ON AN IMPROVED REFLECTING CIRCLE. ■ 



It will be more convenient to have the centre index ato, CdnVentait nsi- 

 "when the fir ft obfervation is made, in order to take the double n, P ulat *>". 

 diftance at one reading, after the fecond obfervation. For 

 ■this purpofe, the rirft part of the procefs may be inverted, by 

 previoufly fixing the centre index at the beginning of the di- 

 vifions, and moving the horizon index H towards o, inftead of 

 moving the centre index A to m, or towards H. 



The Iaft kind of obfervation, in which the incident ray, This Is demfttff- 

 •which produces the firft image upon the centre glafs, may be " a !: ed the tri Wf 

 conceived to run double the angular diftance, pafiing in its 

 \vay over the line of collimation, has been called, by the 

 Chevalier de Borda, the crojfed obfervation. 



The fame procefs may be repeated, by fixing alternately II ma y be re- 

 one of the indexes, and moving the other, and continuing j^ at p 

 fucceftive fets of obfervations ; each fet of two crofted ohfer- 

 vatiom, one to the right and another to the left. The angle 

 given by the inftrument, will be equal to double the angular 

 diftance multiplied by the number of fets obferved, or, in other 

 terms, to the angular diftance multiplied by the number of 

 obfervations, which are always fuppofed to be made by pair- ; 

 an odd obfervation being of no value in this manner of ufing ■ 

 the circle. 



I have expreffed myfelfas if the obfervations cou4d always And will no?r». 



be made by looking alternated at each object through tne q " ire adi y e< ^ 



r ° m J J 2 view °* t ' ie 



telefcope, in order to bring into contact' the doubly reflected brighter objeft, 



image of the other object. This is not the cafe in the obfer- *f th . e P lane of 



l- n i ■*« p i ^ r r> .the inftrument 



vations ot the diltances from the moon to the lun, or a ftar ; it be reveifed at 

 being then indifpenfable to compare, by reflection, the bright- the fe . cond ob * 

 eft of the two heavenly bodies; but there is a very eafy me- 

 thod of obviating that inconvenience. After the contact of the 

 images of S and L is obferved, with the telefcope directed to 

 JL, the pofttion of the plane of the inftrument may be inverted, 

 iurning it round the axis of vifton OBL; the incident ray 

 will then anfwer to the point S', equally diftant from L as- S, 

 and the crofted obfervations will flill give SS', or double the 

 diftance. 



Whether a circle is ufed fimply, as Mayer propofed it, or 

 according to Borda's method, its peculiar advantages chiefly 

 depend on the multiplication of the diftance required. I have 

 therefore turned my attention to the improvement of this prin- 

 ciple ; and, with that view, I have contrived the conftruclion 

 which I am going to defcribe. 



In 



