12 



SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 1 23 



8. CALCULATIONS FOR A PARTICULAR DAY 



The seven elements of the matrix L are obtained from the trans- 

 mission coefficients found for the day at the seven spectrum places. 

 Each one is the negative logarithm of the transmission coefficient (an 

 optical density) minus (see expression (2)) the optical density due 

 to the Rayleigh scattering by the molecules of the air, which latter is 

 given in equation (9). This quantity, which is written for an average 

 value of the atmospheric pressure, has a given value for each spectrum 

 place. These values are contained in table 2. 



0.0353 (AjLl) DA- 



TABLE 2 



19 20 22 24 26 28 30 



0.01099 0.01351 0.021 16 0.02857 0.03783 0.04908 0.06266 



In the following illustrative calculation of the values of the three 

 unknowns the data of September 29, 1953, have been used. Both 8 and 

 t, were of moderate size on this day. The measured values of the 

 transmission coefficients are given in table 3 together with the optical 

 densities (the negative logarithms of these numbers) corresponding 

 to them. 



Table 3 



Place 19 20 22 24 26 28 30 



Trans, coefs 0.961 0.952 0.915 0.894 0.888 0.872 0.847 



Optical densities... 0.01728 0.02136 0.03858 0.04866 0.05159 0.05948 0.07212 



Subtracting from the optical densities of table 3 the corresponding 

 Rayleigh-scattering values of table 2 one has the elements of the 7x1 

 matrix L of equation (7) 



0.00629I 

 0.00785 

 0.01742 

 L= 0.02009 (15) 



0.01376 

 0.01040 

 LO.00946. 



Multiplying now this matrix L for these observations by the 3x7 

 2id]{A'A)A' 



matrix 



\A'A\ 



of (14) yields 



0.256 cm ozone 

 = 0.00149 (microns)^ 

 0.00131 



(16) 



