72 Mr Pearson, On some points in the [May 21, 



We apply these formulae to find the place of Arcturus about 

 the era of Hesiod. 



Taking the mean position of the star as given above: then 

 sinRA.= 9-7299685 (-) 

 cot Dec. = 10 -4427302 (+) . 



10-1726987.(-) = tan 803" 53' 49^' = tan A, 



and (A + co) consequently = 327" 23' 49'\ making « somewhat 

 freely = 231". 



Again, we have 



sm(A + (o)= 9-7314403 (-) 

 tanRA. = 9-8038388 (+) 

 cosec^ = 10-0808999 (-) 



9-t)161790 (+) = tan 202" 27' 5'' = tan L. 



Also 



sini; = 9-5819490 (-) 



cot (^ + ft)) = 10-1940903 (-) 



9-7760393 (+) = tan 30" 50' 28" = tan I 



The next step is, taking the amount of annual precession, it is 

 owned somewhat boldly, at 50"*1, to estimate its amount first for 

 1900 years to bring it to 27 B.C., about the era of Ovid, and again 

 for 700 years, to bring it to that of Hesiod. The first amount is 

 about 26" 26' 30'\ and the second about 9" 44^ 30", which will bring 

 us to 176" 0^ 35" as the Long, in the time of Ovid, and 166" 16' 5^' 

 in that of Hesiod. As it is certain that the inclination of the 

 ecliptic has not changed more than 20' to 30\ within the periods 

 in question, we may safely deal with the Latitude of the star as 

 stationary in the interval. Consequently, L, D being the Longi- 

 tude of the star, in the time of Hesiod and of Ovid: I its latitude, 

 in both: X = 166" 16' 5", T = 176" 3o ', Z = 30" 50' 28", and on 

 these data we proceed to compute its R.A. and Dec, and from these 

 the times of the star's rising and setting at these two epochs. 



sinZ 9-3754437 (+) sinZ' 8-8422274 (+) 



cotZ 10-2239607 (+) cot^ 10-2239607 (+) 



tana 9-5994044 (+) tana' 9-0661881 (+) 



a 201" 40' 51" a 186" 38^ 34i" 



ft) 



23 50 ft) 23 45 



(a-ft)) ... 177 50 51 (a'-ft.)... 162 53 34^ 



sin (a -ft))... 8-5747184 (+) sin (a -ft))... 9-4685814 (+) 



tanZ 9-3880381 (-) tanZ' 8-8435834 (-) 



coseca 10-4324609 (-) coseca 109367372 (-) 



tanRA. ... 8-3952174 (+) tanRA. ... 92489020 (+) 

 .-. R.A. = 12 h. 5 m. 42 s. R.A. 12 h. 40 m. 14 s. 



