156 HOWARD E. PULLING 



length could be measured separately there would be no difference 

 between the normal and prismatic energy spectra for the energy 

 is not redistributed among waves of different lengths by the 

 prism. But since all energy measurements are made by ex- 

 posing small areas to the incident radiation, the crowding of the 

 longer waves closer together than the others gives data that 

 must be corrected for this crowding, the amount of correction 

 depending upon the characteristics of the actual prism used. 

 Of course, if the energy content of the original beam had not 

 been equally distributed among the waves of different lengths 

 the normal energy spectrum graph would not be parallel to the 

 base as in the case above, although the ordinates would measure 

 the relative distribution in the original beam correctly. 



It is at once obvious that no idea of the distribution of energy 

 in a beam of light can be directly drawn from a prismatic energy 

 graph, or from measurements upon a prismatic spectrum. If, 

 however, the abscissas of the graph are drawn accurately pro- 

 portional on a sufficiently large scale to the dispersions actually 

 encountered (or better still if the dispersions themselves are 

 given), coefficients 7 may be obtained by which the prismatic 

 graph can be converted into a graph of a normal spectrum in 

 which equal numbers of wave lengths cover equal areas, i.e., 

 the dispersions are all in the same ratio to their corresponding 

 wave lengths. The proper coefficients multiplied into the 

 values of the prismatic energy ordinates of figure 1 result in 

 the graph of a normal spectrum of equal total energy (equal 

 areas between the curves and the same base line). The values 

 of these coefficients for any range of wave lengths will depend 

 upon the shape and nature of the prism 8 so that a graph of the 

 intensities plotted on u a prismatic scale" affords no clue to 

 the actual distribution of energy in the original beam — the 



7 These may be obtained by plotting the wave lengths as abscissas against 

 the distances of the positions of these wave lengths from a fixed point on the 

 base line of the actual spectrum chart. The trigonometrical tangents of the 

 angles formed by the intersections of tangents drawn from points on the curve 

 to the base line of the chart are the coefficients desired. 



8 The dispersion data used in the construction of figure 1 were obtained from 

 measurements with an actual 60° prism. 



