9 on an Improved reflecting circle. 



The author's In the crofted obfervations made with Borda's circle, the 



confiib^n ap- inc * cxes m °ve alternately through an arch which in the divi- 

 plying an entire fions, is equal to double the diftance : for example, the centre 

 «Z?*efahg' index coracs ' in thc fltft crofled obfervation, from mto m' ; in 

 nonius, within or the third crollcd obfervation, from wl to m", &c. and the ho- 



*l^ he EKh C of riZOn inde *' m the fecond crofred obfervation, to li : in the 

 thefc circles fourth crofled obfervation, to /«", &c. and, by each of the two 

 may be attached indexes may be found the fame multiple of the diftance re- 

 center index or q^ed. Let us now place the Nonius in a circle moving 

 horizon index round the centre, over, or adjacent to, the ufual limb which 

 of acJamp. UrC contams tne divifions : it will eafily be conceived, that, by 

 attaching that circle, which I (hall call the Flying Nonius, al- 

 ternately to each of the indexes, it will ferve as Nonius for 

 both ; and that, after any number of obfervations, it will give 

 the compound motion of the two indexes. Thus, after the 

 firft obfervation, the Flying Nonius will, at each crofled ob- 

 fervation, advance double the diftance over the divifions, 

 while each feparate Nonius, fixed on the indexes, requires a 

 fet of two obfervations, to produce the fame effect in Borda's 

 circle. 

 View and de- Plate I. (XXX. XXXI. and XXXII.) exhibits a perfpe&ive 



fcriptionof the view j> , and a fea j j of th in ft mment which f or the 



unproved re- ' v r ' " ' ' 



-feeling circle, fake of diftinction, I fhall call my Improved Reflecting Circle. 

 (The laft Plate is particularly intended to (hew the compound 

 handle, which I have adapted to the inftrument, in order to 

 hold it with convenience and eafe in every pofition *). Thefe 



three 



* The ufe of Mayer's circle, or ofBorda's, as conftru&ed till 

 r»ow, with only one handle attached to the centre, is extremely in- 

 convenient in feveral pofitions, and particularly when it muft be 

 kept inverted downwards during the obfervation. For this reafon, I 

 thought it of importance to contrive fuch a fupport as would enable 

 the obferver to hold the inftrument with the fame eafe in every di- 

 rection. This is effe&ed by means of the compound handle, at- 

 tached to the horizon index, by the brace V and fcrew X, (Plates 

 XXX. XXXI. and XXXII.) which index turns round the centre 

 with the handle. When Mr. Troughton began to conftruct this 

 fort of inftrument, I recommended to him this improvement, which 

 Jie has adapted to his reflecting circle. 



I fhall obferve here, that Mr. Troughton's circles are not of the 

 kind which I have endeavoured to improve. The fcheme of his 

 conftruftiqn may be faid to ccnfift in completing the limb of a fex- 



tant 



