19-i Wisconsin Academy of Sciences, Arts and Letters. 



adopt a different type of instruments from the European, lighter and more 

 portable, less liable to injury in transportation; but, on the other hand, 

 more care has to be exercised in so arranging our star-lists that all conceiv- 

 able instrmxiental errors shall be eliminated; we cannot depend tonfi,^ 

 upon one particular arc of the circle described by the telescope. A ^nese 

 things considered, it has been the practice of American observers to select 

 their time and polar stars in a much wider range of dechnation than the 

 Europeans employ; and to use the method of least squares in their reduc- 

 tions. 



I have myself employed these methods, both of selection of stars and re- 

 duction, in second Longitude campaigns; and have formulated for myself 

 the practical rules to be followed. The earlier years of this work were 

 spent in determinations at very distant points, accessible with difficulty, and 

 -with quite inferior instruments; so that, as they were also usually in bad 

 repair, it required very careful handling to produce even tolerable results. 



Later, in 1878, I had the use of an excellent transit instrument, which 

 was in first-rate condition; and was then able to apply the rules which I 

 had previously made for myself, to a better state of external circumstances. 

 In the present paper I shall state the conditions for a good series of time- 

 determinations in this country, as I now understand them, with especial 

 reference to the western States and Territories, and the methods of reduc- 

 tion. 



The observations to which I have last referred were made in 1878, at 

 Ogden, Utah, in latitude 41° 13'. The results are given in the Report of 

 the Chief of Engineers for 1879-80 (Executive Documents, 2d Session, 46th 

 Congress, Vol. 5), pages 1983-5. It will be seen that during a space of 2^ 

 months, from July 25th to October 10th, 74 days in all, there were 67 deter- 

 minations of time. Signals were exchanged on 26 nights with the regular 

 observers of Captain "Wheeler's survey; and the observations on these nights 

 reduced by the method of least squares; all these calevilations, as well as 

 the preliminary ones necessary for the other nights, were completed within 

 the two months after'the first exchange, August 12th, so that the method 

 of rediiction is not too complicated to be practicable. 



The following would be, in my judgment, an advantageous selections of 

 stars for a latitude 41° — 44°; the group is arranged nearly as at Ogden, and 

 differs from my ordinary arrangements in those times only because I had 

 then fewer close polar stars available. The stars are taken from the Berlin 

 Jahrbuch, or other ephemerides, and from my catalogvie of 2018 stars pub- 

 lished by the Engineer Bureau: 



