69 83 



Introducing polars s, ip on the diaphragm so that y = s cost// and 

 dS = sdsdi//, changing from s to s ' = s + s cos^^sin $, so that ds' = 

 (1 + slnO cosilj)ds. and proceeding as in obtaining [105], 



/•.. dS f'f-l, s'\ ds' dip 2iTC .,,, 



J ' - 7 s J J \ c / 1 + sin e cos (A cos e 



provided z(- <») = 0. Hence [102] becomes, as a generalization of [107], 



mz + -—- = 2p + (/. [108] 



cose '^^ ^ ^ 



This equation is also obtained easily from a simple consideration of the pro- 

 cess of reflection. 



EFFECT OP AN INFINITE BAFFLE 



Let part of the target consist of a plane baffle extending later- 

 ally to an infinite distance from the edge of the plate. 



If the baffle is fixed in position, its only effect upon [102] is 

 that the range of integration for the integral need be extended only over the 

 face of the plate, since elsewhere z = 0. 



If the baffle is movable, let z^ denote its displacement. Then 

 over the baffle Zj is uniform and is a function only of the time t or z^^(t). 

 Let the integral in [102] be divided as follows: 



It h-. '^s =/|z,(t -A)rfs + /i-[zv, -\{t-iPs 



plate 



in which the first integral on the right is arbitrarily extended over the 

 plate as well as over the baffle, and the error thus Introduced is compen- 

 sated for by the second term in the second integral, which extends only over 

 the plate. The first integral on the right can then be transformed as in 

 [105], since z.(t - s/c) is a function only of ( - s/c, giving 



l7h(t-7)dS =2ncz^{t) 



In terras of the velocity z^^ of the baffle at time t. Hence [102] may be 

 written 



iz = 2p, + 4,-pcz^-^j^[z -■^J,_,dS [109] 



plate 



where all quantities except z - Zj in the integrand are taken at time t. 

 Another form for a special case is given in Equation [19] or [20]. 



