'02 



C I R C L K. 



re H A, mir b computed by iph'rical trigonome- 

 try. '!'< problt-m is very nearly, indeed, similar to the 

 well-known case in i..-.mval astronomy, in which it is 

 rrqmn-d to determine the true distance of a star from 

 the moon, baring given its apparent distance, and thi al- 

 titude of each by observation ; and for each process. Ta- 

 ble have born devised to facilitate the calculation, which, 

 without such aid, would be very tedious and laborious. 

 The zenith distance of a terrestrial object being ditrr- 

 minid with this inttiument, precisely in the same man- 

 ner as the zenith distance of a otar or other celestial ho- 

 dy, nothing here need be said on that part of the pro- 

 cess. We shall, however, subjoin an example actually ta- 

 ken by an instrument of Mr Troughton's construction, 

 to shew with what extreme accuracy a result may be ob- 

 tained by an experienced observer. 



Zenith dittanen of a fixed marl, taken Sept. 4, 1812, 

 ifith a repeating circle of^Ir Troughton' s construction. 



wt 7" 2 



-- 8".7 



24 



/ , 



Mean of the twelve angles given by each! 

 successive pair of observations J " 



In making the above observations the light was favour- 

 able. being steady and uniform ; the sun was always hid. 



Thi- mark exceeded the wire some seconds on each 

 aide, and was not so round as could have been wished. 

 A mark smaller and perfectly round might probably have 

 been bisected more exactly. 



In the 24th observation the day light began to fade, 

 and it was apprehended that this observation was rather 

 less exact than the preceding ones. 



There i every reason to suppose, that in the above 

 experiment the zenith distance of the signal was ob- 

 tainrd within a small fraction of a second. 



To observe the angle between two signals, the plane 

 of the instrument must first be brought into the plane 

 of the two objects. To accomplish this, first set the tri- 

 pod of the instrument, with one of its feet as near as you 

 can fruess, in a line with that object, which of the two 

 you judge to be nearest to the horizon ; and, with the 

 plane of the circle vertical, and the lower telescope hori- 

 zontal, (both to the exactness of two or three minutes,) 



bring the telescope to the object, partly by turning in 

 azimuth, and partly by screwing the foot screw ; 

 turn tli'-- circle round upon the cross axis of the 

 until it srcms by the eye to occupy the proper position, 

 then a second time faring the telescope to the object, by 

 the fo.jt screw and turning in azimuth ; lastly, complete 

 th- operation by bringing the tij.per telescope to the 

 othtr object, by its own proper motion, in conjunc- 

 tion with that of turning round the CTO-.S a.\i>. The, 

 principle of the above rule u this ; the cross axis of the 

 stand and the lower telescope being made parallel, and 

 pointed to the ob|<ct, the circle may be turned round 

 that axis without changing the n i^ular position ot the 

 telescope. When thij verification is rightly performed, 

 the intersection of the wires of tXe micrometer of the 

 moveable telescope should pus over each object in its re- 

 volution round its centre. To effect this readily re- 

 quires some little dexterity and practice. 



The following example was likewise taken by an in- 

 strument made by Mr Troughton. 



Circle, 



The angle thus measured requires to be corrected for 

 the eccentricity of the lower telescope; and this correc- 

 tion depends on the distance of the objects from the 

 observer, and upon the distance of the axis of vision of 

 the lower telescope from the centre of the instrument. 



In circles tonftructed by Mr Troughton, the eccen- 

 tricity of the lower telescope is one inch and four tenths; 

 and the following Table is calculated upon this supposi- 

 tion from Delambre's formula given in L'ArcduMcridicH. 

 Fathoms. 



