Wave-lengths in the Invisible Prismatic Spectrum. 205 



the visible spectrum, whence their constants have been in fact 

 derived. This desirable test we are now prepared to apply. 



The simplest as well as the most widely used formula is that 

 of Cauchy, which, as it is commonly written 



( H=aa+ J» + &)' 



contains three unknown quantities, requiring for their deter- 

 mination three simultaneous equations. Selecting the lines A, 

 D, and H for this purpose, we have from the table just given 

 the three equations 



l-5714=a+ /A ,L m , - 



l-5798 = a+- /A K< ? Qn 



1-6070 = a + 



(0*76009) 2 ' (0-76009) 



(0-58890) 2 "*" (0-58890) 4 ' 



(0-39679) 2 T (0*39679) 4 ' 



from which, by elimination, 



a= 1-5593, 6 = 0-006775, c=0*0001137; 



so that, for this prism, the formula becomes 



_, KKM 0-006775 0-0001137 

 n= 1*5593 H ^ f ^4 ? 



which we find on trial satisfies the observations in the visible 

 part of the spectrum within very narrow limits. When, how- 

 ever, we attempt to extend the application of the formula to 

 the infra-red region, its results are not so satisfactory. Since 

 b and c are both positive, the least value which n can have in 

 our prism, according to the formula, is a, or 1*5593, corre- 

 sponding to a deviation of 45° 35'; whereas the bolometric 

 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 prism, but 

 because below this point the heat is absorbed by some ingre- 

 dient of our atmosphere. 



We conclude, then, that Cauchy' s formula gives grossly erro- 

 neous results when extended far beyond the limits within which 

 the observations on which it is founded are made. Its im- 

 plicit assertion that the lower limit of the prismatic spectrum 

 (however great the wave-length of the ray transmitted) is not 

 so far below A as A is below D is absolutely contradicted 

 by these experiments ; and all extrapolations made by it, far 

 from the visible spectrum in which its constants have been 



