10 0>T AN IMPROVED REFLECTING CIRCLE. 



Leave this clamp fattened, and loofen the clamp A ; thus turn 

 the inftrument, and make a crofTed obfervation to the left, 

 adjuring by means of the fcrew H, after having fattened the 

 clamp D. At the end of this obfervation, the flying nonius 

 will give the diftance. Fatten now the clamp A, and loofen 

 the clamps B and C, leaving the clamp D fattened ; then turn 

 the inftrument again, and make a crofTed obfervation to the 

 right. At the end of this obfervation, the flying nonius will 

 give double the diftance. By fuccettively inverting the ufe of 

 N the clamps, this alternate procefs may be continued ad libitum ; 

 and each crofTed obfervation will increafe the reading, by an 

 arch equal to the diftance. 

 !Umarlci# Let the number of obfervations be v, and the angular dif- 



tance D. The arch given by my improved circle will be 

 £= D (n — 1). In Borda's circle, (reducing the divifions of 

 the fextant to thofe of the theodolite I ufe,) the arch is p£ D 

 X *J if ; and, either n muft be an even number, or the odd 

 obfervation muft be loft. In Mayer's circle, the arch is 52 \ 

 D x f n ; and the number ft, which comprehends the obfer- 

 • vations for the parallelifm of the glaffes and thofe for the dif- 

 tance, muft likevvife be even. The comparifon of thefe ex- 

 preffions, thews at once the relative advantages of the dif- 

 ferent inftruments. 



My con ft ruction offers confiderable advantages, in every 

 manner of ufing the circle. If, inftead of the crofTed obfer- 

 vations, it fhould be wanted to employ the ufual practice of 

 rendering the glaffes parallel, a multiple of the diftance mav 

 ftill be obtained by my inftrument, equal to that of the other 

 method. For this purpofe, the parallelifm of the glaffes may 

 be effected, by means Of the images of the fun, or the horizon 

 of the fea, moving the index F, while the o of the nonius is 

 adapted to 360° of the limb, and the two clamps A, B, are 

 fattened. After this, an obfervation of the diftance to the 

 right may be made, with the clamp A fattened, while the 

 clamp B is loofe ; the clamp D being alfo . fattened, and the 

 clamp C loofe ; and, at the end of this obfervation,. the flying 

 nonius will give an angle, which will be only the half of the 

 diftance in my divifions, but which would be equal to the 

 whole diftance, if the divifions were according to the fextant. 

 After that, and while the clamps B and C are faftened, and 

 the clamps A and D loofe, the parallelifm of the glaffes may 



be 



