CIRCLE. 



Roy in bit trigonometrical measurements ; the calcula- 

 ' ~~" ting of the exact time and distance of the pole star from 

 the meridian, when it is at it* greatest elongation east or 

 ; and by adjusting the instrument to it at that time, 

 ,j off the azimuth on its circle. A her thii, cor- 

 recting the distance of the star from the pole by the 

 iinc of the latitude of the station, you will have the 

 true azimuth of the itar ; the difference of which, from 

 the azimuth observed on your circle, will Rive you the 

 deviation of it from the true meridian. This doe* not 

 require the time to be known or attended to with very 

 great precision ; because the motion of the star in azimuth 

 is very slow indeed. And since it comes both to the 

 east and west of the meridian in the space of every twelve 

 hours, two opportunities of this kind offer every day. 



Another method, where you have the time sufficiently 

 correct, is, to calculate the meridian passage of the pole 

 star above or below the pole. This occurs nearly six 

 hours after the other { when, pointing the telescope of 

 the instrument to the star, and following it in its slow 

 motion, covered or bisected by the meridian wire, till 

 the exact instant it is to come on the meridian, then 

 clamping the instrument there, it will be found very 

 nearly in the meridian indeed. If all the adjustments of 

 your instrument are right, you will probably find it err 

 but a few tenths of a second of time in respect of stars 

 observed afterwards within the tropics. 



These are methods of finding a meridian which seem 

 belt to be recommended with such an instrument; which, 

 describing true verticals and horizontals, and giving the 

 angles of elevation in the one and azimuths in the other, 

 has all the requisites for such a purpose ; and is itself a 

 transit instrument encompassed by a circle, or a small 

 portable Irantil circle, ready for meridional observations 

 as soon as its true position is ascertained. 



For the verifying of this position, or bringing it strict- 

 ly to the truth, two methods may next be recommended : 

 the one by the meridian observation of any circumpolar 

 tar above and below the pole ; the other by the obser- 

 vation of two well-known stars over the meridian which 

 differ considerably from each other in elevation, and ob- 

 serving how far the times of their passage differ respec- 

 tively from the exact time of each by strict calculation." 

 We shall have occasion to consider these methods more 

 at length under TRANSIT INSMU MENT. 



CHAP. III. 



On the Iterating Circle. 



SeCT. I. Description of Troiighton's Repealing Circle. 



THE principle to which the repeating circle owes its 

 ^r<Ir. ~ existence, wag discovered by Professor Mayer of Got- 

 tiogcn. That learned and laborious astronomer, in the 

 year 1758, communicated his invention to the Royal So- 

 ciety of that city, in a memoir upon an instrument which 

 he calls a goniometer, the principles of which he had 

 mentioned to other astronomer* eight years before. The 

 goniometer was intended for observiug angular distances 

 between terrestrial object s in land surveying ; and, although 

 far from being well contrived for the purpose, it was ca- 

 pable of performing this much better than any instru- 

 ment known at that time. 



Dttcnp- It consisted of two bars of about a foot in length ; the 

 (MID of ( lower one wa* attached to a stand and socket like a com- 

 mon theodolite, and capable of being turned round, or 

 ct fast at pleasure. The upper bar wa connected by 



centre work to the lower, upon which it turned nil round, Circ'r. ^ 

 and carried along with it a telescope, with cross wires for > ""V"" 1 

 observation. The instrument had no divided limb, in- 

 stead of which, upon the end of each ruler, was made a 

 fine dot, and the angle by which the bam opened was 

 measured, by taking off the distance between the dots in 

 a pair of compasses, the angular value of which wan as- 

 certained on a line of chords of a proper radius, diagon- 

 ally d'-vidcd to the exactness of 2'. As the two bars were 

 required to be moved quite round upon each other, the 

 two dots could not lie precisely in the same plane, and 

 of course their exact coincidence could not be determined. 

 This error, therefore, as well HS that of the collimatioti 

 of the telescope, required some kind of artifice to remove. 

 This was neatly done, by throwing these errors back in- 

 to an angle on the outside of the real point of commence- 

 ment, as will appear in the following example of the use 

 of the instrument. 



Bisect with the wire of the telescope the object to the Method of 

 left, having the lower bar pointed a little more to that usiui- May- 

 hand, and made fast to the stand. Now carry forwards er '* g ni - 

 the telescope, by opening the angle between the bars, m 

 and bisect the object to the right. The opening between 

 the bars must now be taken in the compasses, and its va- 

 lue ascertained by the scale, which suppose to be 45. 

 With this distance unaltered, carry the instrument hack- 

 ward round the socket of the stand, until it again bisect 

 the object on the left, and again by opening the ban, 

 make the telescope bisect the object on the right. The 

 angular opening of the bars must now again be ascertain- 

 ed as before, which suppose to be 75". It is obvious, 

 that this last quantity is twice the distance of the object* 

 and the exterior angle, and that the former was the an- 

 gular distance and exterior angle ; therefore their differ- 

 ence 30 is the approximate angle between the objects, 

 and this angle taken from the fir.t measured quantity 

 leaves the exterior angle 15. This last quantity enable* 

 us to ascertain the point of commencement besides, and 

 we have proceeded two steps in the business of repetition. 

 The observations must now be continued, by turning the 

 instrument backwards round the socket to bisect the ob- 

 ject to the left, and the telescope alone must be carried 

 forward to bisect the object on the right, and so on al- 

 ternately until a great number of observations have been 

 made ; but care must be taken, that however often the 

 bars are carried round, the operations may finish, when 

 they are in a position that their angle may be measured 

 with the compasses. Suppose we leave off when the in- 

 strument has gone through nearly a revolution, and that 

 the opening of the bars in found to measure 44 5(X, this 

 quantity, as well as 15, the value of the exterior angle, 

 taken from 360, leaves for the whole amount of 10 re- 

 petitions 300 10', and this divided by the number givea 

 30 1' for the true angle. Some knowledge of the ap- 

 proximate angle is useful, to prevent the division being 

 made by a wrong number, in cases where the repetition 

 has been long continued. The intermediate sights, pro- 

 vided tin y are well taken, do not at all affect the result, 

 and no error of the instrument is charged upon the total 

 angle but those of the commencing and ending points; 

 and whatever the errors of these may be, by long conti- 

 nued observation they may be almost annihilated. With 

 this instrument, therefore, and indeed the same may be 

 said of all the repeaters, the patient perseverance of the 

 observer becomes tbc measure of the accuracy of results 

 obtained by them. 



Thus much we have thought proper to say respecting 

 the goniometer, which, although certainly not a circle, 

 belongs to the clan of repeaters, and was ^bc original 



