Wave-lengths in the Invisible Prismatic Spectrum. 195 



unknown cold band whose deviation indicated a (probably) 

 very great wave-length*. We ha\e had up to the present 

 time no way of measuring such wave-lengths directly, but are 

 accustomed to determine them by more or less trustworthy 

 extrapolation formulae, the best known of which is Cauchy's. 

 Accordingly I attempted to calculate the wave-length by 

 Cauchy's formula; but was conducted to an impossible result, 

 the formula declaring that no such index of refraction as I 

 had measured was possible in the p.ism in question. But the 

 measureme it was a fact beyond dispute ; and th's drew my 

 attention to the grossness of the errors to which the customary 

 formulae may lead. 



Every prism gives a different map of the spectrum ; nor 

 when we find a band or line by the prism have we any means 

 of fixing the absolute place, except by a reference to the 

 normal or wave-length scale, or to one derived from it. 



It is desirable to define at the outset the sense in which the 

 term "Normal" is here used as a synonym for "Wave-length" 

 spectrum. 



The amount of energy in any region of the spectrum, such 

 as that in any colour, or between any two specified limits, is a 

 definite quantity,, fixed by facts which are independent of our 

 choice — such as the nature of the radiant body, or the absorp- 

 tion which the ray has undergone, Beyond this nature has no 

 law which must govern us in representing the distribution of 

 the energy, and all maps and charts of it are conventions. 



Did the word "Normal," then, signify "absolute," there 

 would be no spectrum, exclusively entitled to such a name ; 

 but, in this connection, the word is always to be understood 

 in its radical meaning of an accepted rule or type of con- 

 struction. Such a type exists in the wave-length spectrum ; 

 and it has obtained general acceptance, not only on account 

 of its simplicity and convenience, but also of its, at present, 

 unique claim to be a " natural " one. It is properly distin- 

 guished as the " natural " scale from its not merely repre- 

 senting a mental picture of the distribution of the energy, 

 under a very simple law, but of actually being that which we 

 do produce by our most efficient optical apparatus, and make 

 visible and measurable at will. 



While w T e remain at liberty, then, to represent the energy 

 spectrum in terms of the wave-frequency, or of the reciprocal 

 of the square of the wave-length, or of any other function of 

 it, and while we may often find occasion to use these scales 

 for some special purposes, we are (and all the more especially 

 that w^e habitually speak in terms of the wave-length) led by 

 * Since designated as "Q." 



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