[ 9° ] 



made by two perpendiculars to the fame, if Ch be perpendicular 

 to h C, it will be equal to twice B C b ; fo that when this angle is 



nothing, 



the line B A, carrying with it with its own angular motion the lines h d, 1 A and ia, 

 thefe will continue parallel and perpendicular as revolving together in the fame plane 

 with the line h C, which has no motion with refpeft to the mirror ; but the line A I, as 

 interfefting the line of fight £ S, and perpendicular to the mirror, is always in the plane 

 of refle£lion, therefore fo alfo will the other lines parallel to it, and the image will al- 

 ways be feen in fome part of the lints A I, at; but thefe lines have a conical motion 

 round the common axis B C a, and therefore the image will partake of that motion 

 laterally as well as direftly, during the revolution of the mirror from the plane (re- 

 prefented in the fig. by the plane of the paper) in which the diameter h Cm that moft 

 inclined to the axis of motion A B; and the extent of the lateral motion will be 

 limited within the angle C A I hy the line A I and not by any other line a i, becaufe 

 the former terminates both in the axis of motion and alfo in the line of dire£l vifion 

 E 5, and has the fame angular motion about this line, which the plane of refleftion 

 has during the revolution of the mirror ; fo that when the mirror or the diameter An 

 has made 5 of a revolution from its fituation in the fixed plane E S HC, the image 

 will have defcended from the place / to the the diameter h n, palling through the axis 

 A B, and now at right angles to its former pofition ; and will alfo have receded la- 

 terally from that axis to the diftance C I, for it will always be feen in the diameter h n 

 (which is moft inclined to the axis and wherein the line A I refts) during its revo- 

 lution ; and its diftance, as medfured on the furface of the mirror, from the plane 

 E C H S, will be the fine of the angle made by the radius C 7 in its revolution ; and its 

 diftance, the fame way meafured, from a plane paffing through C and at right angles 

 to the former, will be the cofine of the fame angle and defcribed by the radius C i : and 

 from this it appears that the path which the image traverfes on the furface of the mirror 

 by the compofition of fuch direft and lateral motions during a revolution is an ellipfe, 

 whofe vertex is at i, its centre a point in the axis C A, its greateft femiaxis the per- 

 pendicular diftance between; and AC, and its conjugate femiaxis the perpendicular 

 diftance between / and AC, and that the apparent path or locus of the image is the 

 fame ellipfe feen obliquely by the eye at E, whofe greateft femiaxi* is equal to the 



fine 



