184 



SECULAR VARIATIONS OF THE ELEMENTS OF 



Then we find a'=88 13' 39".20 and #=89 3? 32". 202. 



Now having the declination for <=200, <=250, and <=300, we very readily 

 find that the maximum will take place when t=-\- 252.335, or a little before the 

 middle of the year 2102. Computing the place of the star for this last value of 

 t, we find 



a'=89 53' 2".78 and 6'=89 32' 32".973. 



The nearest approach of the pole to the star is therefore equal to 27 27".027. 



Example II. Let it be required to find the declination of Polaris when t= 8000. 

 For the value of t we get z= 53 0' 2".8, z'= 54 34' 37".2, B= 39 24' 51".5, 

 and ^'=+2 43' 48".3. a+z= 36 44' 40".0. 



Therefore the computation will stand as follows : 



a-\-z 



5 



a-j-z 











5 



cos 5 cos (a-f-z) cos =+0.0161008 

 -sin 3 sin 0=4-0-6347087 



cos # cos (a' z 7 y) =-(-0.6508095 

 cos # sin (a' z' $') 



a z' y = 358 37' 49".7 

 =. r >l 50 48.9 



sin 9.7768805 

 cos 8.4151046 

 cos 9.9038016 

 cos 9.8879407 

 sin 9.802721 3n 

 -sin 9.999*53 In 



log. 8.2068-Ki!) 

 " ^.8025744 



" T8134539 

 " 8.1919851re 



a'= 306 47 

 a' sf $' 

 COS (V cos (a' z 7 30 



6' =49 23' 



tan 8.3785312 



cos 9.9998759 

 log. 9.81345:',!) 

 cos 9.81357SO 



From this calculation it follows that the present polar star was r 8000 years ago, 

 distant 40 37 from the pole. 



Example III. In 1850 the place of the star a Cephei was 



a=318 45', 3=+Ql 56'; 

 required its mean place when <=-)-5600 years. 

 In this example we find 



z=+ 36 55' *'+S'=4-37 35', 0=28 44'. 



Then we get a' ^ $'=249 44', whence '=287 19' and #=+87 50'. 

 It therefore follows that the star a Cephei will be only about 2 distant from 

 the pole in 5600 years ; it will therefore constitute the pole star of that period. 



