234 Coast Survey of the United States. 
actness. ‘The observations are continued for several successive 
days. ‘The necessity, as it is generally considered, of using dis- 
tant night signals for this mode of determining azimuths, is 
avoided. 'The superintendent has adopted the suggestion of the 
Astronomer Royal at Greenwich, who proposed referring the 
points of greatest elongation of circumpolar stars, to marks in 
the horizon, by perpendicular lines demitted by means of an alti- 
tude and azimuth circle. Elongation signals are established about 
two miles distant, consisting of a delicate wand by day, and a 
lamp by night, the latter of which is seen through a small hole 
perforated in a board set up for the purpose. 
This method is peculiarly applicable to a large theodolite with 
a micrometer eye-piece,—first the position of the star is observed 
and then the signal with the micrometer, and so on alternately 
for ten minutes before, and ten after elongation. Many observa- 
tions are accumulated in one day, care being taken to ensure the 
steadiness of the instrument and the correct leveling of the axis. 
Measures were made by the reflected, as well as the direct image 
of the star, but this precaution was found to be superfluous. 
The elongation signals are observed in turn with all the other 
signals, and the probable error of the results is found to be less 
than the best on record in the French survey when the repeating 
circle was employed. 'The French used Polaris near elongation, 
but not both elongations. Distant night signals have been at- 
tempted with general success, and for this purpose a lens was 
borrowed from Mr. Lewis. Where these were set up, the are of 
distance from Polaris to the signal, which is the measure of the 
diedral angle formed by the two vertical planes of the signal and 
star, could be taken directly, and this, it is believed, was the 
method most in favor in the recent French triangulation. 
Concerning the observation of terrestrial angles and the use of 
the large theodolite, Mr. Hassler has very justly said, that, ‘‘ Ab- 
solute mathematical accuracy exists only in the mind of man. 
All practical applications are mere approximations, more or less 
successful. And when all has been done that science and art 
can unite in practice, the supposition of defects in the instrument 
will always be prudent. It becomes, therefore, the duty of an 
observer to combine and invent, upon theoretical principles, 
methods of systematic observations, by which the influence of 
any error of his instruments may be neutralized, either by direct 
