APPENDIX NO. 8. TEST OF A TRANSIT MICROMETER. 
477 
Such a conclusion is deceptive for the reason that in observations with the key, 
though the accidental errors are quickly reduced to within very narrow limits, there 
remains in the mean result for a night, and even in the mean result for a pair of sta 
tions, constant errors, which are apparently independent of the accidental errors and are 
much larger than the accidental errors. These constant errors are supposed to be 
mainly due to variations in the relative personal equation of the two observers. 
Thus* in observations with a key the probable error in the result for a night 
arising from accidental errors of observation, and therefore capable of further elimination 
by increased observation, is upon the average ±o s .oi3; while the error peculiar to each 
night, and therefore not capable of elimination by increasing the number of observations 
per night, is ±o s .022; and the constant error peculiar to each longitude determination, 
and not capable of elimination by increasing the number of nights per station, is ±o s .022. 
These are values derived from the adjustment of the telegraphic longitude net of the 
United States. It thus appears that the principal errors in the mean of ten nights of 
observation with a key are of the constant kind. The accidental errors are relatively 
insignificant. The probable error of the difference of longitude of two stations con 
nected by a land line and determined by ten nights of observation, including all three 
of the above classes of errors, is for the primary longitude net zbo s .025. 
If it be assumed that the errors in a transit micrometer determination of difference of 
longitude are all of the accidental class, the result from a single night’s observations of 20 
to 24 stars at each station will have a probable error of from ±o s .020 to zto s .027. The 
value of ±o s .02o is based upon the probable error of dto s .o63, derived from observations 
by J. F. H. with the slow speed of the driving heads; and the probable error ±*.027 
is based upon the probable error ±o s .o84 for a single observation for other observers 
than J. F. H. and with both speeds of the driving heads. On this basis it then appears 
that a pair of observers, either experienced or inexperienced, would secure as accurate 
a determination of a difference of longitude from a single night of observation with a 
transit micrometer as has been obtained, as a rule, from ten nights of observation with 
a key. 
It is to be expected, however, that in regular longitude work the difference in 
atmospheric conditions at the two stations, the possible unknown interposition of repeat 
ers in the telegraph line between stations, the irregular running of chronometers, and 
perhaps other conditions which have not operated to influence this test of the microme 
ter-, may introduce additional errors of both the accidental and the constant class. It is 
the opinion of the writer that such additional errors will be so small that it is safe to 
predict that three nights of observation without exchange of observers will give as great 
accuracy as has been secured from ten nights of observation with the key, including an 
exchange of observers. This is a prediction of which the truth or falsity can only be 
proved conclusively by field experience. The writer relies upon such experience to be 
gained within the next ten years to verify the prediction. 
*See pp. 331-332 of Appendix 7 of the Report for 1898, “Determination of Time, Longitude, 
Latitude, and Azimuth.”