196 Wiscotisin Academy of Sciences, Arts and Letters. 



observations are needed, which I intend to make with a portable instru- 

 ment now constructing for Williams College Observatory; the field observa- 

 tions have confirmed it with sufficient certainty for my purposes. For in 

 my least square reductions I have pursued the course so strongly recom- 

 mended by Gauss (Astr, Nachrichten v. 5, cols. 227 following; Methodedes 

 moindres carres, memoires traduits par J. Bertrand, p. 163) of determining 

 in advance approximate values of the unknowns, and using the least 

 squares only to find minute corrections. And the following are the results 

 for the clock-corrections of the dates in the Ogden campaign, as published in 

 the Report before alluded to: 



The total effect upon the longitude^ of the apialication of least squares, 

 consists in the differences of their corrections for the stations. The ob- 

 servers at the corresponding stations in this campaign had worse instru- 

 ments than I, and were not so scruj)ulous in arranging their star lists; so 

 that the corresponduig corrections came out rather larger. Their time 

 ■determinations did not suffer sensibly from this cause, however; as both 

 "w^ere experienced observers. The average without regard to sign of the 

 26 numbers given above — each of which, with trifling exceptions is the 

 result of two groups of stars — is 0.^0091: and the i^robable error of one 

 preliminary solution +0,^ 0077; or for a single group of 10 stars ±0. ^011. 



It is evident, then, that if the weights are assigned by my formula with 

 approximate corrections — so, for instance as to make sufficient distinction 

 between a very slow-moving and a quiet-moving star — there need be no 

 fear that it is • not correct enough. The objections to the old process of 

 giving all stars a weight unity is that the jjolars of high declination domin- 

 ate too much in azimuth ; this process is about equivalent to leaving out the 

 quicker-moving stars north of 65° altogether. 



Another practice which is quite common is altogether meaningless. 

 When the weights are approximately correct there is no necessity of omit- 



