Ill- 86 



If the surface S(x) is periodic of height h and period — , e may be ex- 



P 



panded in the form 



^UcYS(x),y^ 3^^inpx ^^,_^^3^ 



Then p. (xg, S(x2)) may be written as 



P^^JX3,S(X3)) -"V^ B^ e'^^^n'' (III-104) 



inc 2^_^ n 



n=-oo 



where a =a + -j^ . Let y = (1 - a^)^. As in the previous cases, when cl > 1, 

 Y is chosen so that i y ^0. Then, using (III-99b), we can obtain an expression 

 for f(xi). Substituting this in (III- 101), and after some analysis, we find that p 

 is given by 



— ^ ik(a x+Y z) 



p (x, z) = > A e (III-105a) 



n=-oo 



where 



\~ ~ Z^ Vk\Vk (III-105b) 



n 1 



k=-" 



If S(xs) is of the form S(x2) = h cos pxs, then B^ = (i) J^(kh ), i.e., B^ is of 

 order (kh y)"- Neglecting terms of order greater than (kh Y)^ and assuming 



Y ?aY(i.e., k>l), we obtain 



Ag ^-i+(khYy 





« ikh Y 



-^±3 ' 



« f(khY)= 



(III- 106) 



artliur B.ILittle Jnt. 



S-7001-0307 



