TRUE ABSORPTION SPECTRUM 713 



in a scattering medium, we will find that not only are the valleys less deep, 

 but also the peaks are less high than in a similar plot in a nonscattering 

 system. 



This qualitative explanation of the effect of scattering on selective trans- 

 mission and absorption can be replaced by an exact analysis if the system 

 satisfies certain conditions — namely, random distribution of scattering 

 centers and— in the simplest forms of the theory— equal probability of 

 scattering in all directions. 



Equations for combined absorption and scattering in systems of this 

 t}T)e have been derived by several authors; we will mention here, as ex- 

 amples, the investigations by Wurmser (1941), Duntley (1942, 1943) and 

 Saunderson (1942). Figure 22.37 represents a nomograph constmcted by 

 Duntley (1942). In this diagram, the abscissae are the expressions: 

 {R' + P')/Q', and the ordinates the expressions: log {l/T) + log Q' , 

 whose relation to the absorption coefficient (per unit path), a, and the 

 scattering coefficient (per unit path), a, is shown in the inserted formulae 

 {d being the depth of the layer measured). The constants P' and Q' are 

 characteristic of the asymmetry of the scattermg. If scattering is iso- 

 tropic, and the incident, transmitted and reflected fight are perfectly dif- 

 fuse, P' = and Q' = 1, and the abscissae in the figure are simply the 

 measured reflectances, while the ordinates are the measured optical densi- 

 ties (logarithms of inverse transmittance) . The nomograph remains ap- 

 proximately correct also if the incident light is collimated, if only the re- 

 flected and transmitted fight are completely diffuse {cf. page 676). Under 

 these conditions, the absorption coefficient, a, and the scattering coefficient, 

 a, can both be read from the graph, if reflectance and transmittance have 

 been determined. 



Another method of determination of the two coefficients was described 

 by Saunderson (1942). It requires two reflection measurements — one 

 with a thin layer and one with a layer of "infinite thickness" {i. e., having 

 practically negligible transmission). 



Wurmser (1941) suggested that transmission measurements with two 

 layers of different optical density can be used to determine the coefficients 

 of absorption and scattering, and gave a sample nomograph for two specific 

 depths of the cell (0.035 and 0.1 cm.), which is reproduced in figure 22.38. 

 However, he did not point out that his two-constant formula is correct 

 only if both layers scatter sufficiently to ensure complete diffuseness of the 

 transmitted light. 



Procedures of the above-described type can be appfied with a fair de- 

 gree of reliance to cell suspensions, and it is desirable that future investiga- 

 tions of spectra of such systems make use of them. The application of 

 Duntley's nomograph to leaves or thalli also is possible, but one has to re- 



