40 
similar loss occurs by the reflexion at the first surface of the 
objective, which, like the cover, is plane; and at all the others 
which are uncemented. To compute these last would re- 
quire a plan of the objective’s construction ; but as I only wish 
to give an approximate estimate of the effect of aperture, and 
as the incidences there, and consequently the reflexions are 
comparatively small, it is sufficient to consider the loss of 
light at the first surface and at the cover alone. Further, as 
the first lens is dense flint glass, and the cover of the ordinary 
sort, the loss by the two reflexions may be assumed as equal 
to that caused by the single one of the lens. Taking for the 
dense flint, « = 1°67, we can compute, by the help of a well- 
known formula of Fresnel, Z the intensity of light trans- 
mitted at the incidence @: the element of the hemisphere 
which transmits this light = 27. sin 0. d@; and therefore, the 
quantity of light transmitted by the first surface is— 
For an uncovered object, . . . . 2fZsin 6d6. 
Foracovered, . .. . . . - 2afJ*sinOd0. 
As yet, however, I have never seen an objective which, when 
compensated for uncovered objects, has a very large angle; 
and in some of them the difference is very great. No.4, when 
set to the mark “ uncovered” (which, I presume, was correctly 
placed by its maker), gave only 70°. From the short working 
distance which is inseparable from a large aperture, it is not 
a desirable mode of using them, as there is a great chance of 
the lens being sullied.* 
** The following Table gives a few values of these angles, 
omitting the factor 7. 
*« This reasoning assumes that the light transmitted through the cover 
is not less reflexible that it was before transmission. 
