186 SECULAR VARIATIONS OF THE ELEMENTS OF 



to 90° — ^; and the latitude of the pole will also be equal to 90° — e/, or to the 

 complement of the obliquity of the ecliptic of 1850, at the given time. If we then 

 put X=90° — 4^ /3=90° — Ei, in equations (584), the resulting a and <5 will evidently 

 be the right ascension and declination of the pole of the equator for the time t, 

 referred to the equinox and equator of 1850. Calling the right ascension of the 

 pole A, and the declination D, we shall evidently have 



cos D cos J.=sin e-l sin ^ ") 



cos D sin A= — sin £ x cos ^'-[-cos £ i sni £ i cos ^ f (586) 

 sin -0= cos e x cos ej'-J-sin ^ sin e/ cos 4< J 



Ei denoting the obliquity in 1850, and e/ denoting the obliquity of the fixed ecliptic 

 of 1850 at the time for which the computation is made. If we compare these 

 equations with equations (571), we find sin A= — sin z, and sin D— cos 0. 



Therefore A=—s, and Z>=90°— 0. 



Now since z and are already tabulated we can enter Table X with the argu- 

 ment t, and take out the right ascension and declination of the pole by mere 

 inspection. 



Example VI. What will be the right ascension and declination of pole 5600 

 years hence, when referred to the equinox and equator of 18501 Entering Table X 

 with the argument i!=+5600, we find 2=36° 55' 6". 4, and 0=28° 44' 0".89. 

 Therefore .4=323° 4' 53".6, and Z)=61° 15' 59".ll. The mean place of a Cephei 

 in 1850 was a=318° 45', and £=61° 56'. This star will therefore be the pole- 

 star of that period. 



