December 22, 1893.] 



SCIENCE 



343 



ECP ( + 2295-date in mimber of years) x40.9"=tlie 

 angle ECP at date given, we can calculate tlie value of 

 ■ the side PE, which is the distance of the Pole of the 

 Heavens from the Pole of the Ecliptic, and is conse- 

 quently the measure of the obliquity, and of the Arctic 

 Circles, and Tropics on Earth at the date when the Pole 

 was at P. 



The method of calculating the distance PE, which is 

 the value of the Obliquity, is very simple, and is given in 

 detail at page 74 in 'Untrodden Ground of Astronomy 

 and G-eology" (two sides and the included angle). By 

 this calculntion the Obliquity for the 1st of January, 1800, 

 is found to be 23° 27' 55.3", and for the 1st January, 

 1850, 23'^ 27' 30.9", showing a difference of 24.4" for 

 fifty years during the first half of the present century. 

 But, between 1800 and 1900, calculation gives a differ- 

 ence of 46.5" (see page 75 of the same work). In 

 Article 640 of "Outlines of Astronomy," by Herschel, is 

 the following: "Meanwhile, there is no doubt that the 

 plane of the Ecliptic does actually vary by the action of 

 the Planets; the amount of this variation is about 48" 

 per century." This statement shows how entirely the 

 true cause of the decrease of the obliquity was over- 

 looked. It was positively stated that the Pole of the 

 Heavens kept a constant distance of 23" 28' from the Pole 

 of the Ecliptic. If it did keep at this constant distance, 

 then no amount of change, even of many degrees, 

 in the plane of the Ecliptic, would produce even 1" change 

 in the obliquity, which would always remain 23" 28'. 



That the Polar distance of a star can be calculated for 

 100 years or more, and from one observation only, is 

 proved by numerous examples given from page 52 to 63 

 in "Untrodden Ground in Astronomy and Geology.' 



An examination of the last diagram given in this pajDer 

 shows that the course of the Pole of the Heavens during 

 one Second Rotation caused it to vary its distance from 

 the Pole of the Ecliptic as much as 12", and hence at the 

 date 13544 B. C. the Arctic Circle and Tropics extended 

 12" more than at present, thus causing those vast changes 

 referred to by geologists as "the Glacial Period," and giv- 

 ing the dates for the commencement, duration and termi- 

 nation of this j)eriod, which agree with the latest dis- 

 coveries of geologists. 



The Second Rotation gives accuracy of detail and a 

 complete explanation of recorded facts, whilst by its aid 

 calculations can be made which have hitherto been con- 

 sidered impossible. "A Conical Movement of the Earth's 

 Axis round the Pole of the Ecleptic, as a centre, omits 

 all details, and leaves recorded facts without any clear 

 explanation. First, then, we have for a "conical move- 

 ment of the earsh's axis" a second rotation of the earth, 

 whichcau.se.? a conical motion of the two half axes, and 

 shows how the zenith of each locality on earth is affected 

 by this movement. Second, for the Pole of the 

 Heavens tracing a circle round the Pole of the Ecliptic as 

 a centre, at a constant distance of 23" 28', we have this 

 centre 6" from the Pole of the Ecliptic, and 29" 25' 47" 

 from the Pole of the Heavens, with the results explained 

 above. 



The following are some of the errors which have been, 

 and still ai'e, promulgated in consequence of the true move- 

 ments of the earth being misunderstood by many 

 persons : 



First: On many celestial globes and star maps a circle 

 is drawn round the Pole of the Ecliptic as a centre, and on 

 these, near the circle, is written, "Circle described hy the 

 Pole of the Celestial Sphere in 25,868 years." This error 

 is due to two oversights. First, although it was admitted 

 that the two Poles decreased their distance from each 

 other about 47" per century at the present time, and had 



decreased their distance during all time of which we have 

 any records, yet they always kept 23" 28' apart. The 

 second error was that, because the annual amount of the 

 precession (about 1800 A. D.) was 50.1", this rate was 

 constant for all time, whereas, for a uniform movement of 

 the Pole, the annual amount of the precession varied 

 wiUi, the distance apart of the two Poles. 



Second: It having been assumed by theorists that the 

 Plane of the Ecliptic could not vary from a mean position 

 more than 1" 21', it has been asserted that the Obliquity 

 could not vary more than 1" 21'. This error was pro- 

 mulgated in consequence of the true circle traced by the 

 Pole of the Heavens not having been known. No matter 

 how much the plane of the EclijJtic varied from a mean 

 position, there could be no variation in the Obliquity, if 

 the Pole of the Heavens was, as asserted, kept always 

 23" 28' from the Pole of the Ecliptic. 



The cause of the decrease in the Obliquity of about 47" 

 per century, its present rate, is not due to any change in 

 the plane of the Ecliptic, but is due to the fact that the 

 centre of the circle which the Pole describes is 6" 

 from the Pole of the Ecliptic, instead of being coincident 

 with it. 



Third: It has been asserted that because the decrease 

 in the Obliquity, or angular distance, between the two 

 Poles was about 48" per centurj', therefore in 10,000 

 years the decrease would be 4,800"=1" 20' only. 



Such a statement indicates a want of knowledge as to 

 the cau.se of the decrease, and a forgetfulness of the geo- 

 metrical law that a curve cannot decrease its distance 

 from a jDoint at a uniform rate. 



An examination of the last diagram shows that a varia- 

 tion of 12" will occur in about 15000. 



Fourth: It has been asserted that the Arctic Climate, 

 which reached to about 54" Latitude during the Glacial 

 Period cannot possibly be accounted for by astronomy. 

 Because, ''There is none amongst the slight variations of 

 the Earth's movements which, even with the aid of any 

 extension of time, however indefinitely great, could alter 

 the present angle of the Earth's axis as it lies to the plane 

 of the Earth's orbit. This angle, which is about 23", is 

 firmly fixed by that apparently essential property of 

 matter — Inertia." It is singular that such a statement 

 shou'd have been made, for the Earth's axis is not in- 

 clined to its orbit at about 23", but at about 66" 33', and 

 it varies this angle at about 47" per century at the pre- 

 sent rate of the Earth's gyration, so it cannot be firmly 

 fixed. 



Fifth: The changes produced on various meridians and 

 zeniths by the Second Rotation, are most important, but, 

 notwithstanding this, have been hitherto entirely over- 

 looked. In every observatory the Polar distance of a star 

 is deduced from its observed meridian zenith distance, 

 and its Right Ascension from its Meridian Transit. But, 

 that the zeniths and meridians of two localities, differing 

 in latitude, were differently affected by the so called 

 'conical motion of the axis," has been entirely disre- 

 garded. 



Sixth: The standard measure of time is also affected by the 

 Second Rotation, and a siderial day is at present a vague 

 quantity, only imperfectly defined by the statement that 

 it is the interval which elapses between two successive 

 transits of the same star ; because this interval varies for 

 nearly every star. The only uniform standard of time is 

 the interval between two successive transits of the Pole 

 of Second Rotation (see chapter 13 in 'Untrodden Ground 

 in Astronomy and Geology"). The statement made by 

 Sir John Herschel in a foot note at the end of "Outliues 

 of Astronomy" "that 3m. 3.68s. of j)urely imaginary time 

 was inserted between 1833 and 1834 in order to correct 



