ASTRONOMICAL PROBLEMS. 521 
By a similar process for 1. 1.1755 we obtain 
angle C=37° 47’ 508 ; Ca=44° 48’ 336 
5 a ° 1 OQRI, 
log cos C= 9°8977273 tre ree 
log tan PC= 9°7513982 Qnd arc=20° 46’ 57-8 
log tan Ist are=19°6491255 log cos 2nd are= 9:9707804 
log sin C= 9°7873892 Iesieoss (Gate S uo 
log sin Ca= _9°8480349 19-9107781 
19-6354241 —log cos Ist arc= ; 9:9606402 
—log sin Pa= 9°6560536 log cos Pa= 9:9501379 
log sin P= 9-9793705 Pa=26° 56’ 0” 
P=180° —72° 28’ 46” By Bree ag tes On 586 
= 710m 459 Diff= 0° O° 14 
+719 x 132= 1™ 345-9 
R.A. =182— 75 11™ 398-8 
= 105 48™ 208-2 
By Bradley 105 48™ 228-6 
Diff Ob Om gs-4 
It would be tedious to give any further examples of calculations 
such as those already given, the-principle in each case is the same. 
The constants (angular distance from C and the angle at C formed by 
P and the star) being once established for any year, say 1887, the past 
or future position of the star can be worked out in a quarter of an hour 
to within a fraction of a second of what is recorded as the true position 
of the star in the Nautical Almanack; the log tan of CP and the 
log cos of the same are will recur so frequently that it will hardly 
be necessary to look them out for every calculation, they will most 
probably very soon be committed to memory. 
In dealing with some of the circumpolar stars such as X Ursae 
Minoris there are two or three points to be noted. 
On the Ist January 1887 this star is assigned 
R.A.=195 36™ 46888 and Decl. =88° 57’ 36/5 R 
the constants are found to be on this date 
angle C'=0° 53’ 37” and CrA=28° 29' 9/°5 
CP aBY Des Ay”, 
If a figure be constructed it will be seen that for years later than 
1887 the R. A. will decrease, therefore the value of *°719 per year will 
have to be added, see page 516; the change in R. A. is very great and 
the rate very variable. 
_ This star is a very difficult one to work out because the angle at C 
is so small that the cosines are closely approximating to unity, a 
difference in the 7th place of decimals will cause a difference of several 
