or will be at, for 

 any date. For example, at what date was the Pole at a 

 point in the circle 90° from Q? 90°=324000", and these 

 seconds divided by 40.9" gives 7,921 years from the date 

 2295 A. D., that is, 5626 B. C. We now have an impor- 

 tant triangle to deal with, viz.: the triangle ECP. We 

 have EC=6° (a constant) and CP=29° 25' 47", another 

 constant; when, then, we find the value of the angle 



