184 



In any event, the variation with il is so rapid near U = 0, the tiny 

 pinhole would not actually be exnerimentally very a^^parent, furthermore, 

 this rapid variation of thiclcness indicates thiat at the last moment, v;hen 

 R/a < < 1, the neglect of the constrnint effects might be more serious 

 than otherwise; however, this does not turn out to be the case in general, 

 as shown in the next section. Equation (29) (d) shows that th.e diaphragm 

 assanes a conical shape, as indicated by experiment, whose center deflection 

 is proportional to the initial velocity v. This last is the basis for the 

 use of such diaphragms as inpulsive velocity indicators, as described 

 earlier. Quantitatively there is also fair agreement between these results 

 and experimental observations. Indeed, even the total time for deflection, 

 which has been called the swing time t , of the diaphragm, and is given by 



c 



is seen to be independent of v, to this order of approximation; computed 



values where higher powers of v are included agree rather well with the 



c 

 experimentally observed ones. 



The results of this section on the elementary theory were iirplicit 

 in the writer's first report on the diaphragm theory. In that report, as 

 in this section, no serious attempt was made to estimate the effect of the 

 motion in the central flat region on the explicit; solution of the problem; 

 that is, the non-linear partial differential equations of motion for this 

 region were not taken into account by the introduction of constraints. 



The present article is a generalization of the former one, as will 

 be seen in the next section; there the exact solution of the equations (B) arid 

 (C) are obtained and inform us as to the effect of radial motion and thinning. 



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