ASTRONOMICAL PROBLEMS. 513 
Problem II. Calculate the obliquity on the 1st January, 1437. 
See Fig., problem I. 
angle C= (2295°5 — 1437) 40”-9=9° 45’ 12'"6 
Oo" CIPHBY’ Dsy Ail” 
Ist arc= 5° 54’ 50” 
Qnd arc=23° 30! 57”. 
log cos C= 99936768 
log tan EC= 9:0216202 
log tan Ist are =19-0152970 
log cos 2nd arc= 9:9623456 
log cos HC= 9:9976143 
19-9599599 
—log cos 1st arc= 9°9976825 
log cos HP= 9:9622774. 
By calculation 2. HP=23° 32/115 (Measure of obliquity in 
Observed by Ulugh Beigh 23° 32/ 8” 1437) 
Dimes © OY HK, 
Presumably Ulugh Beigh’s result was obtained by taking half the 
difference of the sun’s altitude at the winter and summer solstices, 
his instruments were probably not very accurate, nor was refraction 
corrected for. 
Problem III. As an example of the accuracy which can be 
obtained by calculation as regards the past or future position of the 
stars, the following example is given : 
In the Nautical Almanack for 1887 for the star 7 Ursae Majoris we 
have x 
mean R.A.=13" 43™ 58-296 
do. Decl. =49° 52’ 38”-76. 
a 
Then in the triangle CP7 we have 
vu 
C, pole of 2nd rotation. 
P, pole of daily rotation. 
n, the star. 
3 
The point C being on the line of no variation in R. A. must have a 
R.A. = 18) hrs. 
Then angle P=18>— 13) 43™ 58-296 —4» 16™ 548-774 
=64° 13! 41'6 ; Pn =90° — 49° 52’ 38’°76 
log cos P= 96382754 =40° 7 21-24 
log tan CP= 9°7513982 Ist arc=13° 46’ 544 
log tan 1st arc=19:3896736 2nd arc=26° 20' 26°84. 
logsin P= 9:9544996 log cos 2nd arc= 99523908 
log sin Pn= 9°8091723 log cos CP= 9:9399977 
19°7636719 19°8923885 
—log sin Ch= 9°7745753 —log cos Ist arc= 9:9873129 
log sin C= 9:9890966 log cos Cn= 9°9050756 
w. O=T77 12! 53". “. Cy =36° 31’ 6”. 
