CIRCLE. 



*)+!* 



-f. 3" Index error to be sub- 



tncted from the observed angle : then suppose at the 

 end of an observation that the verniers stand thus : 



No. 1. ... 183 9 14 10" 



8. ... 7 



3. ... 14 



4. ... SO 



4) 51 



183 14 12.77 

 Deduct the Index error 3 



True angle 183 14 9.77 



As the level and the front telescope turn round one 

 common axis, independent of each other, it should be re- 

 membered, that the circle must always be fixed to, and 

 form one piece with one of the other two. In the front 

 observation which begins the series, it must be considered 

 as forming one piece with the front telescope, and care 

 mult be taken on no account to touch the screw that alters 

 their relative position to each other. On the contrary, 

 in the reverse observation, the circle must be considered 

 as forming one piece with the level, and equal care taken 

 not to separate them from their fixed position. The 

 great danger to an unexperienced observer with this in- 

 strument is, that his whole series of observations may be 

 destroyed by improperly releasing the piece which ought 

 to remain fixed. 



But a little consideration and practice will render this 

 operation easy and familiar. 



A well regulated clock or watch is necessary for these 

 observations ; and they will be rendered much easier, if 

 an assistant attends to the level, while the observer bisects 

 the star. 



It may not be improper to remark, that it is of more 

 importance to make good observations, than to make a great 

 number. The errors of division are so small in our best con- 

 structed instruments, that a very few repetitions will render 

 their effect quite insensible. The observer will soon find 

 that it is the error of observation he has to contend with, 

 arising from the imallness of the radius, and want of power 

 in the telescope ; for this reason, the observations should 

 not be hurried, but sufficient time allowed for examining 

 the true position of the level and the accurate bisection 

 of the star. 



The corrections to be applied to the observations made 

 with the repeating circle are, for the purpose of reducing 

 the meridian altitude, from that observed a short time be- 

 fore or after the passage of the star over the meridian. The 

 hour angle, or distance of the star from the meridian, must, 

 therefore, be correctly known ; and in proportion as the 

 rmte of the clock is well ascertained, may the observa- 

 tions be extended with confidence on each side of the me- 

 ridian. 



The polc-itar, from the slowness of its motion, being 

 the belt adapted for observation with this instrument, we 

 Lave given a table of corrections for that particular star, 

 extending to half an hour from the meridian, beyond 



which the observations should never extend. This table Circl*. 

 having been calculated for the latitude of Paris some years < ""V" 

 since, the numbers must now fur the latitude of Green- 

 wich be diminished ^th, that is, the whole correction 

 multiplied by 0.95 ; and for the inferior passage of the 

 star the whole correction must be multiplied by 0.88. 



Tables II. and III. are general tables for any star, and 

 for any latitude ; they were calculated by Delambre from 

 the following formula : 



Make P = The hour angle. 

 L = Latitude. 

 D = Declination of the star. 

 j- Corrections required. 



If the star pass southward of the zenith x = 



1 sin. ^ P, cos. D, cos. L /2sin.^ P, cos. D.cos. L\' 

 sin. (L D) sin. 1" 'H sin. J D sin. 1" / 



cot. L D sin. 1". 



If the declination be south, change the sign of D. 



If the star passes to the north of the zenith, for L D 

 substitute D L, and change the sign of the terms. 



But if the star passes below the pole, D -f- L must be 

 substituted for D L, the signs remaining the same. 



The numbers contained in these tables arc the factors 



2 "'"'*** and 28 ' n>4 * P , the remainder of the calcula- 

 sm. 1" sin. 1" 



tion is thus reduced to finding the value of the other fac- 

 tors. 



cos. D, cos. L\_., 

 - 



(cos. D, cos. I 

 sin.D L 



and 



(cos. D, cos. LA 1 _. T r 

 re J cot.D L=/. 

 sin. D L / 



Example of an Observation of the Pole Star, by the Re- 

 peating Circle, 'Dec. 4/A 1807. 



Sum 58.9 



147 5' 50" 



294 11 00 

 70 43 58 



81 16 54= 1st Vernier 00 



50='2d 

 58=3d . 

 60=4th . 



58.p= Sum of the corrections. 

 2.9= 



12)56".0 cor. diminished T ffth, 



4.7 divided by the number of observations. 



