evident then that the coefficient of ^ will become divisible by n^ - 1 and we 

 find in place of equation (B) 



y ^H^-fTT-"?^ + ^[^^ - 1 + r^T^f2n2 - 1 -a.)] .,..,-,{c) 

 If, in eq, (C), we substitute the value ofgfroni eq.(l8) and the val- 

 ues of X and ^ from eq. {I4) and place 0"= 0.5, we finally obtain the equation 

 for the critical pressure, 2.' 



(Translator's note: Equation (C) is given Incorrectly in the text where the de- 

 nominator 1 - 2p is omitted. This mistake follows tvom. the use of 1 -Q ^ for 

 (1 -$)^ in the denominator of Xj. This same error also affects the final formula 

 D. The denominator of the last term, given as 1 + ("JTa. )^ in *he text, actually 

 becomes (t;:^)^-! when the corrected equation (C) is used.). 



If we omit the fraction that stands in the parenthesis beside n^ - 1, 

 we have the approximate solution of Southwell, which has been given above. 'S'or 

 the general range of application, eq. (D) gives directly, as can be seen, a use- 

 ful approximation. (Translator's note: Southv/ell's equation and eq. (D) become 

 identical when in (D) we neglect 1 in comparison with(_-^)^ and omit the frac- 



tion notea above, and in Southv;elx's equation we place Z equal to-4-s- . This 



10 



value of Z is derived by Southwell (loc, cit.) for the ideal type of end con- 

 straints which merely keep the ends circular without imposing any other restric- 

 tions upon the types of distortion, and was also used by Cook, - Phil, Mag. , Oct. , 

 1925 »PP' 844-8. The value of ^'^j ^ varies from 40 for the E.M.B. model series 

 III 20OOD5OTI, to 2„8 for the E.M.B. model series III I25D5OTI. ) 



The quantities that stand on the right hand side of eq.(D) are all 

 given directly with the exception of n: that is, the length of the tube, 1; the 

 radius, a; the wall thickness, 2h; and the elastic modulus, 1;. Concerning n, 

 which must be a whole number, more will be said later, 



6. Discussion of Results. 



If we set Q= in eq. (C), we obtain for the tube of infinite length, 

 y = (n^ - 1) X 

 In the z-2,-coordlnate system the lines converge at the origin arid thosewith the 

 greater slopes have the greater values of 11. The smallest value other than zero 

 Is for n = 2, that is, 2. ° 5^> °r» ^^ ""^ substitute in eq. (D), C = OO and n = 2 

 we get p = 2.19 E(-]*« 



