262 Report of the Regents of the University, 



A. Ursse minoris or pole star. 

 7j. Zenith. 

 P. Pole. 



£. Epsilon Ursse majoris, or Alioth. 

 VZ. Co-latitude. \ -V 



R. The place of the pole star at Its greatest azimuth. 



The time required for the pole star to arrive at the meridian, af- 

 ter it is in the same vertical with Alioth, is thus calculated for the 

 latitude of 43° north, on the 1st January, 1833. 



Right Ascensions. JV. polar distances. 

 H. M. s. 



E Ursffi majoris or Alioth, 12 46 42 33° 08' 00" 



A Ursse minoris or pole star, 1 19 1 34 53 



DifF. of R. A. 176° 35' 45" = 11 46 23 



In the annexed figure of the spherical triangles, aPe and aPz. 

 Given the Co-latitude, ZP, - - - . 

 The N. P. distance of the pole star, Pa, - 

 The N. P. distance of Alioth, Pe, - 

 DiiF. of right ascensions, aPe, 

 The supplement of aPe, ePx, - ~ - • 

 Req,uired the angle aPz = the distance of the pole star from the 



meridian at the time of observation. 

 Produce aP, and from P and e let fall the perpendiculars Pw and 



ex. Then, 



1. Cot. Pe I R: :Cos. ePx : Tang. Px, and Px-\-Pa=ax. 



2. Sine ax \ Sine Px; :Tang. aPe : Tang. Pae—Paw. 



3. Cot. Pa \ R'. ".Cos. Paiv : Tang. aw. 



4. Cos. Pa : Cos. Pz'. :Cos. aw : Cos. zw, and zw—aw=az. 



5. Sine Pz : Sine az'. :Sine Paz : Sine aPz; the angle required.* 



* The calculation may also be made as directed by the sixth and seventh cases of 

 Oblique Spherical Trigonometry, given in Simson's Euclid. 



