er: 1 er “peor coverage & late pew rw ieee BL ~ teal ee | Cc n = concentration of particles in air E = original intensity of radiation Ey = intensity after radiation has passed through y cm. of the dusty layer = wave length of radiation y = distance trave-ied by radiation in the dusty layer and in a path normai to it Humphreys assumed that the dielectric constant of the volcanic ash particles was 7, This means that the index of refraction of the particles would be which is considered to be quite high. In this study it has been assumed that the dust particles have an index of refraction of 1.55, For index of refraction equal tov, the value of h is as follows: h = 11717 = ------ eee ee Equation 3 For an index of 1.55, h' has the value of ht = 2.177? ye 4 heewe ee = © -Eguation 4 Humphreys, using the value for h given by Equation 3, calculated that for dust particles of 1.85 micron diameter the eoler radiation is shut out 30 times more efficiently than terrestrial radiation, but if the value for h' is substituted it is seen that solar radiation is shut out approximately 160 times more efficiently. Ze Equation for Diffuse Reflection According to Rayleigh, if the particles are large compared to the wave length of solar radiation, the following equation applies: Ty *le “277 r* ox ss+e#-fe eee = 2 + “Equation 5 Humphreys used Equation 5 to determine that the total amount of 1.85 micron volcanic dust required aloft is 1.734 x 1024 to reduce solar radiation by 10% when the sun is at the zenith, In checking Humphreys calculetions it seems obvious that he must have made a mistake, because if the necessary values are substituted in Equation 5 it turns out that 1.1 x 1025 particles are required eloft,. Be Mie's Theory of Scatter - The complete rigorous theory for the scattering of light by isotropic spherical particles was developed by Mie. The Mie cee ee 5004630 C2=38529