136 BIOLOGICAL EFFECTS OF RADIATION 



where a — 5.735 X 10~^ erg/cm. ^/deg.^/sec, the present accepted value 

 for the Stefan-Boltzmann constant. The radiation exchange between 

 two bodies would then be 



E = <j{T' - T\) 



or for small differences in temperature, we may write 



E = 4<rT'{T - Ti) 



We have therefore an absolute method of determining the radiation 

 exchange between black bodies. A number of instruments have been 

 developed on this basis, known as pyroheliometers and pyranometers. 

 These will be described below. 



Since an ideal black body would absorb totally all wave-lengths, such 

 a type of measurement may be used regardless of the wave-length dis- 

 tribution of radiation of the source. Assuming for the moment that a 

 given wave-length may be separated from other portions of radiation by 

 some means, we may then explore the energy for each wave-length from 

 a given source. On the basis of classical physics, it was predicted that 

 a black body would emit radiation according to the following law: 



_ £1 



While this exhibited a satisfactory relation to the observed facts for 

 short wave-lengths, a marked failure was evident in the long-wave-length 

 range. In an effort to overcome this difficulty, Planck postulated that 

 radiation existed in small bundles hv, where v is the frequency and h a 

 universal constant, h = 6.547 X 10~" erg. sec, and on this assumption 

 worked out the following law: 



A = 0(.- - i)"' 



where 



Jx = the energy radiated in erg/sec. /cm. Vunit solid angle in a direction 



normal to the area of the black-body surface per centimeter 



wave-length. 



ci = 2hc^ = 1.178 X 10-^ erg/sec. /cm.2 



he 

 C2 = -r = 1.433 cm.-deg. 



Figure 3 shows a family of curves for representative temperatures of 

 300° to 6000°K. The logarithm of the radiance J\ in erg/steradian/cm.^ 

 per centimeter wave-length in a direction normal to the surface is plotted 

 against wave-length X on a logarithmic scale in microns, increasing to 



