600 SCIENCE PROGRESS 



in any year, formed by Newcomb from recorded observations 

 supplemented by theory, is as follows : 



(Newcomb) -23 27' 8"-26 - 46"-845 T - '00$gT 2 + -ooi 8 1 P 



Compare this formula with Drayson's and it will be at 

 once seen that Drayson's, being founded on a principle, is far 

 less complicated : 



(Drayson) [229475 (Zero year) — date required] x 40" -8 1 = 

 angle ECp, whereby Ep the obliquity is obtained. 



(Drayson's Formula) _y^—v *■. To find an S le at C and hence E/ 



Zero Year 2294-75 a.d. -|— - j J - —^—^-fe Annual angle 4o""8i 



For any date (2294*75 - date required) X 4o"'8i = angle EC/ 



Now in Newcomb 's formula T represents the time factor, 

 and if its value for the whole time is extracted, the minimum 

 of the values for T is found to be 32,502 years, which is 

 6,640 years in excess of 25,868, but differs only 746 years from 

 the period of Drayson's cycle. One or two critics have at- 

 tempted to belittle this evidential value of T in Newcomb 's 

 formula, saying that its correctness cannot be depended upon, 

 because if Newcomb experimented by extrapolation with a 

 portion of an unknown curve, it is only correct in the neigh- 

 bourhood of that portion, and the correspondence with Drayson 

 is only a coincidence. That is perhaps a plausible argument 

 for an unknown curve, but unfortunately for the critics it is 

 the essence of the astronomical position that the precession 

 curve must be a circle (on Newton's theory), of which any arc 

 is therefore similar in all its parts to any other part of the 

 circle, and again the same astronomical period of 25,868 years 

 is founded on a circle, so that the value of T has a decisive 

 significance. 



The following is an extract from a letter by an astronomer : 



" The maximum variation of the obliquity shown by New- 

 comb's formula is only i£°, so that it is not identical with 

 Drayson's : but that its period of variation should be so nearly 



