1 6 An Account of the Repeating Circle^ 



common to many instruments, even to enumerate them in a 

 paper like this, could hardly answer any usefid purpose. 



Manner of using the Repeating Circle, 



In geodetical observations this instrument gives the angular 

 distance between two observed objects, whatever be their ele- 

 vation above, or their depression below the horizon. The 

 horizontal angle is always the thing wanted ; to obtain which, 

 it is necessary to find by observation how the objects are si- 

 tuated respecting the horizon ; these give the requisite data for 

 ti'igonometrical computation. Previous however to this, the 

 observed angle itself has to be corrected for the eccentricity of 

 the telescopes ; which correction varies according to the qvian- 

 tity of eccentricity, and the measured, or estimated, distance 

 of the observed objects. To place the plane of the repeating 

 circle parallel to the line that joins two objects, the angular 

 distance of which was to be observed, had been no easy task, 

 until about thirty years ago from my little gazebo I attempted 

 to take the angular distance of two spires. Their distance was 

 by no means my object ; it was simply to acquire the habit of 

 observing by repetition, and putting to trial an instrument that 

 I thought well of. After having made three attempts, without 

 effect, to obtain the thing wanted, and a fourth placing me stUl 

 furtlier from the point, I quitted my mstrument, disgusted at 

 my own unskilfulness, and retired to consider whether the in- 

 strument had not within itself some principle from which a pre- 

 cise rule might be made out. This inquiry proved successful, 

 for I saw that by pointing one foot of the tripod, the cross axis 

 and the back telescope towards one of the objects, the fore te- 

 lescope by turning round the cross axis and by its own proper 

 motion might be brought to the other object without altering 

 the angular direction of the back telescope. The rule is this. 

 Set one foot of the tripod as nearly as you can guess in a line 

 with that object of the two, which you judge to have the least 

 elevation or depression ; and with the plane of the circle ver- 

 tical, and the back telescope horizontal (both to the exactness 

 of two or three minutes), bring the back telescope to the ob- 

 ject, partly by turning in azimuth, and partly by turning or 

 propping the foot-screw. Next turn the circle round on the 

 cross axis, until it seems to the eye to occupy the proper posi- 

 tion ; then a second time bring the back telescope to the object 

 by tlie foot-screw, and turning in azimuth ; lastly, complete the 

 operation by bringing the u])per telescope to the other object 

 by its own proper motion in conjunction with that of turning 

 round t.he cross axis. The above operation being performed, 

 (which it is necessary to repeat at every angle that is taken, even 



at 



