88 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



The values of p and p' may be conveniently tabulated for 

 a given latitude with log N as the argument, and for this 

 purpose log p' is best expressed in the form 



log p' = log (15 sec (p) -\- 6 {N V tan'^gj — 2) 



where the two 6 terms given above have been united into 

 a single term whose numerical value is to be obtained re- 

 gardless of the sign of the quantity under the radical, and 

 then to be added or subtracted as this quantity is positive 

 or negative. The following is such a table for the latitude 

 of the Washburn Observatory, 'P = 43° 4' 37", and it should 

 also be noted that the values of log N are limiting values at 

 which the tabular p, p' changes from one value to the next: 



P 



9.97083 

 .97081 

 .97085 

 .97086 

 .97087 

 .97088 



logN 



2.238 

 2.381 

 2.176 

 2.539 



2.587 



P' 

 1.31251 



.31250 

 .31219 

 .31218 

 .31217 

 .31216 



log N 



1.921 

 2.239 

 2.363 

 2.112 



2.499 



The construction of such a table is the only point at 

 which the d terms are required in the application of Dol- 

 len's ephemerides. 



In general the coordinates of the stars and the observed 

 interval *S' — S' will differ from that assumed in the compu- 

 tation of a^o and. N^ and it will be convenient to pass from 

 these latter quantities to the values x, iV corresponding to 

 the actual observation by means of diiferential formula. 



It is evident from an inspection of equations (16) that 

 these differential formulas will contain some terms which 

 involve only the coordinates of the stars and are, therefore, 

 the same for all parts of the earth's surface, while other 

 terms will involve functions of the latitude, and only that 

 part of these terms which is independent of the latitude 

 can conveniently be tabulated. Leaving the reader to dif- 



