Before we proceed to investigate the effects produced by a variation in the length of the reflecting planes, it will be necessary to consider the variation of the intensity of the light in different parts of the reflected sectors. In the direct sector =A O B=, Fig. 2, the intensity of the light is uniform in every part of its surface; but this is far from being the case in the images formed by reflexion. In Fig. 17, take any two points _m_, _o_, and draw the lines _m n_, _o p_, perpendicular to =A O=, and meeting =β O= in _n_ and _p_. Let =O E=, Fig. 18, be a section of the reflector =A O= seen edgewise, and let =O _p_=, =O _n_=, be taken equal to the lines _m n_, _o p_, or the height of the points _n_, _p_, above the plane of the reflector =A O=. Make =O R= to =R E= as =O _p_= is to =E _e_= the constant height of the eye above the reflecting plane, and =O _r_= to =_r_ E= as =O _n_= to =E _e_=, and the points =R, _r_=, will be the points of incidence of the rays issuing from _p_ and _n_; for in this case =O R _p_ = E R _e_=, and =O _r n_ = E _r e_=. Hence it is obvious, that =E R _e_= is less than =E _r e_=, and that the rays issuing from _p_, by falling more obliquely upon the reflecting surface, will be more copiously reflected. It follows, therefore, that the intensity of the light in the reflected sector =A O β= is not uniform, the lines of equal brightness, or the _isophotal_ lines, as they may be called, being parallel to the reflecting surface =A O=, and in every sector parallel to the radius, between the given sector and the reflecting surface by which the sector is formed. As it is easy from the preceding construction to determine the angles at which the light from any points _m_, _n_, is reflected, when the length =O E= of the reflectors, and the position of the eye at =E= is given, we may calculate the intensity of the light in any point of the circular field by means of the following table, which shows the number of rays reflected at various angles of incidence, the number of incident rays being supposed to be 1000. Part of this table was computed by Bouguer for plate glass not quicksilvered, by means of a formula deduced from his experiments. By the aid of the same formula I have extended the table considerably. _Table showing the quantity of light reflected at various angles of incidence from plate glass._