' [ 89 1 



from the poiutCis equal to twlceHCh the obliquity of the fpcculuiXi*^ 

 «r becaufe the angle made by two lines or planes is equal to that 



made 



* When the object S is (o diftant that the ang. C S i is evanefcent, the ray S i 

 will fall on the mirror in the fame direction as S C, that is, in S :' parallel to S C : 

 when the ray fell at C on the diameter H N, the angle of incidence was S C ^4, but 

 in the change of the reflefting plane H C to h C, that ang. receives an increment 

 H C h equal to B C b, and the ang. of refledlion mud receive the fame ; fo that the 

 angular velocity of the reflefted ray is double that of the fpeculum ; and hence if 

 the ang. E Cf be made equal to twice B Ch, Cf will be the refledted ray, and if 

 the eye were at f, it would fee the image at C, but the eye remaining at E will fee 

 it at ;', in a direftion parallel to f C, and at an angular diftance C Ei equal to E Cf, 

 from the point C ; becaufe there the angles of incidence and refleftion s i a, E i a are 

 equal, being the fame as S C J, f C d. But if the objeft S be fo near that the 

 angle C S« or j- » S is of a fenCble magnitude, then the incidence Sia is lefs than 

 it was before, by the quantity of this angle, and the angle of refleftion E i a mud 

 be equally diminifhed, or both receive equal and contrary alteration, which will be 

 when the image is formed at that point k, between i and C, where the angles of in- 

 cidence and refledlion S k m, Ekm will receive, the former fuch an increment k S i, 

 and the latter fuch a decrement L El, as will reftore their equality. Hence it appears 

 that if the diftance of the eye remains unvaried, and alfo the elevation of the objeft 

 H C S at the point C, the nearer the object S approaches this point, the nearer will 

 the image approach to it ; becaufe as the objeQ accedes; the ang. C S i enlarges, and 

 confequently C E i muft diminifh. 



But the various motions and pofitions of the image caufed by the obliquity of the 

 mirror to the horizon, cannot be clearly underftood but by inveftigating its path or 

 place during a revolution of the mirror round the plumb-line. Let the line of diredt 

 vifion £ S be drawn, i C be produced to d, and from the interfe£tion A oi SE and B C 

 produce^, let A I he drawn parallel to it, and from i let i a be drawn alfo parallel 'till 

 it meets the axis B C produced, in the point a ; Cnce J C js perpendicular to the mirror, 

 fo alfo will be I A, ia (El. 1 1. 7.) ; and if the mirror be fuppofcd to revolve round 



Vol. VIII. M the 



