516 ASTRONOMICAL PROBLEMS. 
of C are uniform and & gains on C, this rate of decrease in the angle 
subtended by HC with the successive positions of the Pole of the 
Heavens can be calculated. 
Thus angle HCP=3° 24’ 30” (300 x 40’9) 
CP=29° 25! 47” 
HC=6". 
And by calculations similar to those on pp. 512 and 513 we get 
LP =23° 26’ 333 
sin poe .. logsin O= 8°7741633 
a logsin HC= 9:0192346 
17:7933979 
—logsin HP= 9:°5996974 
log sin P= 871937005. 
angle P=0° 53’ 42°13. 
Similarly in the triangle ACR. 
HR =23° 27’ 58” and angle R=1° 29’ 21” 
subtract angle P= 53’ 42” 
rate of decrease in 200 years= 35’ 59” 
=2159” 
in 100 years=1079”. 
Convert this into time by dividing by 15 and we get the annual 
Re ==" 1, 
When any date is fixed upon as a zero the allowance thus found 
of *°719 per year must be made to find the recorded R.A. as at present 
used by astronomers. 
Let Ist January 1887 be the zero date, then for dates after 1887 
the allowance will be —, for earlier dates +, for as the Pole of the 
Heavens advances, R. A. will increase for all stars except a few circum- 
polar ones of which a list can be easily made out. 
Problem VI. Calculate the R.A. of 7 Ursae Majoris for Ist 
January 1895, from data obtained on 1st January 1887. 
We have already seen that the N.P. D. of this star was found to be 
(page 514) 
=40° 9’ 45” -87, 
Cn =36° 31’ 6” and angle C=77° 18’ 20’-2 
then sin P=sin 0 2 oh 
in Py 
log sin C= 9:9892521 
log sin Cn= _9°7745740 whence P=64° 10’ 18” 
19°7638261 =4b 16™ 418-2 
—log sin Pn= 9°8095335 SOR a ALO)— 58-7 
log sin P= 9:9542926 R. A. =185 — 4h 16™ 358°5 
* Another way of getting the rate after 1995 is to divide the value of angle P by 
300 x 15 to get the answer in Time, this comes out 8-716 per year; the rate is of course a 
decreasing one. 
