£. C. Pickering on different forms of the Spectroscope. 308 
dence, the amount transmitted would be 3[(1—A’)?+(1— B'}*] 
and after passing m surfaces 3[((1—A’")+(1—B’)”). 
This formula can be applied directly to the m surfaces of the 
risms of a spectroscope, since in the position of minimum 
deviation 7 and r are the same for all, and therefore the amount 
transmitted is the same, whether the passage is from glass to 
air, or from air to glass, 
The formulas of Fresnel are used in preference to those of 
Cauchy, although the latter have been proved, by Jamin and 
others, to be more correct. But the coefficient of ellipticity 
which they involve is neither so commonly, nor so easily found 
as the index of refraction. Furthermore, for glass the difference 
would probably be so small that it could be neglected. 
3. Absorption—The average length of glass traversed by 
the light is one half the base AB, multiplied by N the number 
of prisms, and the amount escaping absorption is proportional 
to the log. of this distance, or to log Nx BC sin3e, or in prisms 
admitting the same amount of light (that is in which BD is the 
ipo 
same) to log BDxN = =, since BU= i but the dispersion 
is proportional to N a 
equally and composed of prisms of the same material, the Joss 
y absorption will be the same in all, so that as far as the ab- 
sorption is concerned, it makes no difference whether a spectro- 
Scope is composed of a large number of very acute angled prisms, 
or of a less number in which the angle is more obtuse. 
hus we avoid a difficulty which seemed at first sight insur- 
mountable, since the actual amount of light absorbed varies not 
only with the material, but with the refrangibility of the rays, 
and according to laws not yet discovered. : : 
The following tables give the deviation, dispersion, and 
amount of light escaping reflection, of spectroscopes compo 
of from one to ten prisms of indices of refraction 1°5, 1-6 and 1°7. 
ey TABLE I.—45° Prisms. 
) hence in spectroscopes dispersing 
surface.| 1 prism. | 2 p. 3p. 4p. 5D. 10 p. 
20” 4° 150° 8/76? 12'/100° 16’}125° 20’ 250° 407 
"30° 307619 0’| 91° 307/122° 07|152° 307305 07 
36° 10” 72° 20’/108° 30’|144° 40’|180° 50/3614 40’ 
1870 | 2304 | 3.739 | 4-674 
1-936 | 2-904 | 3 ; 
2-016 | 3-023 | 4-031 | 5-039 
"ta | -424 | 66 
m99 | -719 | -651 | “692 | 
53 | “578 | “51 
