212 Mr. S. P. Langley's Experimental Determination of 



Now, when a and c are indefinitely small, b and d are the ordinates of 

 the prismatic and normal energy-curves, respectively, at a given wave- 

 length, and is the angle formed by the tangent to EF at their point of 

 intersection. Hence, to find the height of the normal curve at a given 

 wave-length, the corresponding ordinate of the prismatic curve must be 

 multiplied by tan (p. 



Such a construction was applied to the prismatic energy- 

 curve of the Hilger prism. 



The true normal energy-curve with all its inflections, 

 maxima and minima, is easily drawn after this (dotted) 

 bounding curve of normal energy* is plotted, for the parts of 

 the ordinate of the latter below and above its intersection 

 with the former irregular curve bear the same proportion to 

 each other as in the prismatic spectrum, and we thus finally 

 attain the object of the preceding labour. 



If now it is desirable to map the distribution of the energy 

 on any other scale, such as that on which the abscissae are 

 proportional to the times of vibration, this can be done with 

 facility. Thus, in the supposed instance, we have only to find 



- for each vibration, number to get the abscissae, and (obser- 

 ving that since y now= - -~ — — — 2 \ to use the multiplying 



factor — 2 to obtain the height of the new ordinate in each 



instance. If the length of the new energy-curve between the 



limiting perpendiculars (which now represent the reciprocals 



of the wave-length) is to be the same as in the old, we must 



introduce a constant multiplier n, writing the equation of the 



n 

 interpolating curve y = r ? so that the multiplying factor 



becomes— ™ 2 « 



A, 



I have drawn in this way (on a smaller scale than that of 

 the normal or prismatic curves, and following the smooth 

 curve in the former as my original) four different schemes 

 for the distribution of the energy. Curve A, PI. IX., represents 

 the distribution of solar energy (after absorption by our atmo- 

 sphere) on the normal scale. Curve B represents the same 

 distribution on the scale of wave-frequency (general equation 



of interpolating curve x=^, proposed by Mr. Stoney). Curve 



* This Journal for March 1883, plate iii. (where, however, the 

 maximum ordinate of the normal curve is, through an error in the draw- 

 ing, not shown quite in its true position, nearly at A =0*55). 



