* ON AN IMPROVED REFLECTING CIRCLE. 



Objection. It Is o^er index fhould touch it when the glafles were parallel ; 

 inconvement to ^ an adjuftment of this nature muft be fubjea to great er, 

 juftments for ror % a "d was never adopted in practice. The Chevalier dc 

 parallelifm. Borda, wifhing to remove that imperfection, had the happy 

 oflBordafoMe- ^ ca of rendering the parallelifm of the glafles unneceflary, by 

 moving it. fubftituting the obfervation of the angular diftance of the two 



objects, to that of the coincidence of the images of the fame 

 object. This conftitutes the fecond great improvement of the 

 reflecting circle, which it is neceflary for me to explain, before* 

 I proceed to the account of my own inveftigations *. 

 By a flight al- In Borda's circle, the telefcope is fixed at fome diftance 

 co^ftnlftion he ^ rom tne centre, and the horizon glafs is carried near the bor- 

 renders it prac- der of the inftrument, as in Plate I. Fig. 2. By this ar- 

 ticabletoob- rangement, the rays of light can arrive at the centre glafs, 

 angle twice, by both from the heavenly bodies utuated to the right of the ho. 

 moving the in- r j zon j n dex ; as S', and from thofe fituated to the left, as S. 

 dire&ions with- Thus, if the glafles are parallel to one another, when the 

 out Shifting the centre index is at o, it is obvious that there are two ways of 

 ftrument . making the obfervation*. While the direct image of the moon 



L is fecn through the telefcope, the angular diftance to the 

 fun, if at S, may be meafured by moving the centre index to 

 m, in order to produce the contact ; or, if the fun is at S', the 

 lame operation may be performed, by ufing the contrary mo» 

 tion to in'. The firft kind of obfervation, the Chevalier do 

 Borda calls obfervation to the left ; and the fecond, obfervation 

 to the right. Suppofe now, that (the horizon index being fixed 

 in tlm fame pofition) the diftance from L to S is obferved to 

 the left, by bringing into contact the doubly reflected image of 

 S with the image oH L, feen without reflection ; let us then 

 turn the inftrument round, keeping it in the fame plane, fo as 

 to have the direct image of S through the telefcope, and thus 

 vhieh gives the make an obfervation of the fame diftance to the right ; the po- 

 doubie diftance, ft tion of the centre index being in the nrft obfervation at m, 

 any adjuftment an 'l m lnc fecond obfervation at m, it is clear, that if o is the 

 for parallelifm. point where the parallelifm of the glafles takes place, o?nh 

 equal to o vi ; and, that the arch m m', determined by the two 

 pofitions, will give double the diftance. 



* It does not belong to my prefent plan, to explain the effect of 

 Borda's improvement in correcting the errors which arife from the 

 want of parallelifm in the furfaces of the glafles. This will be 

 fully confidered in another Paper, where I intend to give an ac- 

 count of feveral inveftigations which I have made upon that parti- 

 cular fubjecl. 



It 



