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(10.) UNIFORM TABLES OF TIME-REDUCTIONS AT RECEIVING-STATION-Continued.
CHEYENNE, WYOMING TERRITORY, October 21, 1872.
The following table shows the corrections and the rate of the chronometers used at Cheyenne and Salt Lake City:
(11.) GROUPING OF SERIES OF EXCHANGE-SIGNALS.
This table shows the result obtained for longitude each way each night and the mean of all the nights:
(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 longitude. 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 chronograph. 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.
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 evening'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 collimation (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 14th 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,
From the foregoing I conclude that the difference of longitude between Salt Lake City observatory and the station at Cheyenne is 28m 195.437; which difference, however, 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 longitudinal difference will be reduced by the extent of, perhaps, o.2 of a second.