15G MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



^ K70Q ft _|_ ^ |_ ^ 



l.(i070 = a + ^l^^^, + (0.39679)' 

 from wliicli by ('liiiiiiiation 



« = 1.5593 6 = 0.006775 c= 0.0001137 



so that for this prism, the formula becomes, 



, .^Ko, , 0.006775 , 0.0001137 

 « = 1.1 5593 + -- ^^ + - ^^ 



which we find on trial satisfies the observations in the visible part of the spectrum within very 

 narrow limits. When, however, we attemjit to extend the application of the formula to the infra- 

 refl region, its results are not so satisfactory. Since h and c are both positive, the least value 

 which n can have in our ])rism, according to the formula, is r/, or 1.5593. corresponding to a devia- 

 tion of 45° 35', whereas the l)olonietric measurements show that in this prism the solar spectrum 

 after absorption extends as low as 44°, with every sign that if it do not extend yet further, it is 

 not on account of the i)risni, but because below this point the heat is absorbed by some ingredient 

 of our atmosphere. 



We conclude, then, that Cauchy's formula gives grossly erroneous results when extended far 

 behind the limits within which the observations on which it is founded are made. Its implicit 

 assertion, that the lower limit of the prismatic spectrum (however groat the wave-length of the ray 

 transmitted) is not so far below A as A is below D, is absolutely contradicted by these experi- 

 ments, and all extrapolations made by it, far from the visible spectrum in which its constants have 

 been determined, are wholly untrustworthy, as will appear more fully later. 



Redtenbacher proposes the formula 



'TV' V' 



for expressing the same relation. Using the same lines as before for determining the unknown 



constants, we have for the Hilger prism 



1 00,39220 



., =0.412297-0.00093711^.2— ^^^^J- 



a formula which also satisfies the observations in the visible si)ectruin, but fails when extended to 

 the invisible. The curve representing it has a minimum point corresponding to h = 1.5647 for a 

 value of A found from the equation A^= ,or in the special case of the formula above, where is 



positive, A = 1.430; so that for every value of n greater than 1.5647, there are two real values of A. 

 This formula therefore is even less satisfactory than that of Cauchv. 



Briot gives a formula which has been asserted by other investigators* to represent satisfac- 

 torily the results of observation throughout the whole spectrum, namely: 



i-+<9+'C9+K:;;) 



From four equations like this, using values of n and A corresponding (o the Fraunhofer 

 lines A, C, F, and H, the values of the constants were determined t as follows: 



a=0.41028 6=— 0.0013495 c=— 0.000003379 A- = +0.0022329 



*MouTON, Comptes Rendus, vol. Ixxxix, p. 291, and vol. Ixxxiii, p. 1190. 



\ This formula has the practical inconvenience of leading to cubic oi|uations, eitlici- in «- or PI-, the solution of 

 which is so tedious as to forbid its use where many places arc to be iiiilepeudently found. 1 have been aided in the 

 present lengthy numerical computations by Professor M. B. Gofp. 



