In the particular case 9=0 (tube of infinite length), equation (A) reduces to 



y (1 + x) = x(n^ - 1) (19) 



From the definition in eq. ( I4 ) it follows that ^represents the mag- 

 nitude of the elastic compressive strain of the tube wall under the pressure £. 

 Even though we go beyond the proportional limit of the material 'see further be- 

 low), ^ for iron or other metal will amount to not more than a few thousandths 

 at the most. Now the horizontal asymptote of the hyperbola, eq. (19), has 

 the ordinate n'^ - 1, which is at least 3« li''® see, therefore, that the partic- 

 ular part of the hyperbola in question has only a very slight curvature and can 

 therefore be represented by a straight line with sufficient accuracy. Vi'e omit, 

 accordingly, the last member to the right in eq. (A) and bring the value of ^, 

 considerably shortened, on the other side. (Translator's note: The omission of 

 the z^ term is completely justified since x is always very small and the coeffi- 

 cients of the z and xf_ terms are of the same order of magnitude. An actual com- 

 putation for the E.M.B. model S III I25D5OTI gives x =-2.632 z 10"°, z^ = 6.927 

 X 10"^^, p = 0.3815, and using n = 16, eq. (A*) reduces to 

 yd + 3.93 z lO"*^) = 519.2 z 10"^ + 668. 5z + 116. 9z^ 



= (519.2 + 1759.2 + 0.00081) z 10-6 

 Since the xf_ term contributes only O.OOO8I as compared with 1759*2 for the z tern 

 it Is surely negligible.). If we remove, then, the factor (n^ - 1)^ from the co- 

 efficient of z we have: 



ivhere 



^ i~^ -' (B) 



(Translator's note: Tn the tezt, the denominator of A, is given 1 - Q^)» 



In general, it is sufficient to regard ^ as a small quantity and to 

 neglect higher powers of p in computing X. (Translator's note: The values of g 

 for E.M.B. models S III 2000D 5OTI to S III 125D 5OTI, which represent lengths 

 of from 2D to O.125D, vary from O.O24 to O.33 and their squares vary from O.OOO6 

 to 0.11. The neglect of q^ terms causes an error of less than 1^ for models 

 whose frame spacing Is equal to one half the diameter or greater. However, for 

 the E.M.B. model SZ I54D 5OTI with a frame spacing of 0.i37D, the error is 17^. 

 This frame spacing corresponds to that commoaly used in submarine design. The 

 slight error noted in (A) where ^ is given In place of j^^ ^ is unimportant 

 since it is multiplied byQ^ in the last tei-m of (B) and disappears.) It becomes 



