184 



SECULAR VARIATIONS OP THE ELEMENTS OE 



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



Now having the declination for 2=200, 2=250, and 2=300, we very readily 

 find that the maximum will take place when 2=+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 ^'=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, 0=— 39° 24' 51".5, 

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



Therefore the computation will stand as follows : — 



a-\-z 

 B 



cc+z 

 

 

 h 

 cos h cos (oc+z) cos ©=+0.0161008 

 —sin h sin 0=4-0-6347087 



cos h' cos (a'— z 1 — 30 =+0.6508095 

 cos <$' sin (a' — z' — 3') 



a'— z'— 3' = 358° 37' 49". 7 

 z'+3' =— 51 50 48.9 

 a' = 306° 47' 0".8 

 a'— rf-,3.' 

 cos o' cos (a — z' — 3') 



6' =49° 23' 



sin 9.7768805re 



cos 8.4151046 



cos 9.9038016 



cos 9.8879407 



sin 9.8027213re 



-sin 9.9998531ra 



log. 8.2068469 



" 9.8025744 



" 9.8134539 



" 8.1919851m 



tan 8.3785312re 



cos 9.9998759 

 log. 9.8134539 

 cos 9.8135780 



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

 distant 40° 37' from the pole. 



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

 a=318° 45', S=+6.1° 56'; 

 required its mean place when 2=+5600 years. 

 In this example we find 



z=+36° 55' z'+3'=+37° 35', 0=28° 44'. 



Then we get a'— z'— $'=249° 44', whence a'=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. 



