Use of the Zenith Telescope in Determining Latitudes. 195 
Sin 2A, in which z is the correction, H the hour angle, and A 
the polar distance of the star. 
hese corrections were formerly tabulated, but now are gen- 
erally avoided by the mode of observing, and the cases in which 
they occur are computed separately. In general, the tendency is 
to avoid methods which introduce tedious calculations, unless at- 
tended with decided advantage. 
One of the great advantages of Talcott’s method is, that the 
correction for refraction is very small; being for the difference, 
merely, of the two refractions on each -side of the zenith. The 
correction for temperature and pressure of the air is, usually, in- 
significant ; amounting, at the distance of 25° from the zenith, 
and for a difference of 20 minutes of zenith distance, two inches 
of the barometer, and 50° of the thermometer, (Fahr.), to only 
002. The whole correction for refraction is obtained by the 
following easy method, first used, I believe, by Prof. Gibbes, of 
Charleston: The refraction being nearly proportional to the tan- 
gent of the zenith distance, the differences for the two stars of 
the pair will be nearly the differential of the tangent of the zenith 
distance of the star south of the zenith, and will be’ inversely 
proportional to the square of the cosine. : 
Zs the true zenith distance of the star south of the zenith, 
and Zn the same for the star north of the zenith. 
Then in each case the true zenith distance = the observed dis- 
' tance + the refraction, which is proportional to the tangent of the 
zenith distance ;—or calling Zs, and Zn, the observed zenith 
distances of the star S and N of the zenith, 
Zs=Zs,+mtanZs, and Zn=Zn,+m tan Zn 
Zs—Zn=Zs,—Zn,+m (tan Zs—tan Zn). 
Since tan Zs— tan Zn= tan (Zs— Zn) (1+ tan Zs tan Zn) a 
ble may easily be rigorously computed, or approximately, 
IZs 
d tan Zs= eae? Us : 
eta _ _ msin 1” diff. zen. dist. 
And the log correction is Log Te eee Ee cs 
@ table is easily constructed. te, 
he Glioiing table for correction for refraction to the ae 
hundredth of a second, for different zenith distances and 7 a 
ences of zenith distance, has been computed by this metho » RY 
sub-assistant G. W. Dean, of the U. 8. Coast Survey : 
, from which 
