where b is a constant to be determined, together with B^, D-^, B2, and Dg. 



From the properties of * ( x ")it is known that <& (0) = o and $(co) = 1. 

 Fitting boundary conditions (7), (8), and (9) in (10) and (11), with the 

 use of (12) , the following equations results 



= r 



(13) 



b,+ ». * tsfer' ; (u) 



B*+ °a* (lk) =0,ond (15) 



B 2 + D 2 = C 2 j < l6 > 



while (10), (11), and (12) in connection with (6) give 



Solving equations (13) to 0-6) for D^ and D2 yields 

 and substituting these values in (17) finally gives 



k i c i g 40C i . k 2 C 2 g 4qc 2 ^gr (19) 



This derivation is due to Neumann. 



This transcendental equation (19) can be solved for b by plotting 

 the curves 



y _ _vC|Ll/> b and y = f ( b ) , 



where f(b) represents the left hand side of (19). Then b is found as 

 the abscissa of the intersection of the two curves. 



Figure 1 shows a graphical solution of (19) by this method, using 

 the following values for the constants involved: 



