286 Variation in the Obliquity of the Ecliptic. [July, 
20’ annually, and a closing in—as we may term it—of the 
pole of the heavens to the pole of the ecliptic of about 
0°45" per annum, at the present time: that is to say, the 
pole of the heavens traces on the sphere of the heavens an 
arc, which, when referred to the fixed stars, indicates a rate 
of about 20” annually, and towards that part of the heavens 
indicated by the first point of Aries. This arc approaches the 
pole of the ecliptic, and may be fairly represented by the 
arc PP’ Pp” Pp’, whilst E is the pole of the ecliptic. 
Fic. I. 
E 
P @ e Cc 
Pp’ 
p* 
p™ 
The angular distances, EP, EP’, EP”, EP, will be the 
angular distances of the pole of the heavens from the pole 
of the ecliptic, at those dates at which the pole of the 
heavens was located at p, P’, P’, &c.,—and these distances 
represent the value of the obliquity at those dates. The 
records of these measures of the obliquity exist, and records 
of the rate of the movement of the pole exist ; consequently 
the curve P, P’, P’, P’” can be defined, as regards E, the pole 
of the ecliptic ; and this curve is part of a circle, or part of 
an ellipse which does not differ much from a circle, the 
centre of which circle is 6° from the pole of the ecliptic, and 
so situated that at the date A.D. 2298 the pole of the 
heavens, the pole of the ecliptic, and the centre c, will be 
in the same great circle of the sphere. The curve thus 
traced out corresponds exa¢tly with the recorded observa- 
tions of the past as regards the decrease in the obliquity. 
It explains why the annual decrease in the obliquity is now 
less than it was found to be one or two hundred years ago, 
for it will be evident that the nearer we approach the date 
A.D. 2298 the less will be the rate in the annual decrease in 
the obliquity, whilst the further we go back the greater will 
be the annual rate; and this variation in the rate is in 
stri@t accordance with recorded observations. 
We have, again, another fact to deal with, carrying back 
into the past the curve (either as a circle or an ellipse very 
closely corresponding to a circle) thus defined we should 
obtain a variation of at least 12° in the extension of the 
