g h would fall on the glass b, and be again reflected to the 

 eye at e.* 



But if the rays forming the ijnage are reflected from the 

 middle part only of the mirrors, the image of m orn could 

 not be seen to coincide with C by the eye at e ; for if the 

 incident ray were different from c «, as suppose m a, the re- 



* Int)rder to understand the theory of the reflection of the rays forming the image 

 seen in the back horizon glass, the following circumstances are to be considered : 



1st, Because the speculum b is parallel to B, whatever inclination B has, which di" 

 verts the image of the object C from the point c to m, the same inclination 6 also has, 

 tending to divert the image of c to o, let the reflected rays g b or ad fall where they 

 will on the speculum, or with whatever inclination. 



2d, If the mirrors were at right angles, the rays m a, m g would be reflected from 

 the mirror b, in a direction parallel to themselves, i. e. the ray m a falling on the point 

 d ill the mirror ft, would be reflected in d o parallel to m a; and the ray m g falling on 

 h, in the mirror b, would be reflected in h i parallel to m g : but when the mirrors are 

 inclined to each 6ther, the rays d o , and h i will decline from such parallelism in an 

 angle equal to c am double the inclination of the mirrors. 



3d, When the angle cam exceeds the angle a m g subtended by half the length of 

 the mirror a, by a difference equal to, or exceeding the angle, subtended by half the 

 length of the horizon glass at the middle of the index glass ; all the rays reflected from 

 the latter will fall without the horizon glass, and not be reflected by it ; but when the 

 angle c a m is less than this, some of the rays incident on the index mirror a, will fall 

 from it on the mirror b, and be again reflected : and since the object c or m is so near 

 that there is a considerable diffierence in the incidences of the rays diverging from it on 

 the mirror a, from the point a to g, (the greatest difi'ereuce equal to a »i g), and the 

 same in the reflections from the mirror 6, the image of the object c placed at m, may be 

 seen in different places by some of the rays diverging from this mirror. 



4th, The diffierence of the incidences of the jays m a and mg is that of their reflec- 

 tions in a d and g h ; and the difference of the incidei»ces of a d and g h will be that of 

 their reflections from the mirror b ; and the angular motion of the speculum b will be 

 half of either these or those, in order to its reflecting one of these rays in the same di- 

 rection in which the other liad been reflected. 



