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The observations for latitude were made under very unfavorable circumstances. Undulations in the atmosphere, heavy winds, and great changes in temperature constantly affected the instrument.
It is customary in this office to select for latitude only thirty-five pairs of stars, which have to be observed on five different nights. But the observer is dependent upon the weather, and is frequently disappointed, although after waiting I preferred to select a greater number of pairs, believing that the final result of a latitude is better when depending upon various star-places, giving the probability that the errors resulting from the declination-places of the stars will more nearly compensate each other, and that this part of the probable error of the final result will come within that resulting from observation alone.
The mean latitude is obtained by taking the mean of all single results. For the different days the mean latitude is found to be as follows:
showing a great difference between the first and second day, arising from the disturbed condition of the air.
where v is the difference between the mean results and the single results and n the number of observations; therefore the probable error of the mean result is,
If it is proper to place all the observations in the final result with the same weight (as in determining the longitude of a station from different nights' work) the formula should be used in this way; but in determining the latitude of a station, every single result obtained also depends upon the places of the stars forming the different pairs. It is certainly wrong to determine the probable error of the latitude-result by this formula, (it would give, for latitude of Colorado Springs, a probable error less than o".01,)
though it is frequently done. If nearly the same number of stars are observed every night under the same conditions, I should prefer to determine the probable error of the final result after the manner of Mr. John H. Clark.
Probable error of one pair of stars, including constant errors
of zenith-telescope observations
Probable error of one observation .
Number of pairs used at the station
then probable error of the final result,
The formula shows that if the stars used are not very good, it is then better to select a larger number of pairs of stars, giving the probability that the final result will be more independent of the declinations.
From all the observations of pairs of stars observed on three or more nights, I find the probable error of one observation
Taking the value for &, found by Maj. C. B. Comstock, of the United States Lake Survey, for stars taken from Professor Safford's Catalogue for 981 Stars, o".53, the probable uncertainty of the final result will be, o".082.
Resulting Astronomical Co-ordinates for the Astronomical Monument at Colorado Springs, Colorado Territory, using, for the longitude of Washington and Salt Lake, the same data as in Clark's report.
UNITED STATES ENGINEER OFFICE,
GEOGRAPHICAL AND GEOLOGICAL EXPLORATIONS AND SURVEYS
WEST OF THE 100TH MERIDIAN, May 1, 1873.
Memorandum of instructions for conducting observations for longitude and latitude at a main or primary astronomical station for the field-season of 1873.
The fixed observatory, with which connection will be made, is in Temple Square, Salt Lake City, Utah, and in charge of Assistant John H. Clark. Every observer is responsible for the receiving of the signals from the connecting-stations for certain reductions of results, as full as possible, and will follow such other instructions that may, from time to time, be given. This station will be changed during the season, probably in the month of August, to the United States engineer observatory, to be constructed at Ogden, Utah.
1.-Observations for Longitude.
In carrying on the astronomical campaign, preference will be given to the longitude-results for those nights that are clear at both stations; that is, the observers in charge, after having completed the necessary arrangements for the observations and exchange of signals, will, from this time on, exchange signals each night that shall be fair at the two stations, unless unavoidable difficulties arise to prevent.
It will be carefully observed that weather-signals are sent by telegraph each evening about 6 p. m. while the exchanges are going on and until the full series at a station shall have been completed. In case of uncertainty as to the possibility for observing for any one night, this may be indicated in the first dispatch; and subsequent dispatch or dispatches, between this time and 10 p. m., shall determine whether exchanges shall be made that night or not.
Some convenient and concise form will be adopted for the weather-signals, and in no case must there be a failure as regards forwarding them.
It may be admissible, contingent upon the stage of the prosecution of the work, should the weather at Salt Lake at about 6 p. m. look unfavorable, that the observer at the distant station should at once conclude to take that night for latitude-work, which may be done after informing the observer at the Salt Lake or the receiving station.
For the conducting of the observations for the exchanges for a single night, the following instructions will be adhered to: The transit of stars for time-determinations, consisting of not less than three time and two circumpolar stars in each position of the instrument, both before and after the transmission of the signals, will be taken. Of course, should the night be sufficiently clear, so that it seems possible to make the time-determinations at both stations, by the modification of the above, so that at one or both of the stations the transits of stars may be made entirely before or entirely after the sending of the signals, the strict following-out of the above is not
These instructions are made with the understanding that a twenty-six
two inch Würdemann instrument is used, with recording-apparatus in shape of a chronograph or register.
The time set for the transmission of signals should be as near 9.30 p. m. local time of the Salt Lake meridian as possible; and great care should be taken that both observers shall be on hand simultaneously, so that as little delay as possible shall ensue in the use of the telegraph-wires.
In the transmission of signals the record is to be made upon the chronograph or register at the two places over a space of five minutes in time, the connecting or Salt Lake station sending for the first five minutes and the distant station receiving, and
In addition to these, which may be known as the chronograph-signals, arbitrary signals will be sent, by the use of a break-circuit key, at about ten seconds apart, at fractional parts of a second, making a series of thirty-one arbitrary signals during
the five minutes.
In order that the observer at a station may conclude that he has accomplished six nights of first-class observations, it becomes necessary that there should be an exchange of the approximate results. Each observer will therefore send to the other, upon each subsequent night or as soon thereafter as practicable, the approximate error of his chronometer and the mean of seven arbitrary signals, sent and received, selected from the middle of the set of thirty-one. This may be concisely expressed in a telegram.
For the full satisfaction of an observer at the distant station, such further computation shall be sent and received as shall seem necessary to a clear understanding of the case; as an observer will be held responsible should he leave the station and go to another before he is certain that the results upon final computation would prove satisfactory.
2.-Observations for Latitude.
These will be conducted through five complete and clear nights, so that there shall not be less than 175 pairs of observations upon 35 separate and distinct pairs of stars, each pair of which observations shall give a first-class result.
These instructions are furnished to the observers with a view to their clearly understanding the class of results intended, and will always be carried out, unless unforeseen difficulties arise, in which event, as the observers will not hereafter be within speedy communication of these headquarters, it will be necessary for them to adopt immaterial modifications upon their own responsibility. It is, of course, understood that each observer is responsible for and receives the credit of his own work.
A report will be made by each observer, at intervals not exceeding fifteen days, of the work under his charge.
A full daily journal will be kept by each observer. Great care will be taken as to the character of the record upon this journal, which should be clear and explicit. The position of the station in reference to surrounding natural objects should be clearly described, and imperishable meridian-marks firmly planted. When possible, a special survey and plat will be made.