40 Mr. E. C. Pickering on the Comparative Efficiency 



The dispersion then increases much more rapidly than the 

 deviation ; hence in spectroscopes whose deviation is the same, 

 that one will disperse most, in which i and therefore a is the 

 greatest. 



The above discussion applies strictly only to the emergent 

 ray; but in the position of minimum deviation, the dispersion of 

 a prism is just double this, as may be seen from the general for- 

 mula for dispersion (Radicke's 'Optics/ vol. i. p. 179). I pro- 

 pose hereafter to discuss the question whether greater dispersion 

 with the same loss of light could not be obtained by some other 

 position of the prism. 



2. Reflection. — In estimating the loss by reflection, it is usual 

 to assume that the same proportion of the incident light is lost 

 at each successive refraction. But in reality the light so refracted 

 is partially polarized, and in this state another law determines 

 the amount reflected. Fresnel showed that of a ray polarized 

 in the plane of incidence, the proportion reflected 



jy__ tan g (t-r) 3 

 tan 2 (i+r) 



while a ray polarized in a plane perpendicular to the first, would 

 lose by reflection 



A': 



sin 2 (i -f r) 



Regarding common light as composed of two beams of equal 

 intensity polarized at right angles, the amount reflected would 

 be P/ + IB', and that transmitted J [(1-A') ■+ (1-B')]. On 

 meeting a second surface inclined at the same angle of incidence, 

 the amount transmitted would be J[(l — A') 2 + (1— B f ) 2 ], and 

 after passing m surfaces -J [(1 — A') 7 "-}- (1— B')™]. 



This formula can be applied directly to the m surfaces of the 

 prisms of a spectroscope, since in the position of minimum de- 

 viation i 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 Jam in 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 



