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196 GBSERVATORY AT WEST POINT. 
black line was drawn upon the equatorial and horizontal surface of the stone, perpen- 
dicular to the line of intersection of these surfaces at its middle point, and the latter sur- 
face being kept horizontal by means of a large spirit level, the stone was moved till the 
traces were brought into the meridian, as indicated by a sweep of the telescope of the 
theodolite. ‘The instrument was then put up. 
The following conditions must be fulfilled by an equatorial in perfect adjustment. 
1. The polar axis must be parallel to that of the heavens. 
2. The declination axis must be parallel to the equator, or perpendicular to the polar 
axis. 
3. The line of collimation of the telescope must be perpendicular to the declination 
axis. 
4. The index of the declination circle must point to zero, when the line of collimation 
is parallel to the equator. 
5. The index of the hour circle must point to zero, when the line of collimation is in 
the meridian of the place. 
M. Littrow has given in the Mem. of the Ast. Soc. Vol. IL part I. p. 45, formule for 
the determination of the true apparent place of a heavenly body from the place as indi- 
cated by an equatorial out of adjustment. These were improved by M. Kriel, Mem. of 
the Ast. Soc. Vol. IV., p. 495. The adjustments have been made by these formule, 
which are 
s=o+Ao-+2. sin (p—s). tan d+ tan d+y sec. 3. . (1) 
pH=At+A AA, COS (P— 3S). ese ee cece eer ennes (2) 
In which s is the true, and o the instrumental hour angle, corrected for refraction; p 
the true, and 7 the instrumental polar distance corrected for refraction; Ao and A x the 
index errors of the hour and declination circle respectively; A, the distance, in are, between 
the pole of the heavens and that of the instrument; ¢ the hour angle of the instrumental 
pole, estimated from the meridian to the west; u is the difference between 90° and the 
angle which the declination axis makes with the polar; » the difference between 90° and 
the angle which the line of collimation makes with the declination axis; and 9 the de- 
clination of the body. The adjustments of the several parts of the instrument, with 
respect to each other, were first made by means of terrestrial objects. These are always 
at hand, and vary in declination, from zero to the complement of the latitude of the place, 
which, in the present case, is 48° 36’; the former being in the instrumental east and west, 
and the latter in the instrumental north and south, 
INDEX ERROR OF DECLINATION CIRCLE. 
The telescope was directed to a well defined object in any part of the horizon in the 
direct and reverse position of the instrument, and equation (2) gave 
p=n+A n+. cos (¢—S) 
p=n—A a+A. cos (¢—s) 
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