150 MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



mental picture of it. It is certainly a practical consideration of the first importance that no such 

 apparatus actually exists ; but still, whether it exist or not, in so representing the distribution of 

 energy, we should break no law except that imposed by considerations of simplicity and con- 

 venience. 



Did the word " normal," then, signify " absolute," there would be no spectrum, exclusively 

 entitled to such a name; but, in this conuection, the word is always to be understood in its radical 

 meaning of an accepted rule or type of construction. Such a type exists in the wave-length 

 spectrum; and it has obtained general acceptance, not only on account of its simplicity and con- 

 venience, but of its, at present, unique claim to be a "natural" one. It is properly distinguished 

 as the "natural" scale from its not merely representing 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 we remain at liberty, then, to represent the energy spectrum in terms of the wave fre- 

 quency, 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 we habitually speak in terms of the wave-length) led by considerations of a 

 very practical kind to take as our normal or standard scale that of the wave-length itself. 



Since we have this normal spectrum actually before us, through the concave gratings con- 

 structed by Professor Rowland, it may seem as though we might dispense with the prism ; but 

 this is not as yet possible for the lower part of the spectrum, where overlapping spectra and feeble 

 heat make the use of the grating too difQcult. If we could use the solar energy here, not in the 

 form of heat, but of chemical action, as in photography, a great advance might be made ; and there 

 is reason, I believe, to hope that the labors of Professor Rowland and Captain Abney will ere 

 long do this for us with precision. At present, however, we have only heat, and the thermopile or 

 the bolometer; which latter, though less sensitive than the camera, can be made, as I shall show, 

 to determine experimentally, within known limits of error, the actual wave-lengths corresponding 

 to given indices of refraction, and hence to afford here valid experimental data for passing from the 

 prismatic spectrum to the normal one. The reason why this so desirable information has never 

 been obtained before is two-fold : (I) While the measurement in question can best be made by 

 means of a prism and grating conjointly, the heat, which in the lower prismatic spectrum is very 

 faint, becomes almost a vanishing quantity when it has passed the grating also, where the heat is 

 on the average less than one-tenth that from the prism. We must use too, if possible, a narrow 

 aperture to register this heat ; for a broad one might (on account of the compression of the infra- 

 red by the prism) cover the whole field in which its work should be to discriminate. (2) We must 

 have not only an instrument more sensitive than the common thermopile, but we must devise some 

 way of fixing, with an approximate precision, the point at which we are measuring when that point 

 is actually invisible. 



The apparatus I have devised for this double purpose has done its work with a degree of 

 accuracy, which if it may be called considerable, as compared with what we have been used to in 

 heat measurements, is yet necessarily inferior to that obtained by the eye, and less than we may 

 hope for at some future time, from photography. Nevertheless it has, I believe, given experi- 

 mental data very far outside the visible spectrum, by which we may either construct an empirical 

 formula and supply its proper constants so that it will be trustworthy within extended limits, or 

 test the exactness of such formula; as Cauchy's, Redtenbacher's, &c., which, while professing 

 a theoretical basis, only agree in their results within the limits of the visible spectrum (from which 

 they have been in fact derived, and where they are comparatively unneeded). They contradict 



