512 ASTRONOMICAL PROBLEMS. 
positions in 1820 and 1755 were similarly determined; these dates 
were taken for the reason that as Major-General Drayson happens to 
possess copies of the Nautical Almanack for 1820, for 1895 and 
Bradley’s Catalogue for 1755, the differences between the calculated 
and observed positions can be readily obtained. 
It should also be mentioned here that between the years 1833 and 
1834 three minutes of arbitrary time were found to have been put into 
the Nautical Almanack; this correction may be accountable for some of 
the differences in R.A. as of course Major-General Drayson’s time is 
that of the Nautical Almanack for 1887. 
Our standard of Time is at present determined by the interval 
between successive transits of the Ist point of Aries, but owing to the 
movement of the Pole of the Heavens and the amount of the obliquity 
this point precedes its time by a few seconds annually. Were the 
standard fixed by the interval between successive transits of the centre 
about which the Pole of the Heavens is moving we should have by 
these successive transits a uniform standard measure of time, whereas 
at present we have a variable quantity to give us our standard, for 
although the movement of the Pole is uniform, the amount of obliquity 
is changing at a yearly decreasing rate. 
In order to determine with accuracy the are over which the Pole of 
the Heavens moves annually, the recorded observations of Stars having 
0" and 125 R. A. for any year are compared with those for, say, 10 years 
previously so as to get their mean N.P.D.’s. This mean rate for 
10 stars was found by General Drayson to be 20092 annually. In 
these problems the movement of the Pole has been taken at 2009 and 
this gives the rate of Precession at 50-4758 for 1887 a. = oe Is 
sin. obliquity 
in this case the obliquity has been taken at 23° 27’ 14", the calculated 
value, and not at the value given in the Nautical Almanack; the 
difference is not appreciable at the fourth place of decimals. 
Problem I. Calculate the obliquity on the 
Ist January, 1887. e 
CIP =e WY A, HOO 
angle C=(2295°5 — 1887) 40” 9=4° 38! 27-65. 
log cos C = 9:9985737 29° 25! 47” E 
log tan 6°= 9:0216202 Ist arc= 5 58’ 49”-69 
log tan Ist are 19:0201939 gnd arc=23° 26’ 57°31. 
log cos 2nd arc= 9°96256485 
log cos 6° = 9°9976143 
19-96017915 
— log cos Ist are= 9°99762987 
log cos HP= 9:96254928 
by calculation HP=23° 27’ 14-3 (Measure of obliquity 
by Naut. Alm. 1887=23° 27’ 14-22 of the Ecliptic) 
Difi= 0° 0” 07-08, TOTP 
