CIRCLE. 



507 



Lirclc. 



TABLE IV.-^ 



It has been shewn, how, from the oblique angle of 

 two objects, A and B, as seen from a point C, we can 

 obtain the horizontal or azimuthal angle ; but it is neces- 

 sary, for the truth of our conclusion, that the point C re- 

 main the same for the zenith distance observations as for 

 the oblique angles. If we examine the construction of the 

 repeating circle, we shall find that its centre C is lower 

 in the vertical than in the horizontal position : this cir- 

 cumstance seems to have been overlooked by the French 

 astronomers ; or they have probably included it in the 

 requisite correction employed for the difference of height 

 of the signal above the centre of the circle. To apply 

 this correction, we are to consider what would be the 

 zenith distance of an object if the centre of the instru- 

 ment were elevated or depressed a given quantity. 



The correction is as follows : 



Let JH be the difference of altitude of the two posi- 

 tions, D the distance of the observed signal, 3 the zenith 

 distance required to be corrected ; then the corrected 

 distance will be 



sin. 3 



Circle. 



If the instrument is advanced before the signal, the 

 distance corrected will be 



r_being the distance of the centre. 



In Mr Troughton's circles the centre of the circle is 

 5.4 or 5.5 inches lower in the vertical than in the hori- 

 zontal position. 



SECT. III. On the Use of the Repeating Circle as an 

 Astronomical Instrument. 



We have seen that the principal advantage of the *e- Use of the 



peating circle consists in the contrivance by which the r fP" tm g 



' .. , ... circle as an 



angular distance of two points may be measured with astrom)m i_ 



extreme accuracy. Now, it is evident, that if we could C al instru- 

 always command a visible terrestrial object, placed ex- menu 

 actly either in the north or south point of the horizon, 

 and if at the same time a star could remain stationary on 

 the meridian, its meridian altitude might be obtained by 

 the process above described, without farther explanation ; 

 for the angular distance between the star and the ter- 

 restrial object would be the meridian altitude required. 

 But neither of these conditions can be obtained. The 

 stars are apparently in constant motion ; and a terrestrial 

 object as above defined, (even if it could be obtained,) 

 would be invisible by night ; hence arise two difficulties, 

 the one produced by the motion of the star, and capable 

 of being obviated by appropriate tables, the other is re- 

 medied by substituting a spirit level instead of the back 

 telescope. This substitution will effect some little 

 change in the mode of observing which we shall shortly 

 describe, and will require some few additional verifica- 

 tions, (see page 501, col. 1.) of which the following are 

 the most essential. 



Verification of the Verniers. 



Call the vernier which is connected with the clamp- Verifica- 

 screw No. 1, the others No. 2, No. 3, No. 4, in succes- tion . of tne 

 sion, according to the divisions of the circle. Place No. 1 . venuer ' % 

 at zero, read off all the others, and set down their devia- 

 tions with the sign -f- or , as they exceed or fall short 

 of their respective divisions, add these quantities, and di- 

 vide the sum by 4. This quotient may be called the 

 index error, and must be applied to the observed angle 

 with a contrary sign. For example, 



