Collapse of Tabes by External Pressure. 



and 



Q' = (jn +- n)(T.2 + (in — n)a%, 



691 



= (m-frc> 2 + (m — n)<r 3 + -j (m + ^)(-7T ) + ( m -" n )(~77 )} ]i ' ' 



,, . 4?n?i 

 = EA + — — <j 2 



?>t + n 

 + A'| EAi-* 



so that 



/ ^5 

 \dd> 



A 



(»i + n)a I <^</> ' m + n 2 



to 1 d 2 



a a d<p 



to*) J' 



G'=- Q'AV/A', 



-A 



= -IA 3 



EA,+ 



4»m ( rf'sr A „ i« 



7 T"< -JJ-\ E <^2 



( in + n)a { a<p in + n a 



ldho\l 



adA 2 ) J 



correctly to terms in A 3 . (11) 



Now W, being the increment o£ stress produced by distor- 

 tion, vanishes at the surfaces of the tube ; and the surfaces 

 are never subjected to tangential stress. Hence the terms 

 AA 3 _, AJi z , ot7i 3 may legitimately be neglected in the expres- 

 sion for G' *. We have then 



G' = 



Smnlt 5 



2>(m-\-u)a 



E(7 2 +- + 



w 1 d 2 w 



a 



a dcj) 2 _ 



(12) 



[Now from the first and third of (5) we see that T' must 

 be of the same order as G' ; and 



Y=\ h Q'dh', 



-a 



= 2h TeA+ i^ cr 2 "l + (terms in A 3 ... etc.). 

 L m+n J v J 



in + n 

 It follows that the quantity 



-n * a mn 

 EA + 4 — — <r 2 , 

 m + n 



and therefore also cr 2 , is of order h 2 at least ; wo shall there- 

 fore obtain G' correctly to terms in A 3 if we neglect cr 2 in 

 equation (12). 



* See p. 229 of Mr. Basset's article, and references on p. 223 ; for 

 arguments in favour of this hypothesis. 



