166 PROCEEDINGS OF THE AMERICAN ACADEMY 



The reduction of the observations for time and latitude is simple 

 enough, and the methods are given in the ordinary books. Some discre- 

 tion, however, is desirable in applying them. 



The application of least squares to time reductions is considered by 

 Struve often unnecessary ; nor is it generally practised in Germany 

 and Russia. Where it is applied, weights should be given to the ob- 

 servations depending upon the star's declinations. I am inclined, in 

 case the observations are fairly complete, and depend on about the 

 same number of wires, to consider the expression 



as a fair representation of the probable error in different declinations. 

 Hence the weight will be expressed by 



2 



" ~ 1 + sec 52, 



that at the equator being taken as unity. If azimuth, collimation, and 

 clock-error, or rather small corrections of their adopted values, are the 

 unknown quantities, their co-efficients, multiplied by y/ co, will be 



^ V^ = sin (cp-d) sec 8 t/ZZHZ =sin (cf-8) J '^ 



Y 1 4" sec 0^ » 1 + cos ^ 



CsT^ = J ! 



^ Vl-fcosfi2 



-j- sec d 



and their required squares and products 



A^ (0 = sin 2 (g) — 5) C^(o 

 AC oi = sin ( qp — d) C- a 



1 -j- cos 0- 

 Aco = sin (qp — d) Ceo 

 2 



C(o = 



sec S -f- C08 8 

 2 



^ — 1 + sec 82. 



I have tabulated the values of C'-w, Cw, and «, together with their 

 logarithms, according to these formuliB, and give them in Table I. For 

 any station, the preparation of A'-m, A Coo, AXo, is at once very simple. 



Tlie best results are not obtained from poor observations by cooking 



