SECT. 4] T.IOHT 401 



tlic orientation of the beam, and of the existing hghting conditions within the 

 medium. The second class contains such quantities as the i^-functions, the 

 distribution functions and the reflectance functions. These describe the be- 

 havior of light fields as they exist at the moment of the experiment ; they are 

 properties which depend jointly on the inherent properties of the medium and 

 the geometrical structure of the light field. 



The apparent optical properties depend in a rather complicated way on the 

 inherent properties and at the same time are dependent on external lighting 

 conditions ; however, the former are worthy of study and classification because 

 of the following three facts. First, the gross experimental behavior of these 

 properties are strikingly regular. Secondly, there are useful theoretical relation- 

 ships between the inherent and apparent optical properties which hold regard- 

 less of the lighting conditions that exist inside or outside of the medium. 

 Finally, the use of apparent optical properties reduces to a practical level the 

 solution of underwater visibility problems and pertinent problems of marine 

 biology. By experimentally determining the apparent optical properties of real 

 media, we are in effect solving on a practical level certain particularly difficult 

 analytic procedures to which we would otherwise have to resort. 



D. Inherent Optical Properties 



a. Volume attenuation coefficient 



Consider the experimental arrangement shown in Fig. 3. The source, S, has a 

 surface radiance No as measured by the Gershun (1939) tube, G, when the latter 

 is at zero distance from the source. The Gershun tube is now moved away from 



(2) 



Nr 



A/a 1= 



Fig. 3. Schematic arrangement for measuring the volume attenuation coefficient, a. 



the source but in such a way that it always looks into the beam and in the 

 direction of the source. Let Nr be the radiance measured by G when at a dis- 

 tance r from S. If the intervening region between G and S were a vacuum, then 

 it is clear that for any distance, r, we would have Nr = No. But now the inter- 

 vening region is assumed to be uniformly filled by the material of some natural 

 hydrosol and the values of Nr are observed to decrease with increasing r. When 

 we plot the quantity In {NrjNo) for each r, we see that the resultant plot over 

 a certain range is a straight line with negative slope (Fig. 4). Let the absolute 

 14— s. I 



