122 Dr. J. Prescott on the Equations of Equilibrium 

 plate. Its value in terms of C is 



P = i(2;9 2 E 2 )*O. ..... (91) 



Also ^-(]-512 P 3 A 2 



Si 1 p 2 Er 

 Hr 2 



say. ....... (92) 



r o 



Let the radius of the plate be a, and let Pi=T at the rim. 

 Then 



T-P il_ 1Ha2 i 11 ^ 13 W \ fw 



1 - r °l i 2P 3 6 TV U4:~W~'"r { } 



If P is given, this equation determines T directly ; but i£ 

 T is given, it determines P indirectly. Inverting the series 

 to give P in terms of T, we get 



r — 1 | ±+ 2 T 3 3 T 6 144 i T 9 J" ^ ' 



The first approximation, namely 



Po = T, . (95) 



makes P x constant over the plate, which is the usual 

 assumption in dealing with stretched membranes. 

 The second approximation is 



Po = T+^~ ..... (96) 



and the corresponding value of the radial tension at any 

 point is 



lHr= 



Pi=Po- 



2 P » 



= T+ iirfS^-'" 2 )- • • • -< 97 > 



The third approximations are 



1 Ha 2 1 H 2 a 4 

 Po = T+2^p2 o ~~^r (98) 



and P f = T+ | r ^(a 2 -r 2 )~g ^(a 2 -r 2 )(2a 2 -r 2 ). (99) 

 Equations (94) to (99) are valid only on the assumption 



