NO. 3 MEASUREMENT OF OZONE — WULF AND ZIMMERMAN 



II 



absorption coefficients and the wavelengths of the spectrum places, do 

 not change from day to day. The evaluation of this portion of equa- 

 tion (7), namely — i ^, ^! — > ^s as follows: 

 The matrix A is 



(10) 



where the first column comprises the values of the ozone-absorption 

 coefficient at the seven spectrum places, the second column comprises 

 the values of A~- (A in microns) at these places, and the third column 

 comprises the values of the coefficient of C which are all unity. 



Multiplying A by its transpose A', which is a three-row by seven- 

 column matrix, one obtains the 3x3 matrix 



AA = 



0.006496 



0.51307 



.0.170 



The adjoint oi A'A is 



adj^'^ = 

 The determinant of A' A is 



39-254 

 0.12302 



L- 1-3373 



0.51307 

 73.811 

 21.850 



0.12302 

 0.016572 

 -0.054717 



0.170" 

 21.850 



7 



-1-3373 



-0.054717 

 0.21624 



\A'A\ =o.ogoy6g 



(II) 



(12) 



(13) 



These are the quantities needed for the evaluation of the right-hand 

 side of equation (7) exclusive of the matrix L. They yield the 2^7 

 matrix 



a.d](A'A)A' ^ 



\A'A I 

 -9.11 -5.80 10.05 11-93 3-46 -3-67 -6.87 

 — 0.2431 —0.1959 —0.0520 0.0296 0.0842 0.1480 0.2291 

 1. 1 23 0.895 0.061 —0.239 —0.204 —0.230 —0.406 



(14) 



When the 7x1 matrix, L, is multiplied by this matrix there results 



'x' 

 the 3x1 matrix 8 



we seek. 



which comprises the three unknowns that 



