9 . 



directly through the middle, so as to prevent the separation 

 of the images ; because when the rays which form both 

 imafes, cross one another, and proceed in different direc- 

 tions, though they should even cross in the same point in the 

 mirror, yet they will penetrate the eye diverging, and form 

 different images on the retina. But if the image may be 

 seen by reflection from any part of the index-glass a, the 

 angle of incidence of a ray m g, (of the near object c re- 

 moved to m,) falling on that glass at a point g distant from 

 its middle point a, will be less than that of a ray incident on 

 the point a, by the angle a m g: (for if the line a g were 

 produced, the external angle at g would be equal to the 

 angle at a and also to a m g together ; and therefore as much 

 as the external angle at g is encreased above that at a, as 

 falling toward a perpendicular from m to the line ag (El. 1. 32. 

 cor.) the internal one, or the angle made with the mirror, is 

 diminished ;) but if the incidences on a and g were equal, the 

 reflections would be so too ; i. e. both m a and m g, and 

 also ad and gh would be parallel ; which is the case when the 

 object is very remote, the angle a m g then vanishing. Also 

 since by reflection from any number of plane mirrors, the 

 direction of the rays is changed, but not their inclination to 

 each other, the ang. am g made by the rays incident on the 

 index-glass, will be likewise the measure of their divergence 

 reflected from the horizon glass. * If therefore the glasses 



* The angle b a d h equal to c a m, and the angle made by e J and o d is equal 

 to either ; and au angular motion of the speculum 6 equal to half of any of these 



VOL. XII. C 



