3o6 REPORTS ON THE STATE OF SCIENCE, ETC. 



Now what is meant by the physical intensity of a stimulus in these 

 experiments ? We should usually define it as the rate at which radiant 

 energy is incident on unit area of the photometer screen. This is what we 

 intend our physical intensities to mean, but there is a difficulty. Intensity 

 of radiation can be measured as an A magnitude for all samples of radiation 

 of the same spectral quality, because in comparing such samples the pro- 

 perties of the measuring instrument are completely eliminated and equality 

 in its response implies equality of radiation intensity. It is a different 

 matter when we wish to measure samples of radiation of different spectral 

 qualities ; for example, monochromatic samples of different wavelengths. 

 A physical detector of radiation operates in virtue of some interaction between 

 radiation and matter, and in general the efficiency of radiation in producing 

 the response characteristic of the detector varies with wavelength. In 

 other words the sensitivity of the detector is a function of wavelength. It 

 is evident that when we compare samples of radiation of different wave- 

 lengths Xj and Xg for which our detecting apparatus gives equal response 

 we have not necessarily got equality in the rates of energy flow Exi and Fa 2, 

 but in the products ctaj/Tai and ffA2^A2> where c-;^ and cta2 are the sensi- 

 tivities of the detector for these wavelengths. Our experimental criterion 

 of equality is not equality of E\ but equality of E,\ c!\, where ox is some 

 function of wavelength. This is true whatever type of detector we use to 

 provide a practical criterion of equality in radiation measurements. In 

 principle we cannot get beyond it. 



We cannot formulate a practical criterion of equality for E\ alone, but 

 only for the product of E\ and another function of wavelength characteristic 

 of the particular instrument used to provide the criterion of equality. Now 

 we have seen that in the measurement of an A magnitude quantitative 

 knowledge of the properties of the instrument used to establish equality 

 must not be assumed. This requirement is fulfilled in the present case if 

 we regard as our measureable magnitude not the quantity E\ but the 

 quantity Ek a,,. This is, in fact, the quantity measured by any radiometric 

 operation, and it is evident that different types of detecting instrument for 

 which a\ is not the same function of wavelength will measure different 

 magnitudes. It so happens that some types of detector can be constructed 

 for which c7x is nearly independent of wavelength . Thermopiles and other 

 instruments with lamp-black receiving surfaces or with nearly-closed radia- 

 tion traps are of this class. In a well-blackened thermopile, for example, 

 cta is so nearly constant over large ranges of wavelength that for practical 

 purposes it may be regarded as constant. With such an instrument the 

 magnitude E\ a\ may, to a close approximation, be written HEa and it is 

 usual to leave the constant out altogether and regard the magnitude as E\. 

 For practical purposes this is quite legitimate. Our results are the same 

 to within the errors of observation as they would be if we really did measure 

 E\; but for an understanding of the significance of a criterion of equality 

 in any metrical process, it is fatal to ignore the factor ax even when it is 

 constant. This is the same kind of philosophical error as we make when 

 we regard the arithmetical ratio n/i as identical with n, ignoring the division 

 by unity because it does not affect numerical results. The two ns are, 

 however, quite different things ; one may be the cardinal number n, the 

 kind of number used for counting eggs, whereas the other denotes a relation 

 between two numbers, one of which just happens to be unity. In the same 

 way there is a fundamental difference in significance between the magnitude- 

 Ex and a magnitude consisting of the product of E\ with a function of 

 wavelength, and this difference in significance is not eliminated because in 

 some particular case the function of wavelength is a constant and may be 



