30 



(12.) PERSONAL EQUATION. 



Whatever differences there may have been between Mr. Austin and myself in 

 recording time, technically known as the personal equation, is still involved in the lon- 

 gitude. To determine this difference, we had two nights' observations together; the 

 one at Salt Lake in September, 1872, the other at the Naval Observatory, May, 1873. 

 In Salt Lake we used different instruments on the same stars, in Washington the same 

 instrument on different stars. The record, in both instances, was made on a chrono- 

 graph. The result shows a large difference Mr. Austin observing later than myself, 

 as may be seen by a statement of the following clock-errors: 



SALT LAKE CITY, UTAH, September 13, 1872. 



m. s. 



Clark ! 2 37.95 



O S .2O 



Austin 2 38. 1 5 



NAVAL OBSERVATORY, May 17, 1873. 



s. 



Clark +i 1.22 



Austin + 10.92 



Though this is not considered sufficiently satisfactory to apply without further 

 data, it is positive evidence of the existence of an element affecting our results ; and I 

 have the more faith in it because it expresses the sign between us which I would indicate 

 reasoning a priori. I am convinced that, in my own case at least, personal equation is 

 a variable quantity, and introduces an error which cannot be easily eliminated unless 

 some means be devised by which it may be determined in the course of every even- 

 ing's observations. 



(13.) PROBABLE ERROR. 



The computations were made by the method of least squares. The conditional 

 equations were sometimes formed with and sometimes without the correction for colli- 

 mation (c) ; in the former case it was obtained from a preliminary reduction. All the 

 observations at both stations were made under the same circumstances and conditions, 

 except the night of the Hth at Cheyenne, when the signals had to be received by 

 sound in consequence of the failure of the chronograph to work. It accords with the 

 rest, and is included with full weight; and the probable error of the final result is by 

 the formula, 



Errors 0.6745 x /- TT= - OI 7- 



(14.) RESULTING LONGITUDE. 



From the foregoing I conclude that the difference of longitude between Salt Lake 

 City observatory and the station at Cheyenne is 28"" i9 s -437; which difference, how- 

 ever, is still subject to correction for personal equation; and if any weight is to be 

 given to what is indicated as this equation between Mr. Austin and myself, this longi- 

 tudinal difference will be reduced by the extent of, perhaps, o s .2 of a second. 



