AlT-lCl 52 



V = Vq + 6 V^ + b^Vg + & ~^V + bS^ + ... 

 we have in terms of orders of magnitude near x = 0, 



-1/3 

 or factoring out the 0(e ), we have 



V = 0(e'^^^)[l + 6e"l/3 ^ (se"^^^^ ^ ,^^ ] ^ 



The perturbation scheme may be expected to be valid 



-1/3 

 provided be < 1, V\/e can expect a fairly good approximation 



from only the first tv/o terms provided the more stringent con- 



-1/3 -1/3 



dition 6e << 1 is imposed. If be = 1/5 ^ the error 



involved in neglecting the third term is no larger than 5% of 



the first term, 



-1/3 

 For yearly variation of the windj 6e ~ 1/6. Hence 



we shall keep only the first tv/o terms of the series. It should 

 be noted that a determines the magnitude of the effect of the 

 perturbation but it has no bearing on the validity of the ex- 

 pansion. 



Numeric al Example 

 In order to discuss the above solution, we shall pre- 

 scribe numerical values for the constants of the problem. Let 



r-j_ = 6, 5 X 10 cm P = 2 x 10 cm" sec"-'- 



o ix 



s = 5 X 10 cm D - 5 X 10 cm(C = 200m. , d = 600m, ) 



