The Jieduction of Transit Observations. 199 



I have annexed to this paper, a table for Og-den observatory, latitude 

 41° 13' 8". 6, which is calculated according to the formula. 



1.3 



P=l + 0.8sec2(5 



^— cos 5 

 1 



"cos S 



The columns p, C j), C , p hold good for any station; tlie values of A p, 

 A 2 p, A C p must be recalculated for every new latitude. But I have not 

 omitted them, as their values will serve as a control for a good many 

 places near the same parallel. The numbers are given to four decimals, to 

 enable the computor to interpolate readily to three. 



The 53 nights out of 78 upon which signals were not exchanged at 

 Ogden, afforded an excellent opportunity for the criticism of the instru- 

 ment. A peculiarity of much far western longitude work is that the tele- 

 graph lines are in bad order much of the time, and do not afford oppor- 

 tunities for long exchanges. On some nights of the exchanges with Fort 

 Bliss (Texas), it was impossible to get a circuit through on the more direct 

 route, by way of Cheyenne, Denver, and Santa Fe, and recourse was had 

 to a line of 2,000 miles in length via San Francisco, Southern California, 

 and Arizona. The time expended while waiting is, under such circum- 

 stances, best applied to the study of the iDeculiarities of the instrument. 



In conclusion, I will indicate the principal points of this paper as a sum- 

 mary of directions for the determination of time in latitudes 25° to 49°. 



1. A group of time-stars should contain about 10 stars in all, with one 

 reversal. 



2. It should contain no more than two or three polars; one of which 

 may be within 10 degrees of the pole. 



3. Stars north of the zenith, not polars, should be included; and may 

 take the place of polars to some extent. 



4. Lower culminations should in general be avoided; and time-stars far 

 south of the zenith. 



5. The stars of a group should so balance at the zenith that the co-effi- 

 cient of azimuth and coUination in the normal equation for clock-correc- 

 tion should be very small, and the weight of the clock-correction large in 

 proportion to the number of stars. 



6. With proper blank forms the preliminary reduction without least 

 squares can be very simply effected, and this should always be done. 



7. The least square deduction is of little benefit except in removing the 

 effect of any arbitrary assumptions in the previous pi'ocess; and should be 



