17 



[Translator's Note: The use of Eq. (a') gives: 



~ - 2,60 x 2.125 x 10 6 x (0.00406j** '_ A n . . nay , en „ m _ „ fl .1 

 p = *■ p==± 8.04 kg. per sq. cm. - 7.8 atm. [ 



0.750 - 0.45 x y 0.00406 • J 



The experimental pressures 12.2, 9.2, and 8.5 atmospheres are to be compared 

 with the three calculated values thus obtained, 11.9. 9.3, and 7.7 atmospheres. 



[Translator's Note: These values are given as 12.8, 9.5, and 8.1 in the textj 

 We see that there is good agreement. 



The number of lobes, n = 14 - 15, observed in the third test as compared to 

 the theoretical number, n = 7, cannot be explained. Probably it is due to an error 

 made by the observer. In both the other tests it was impossible to determine the 

 number of lobes after failure. 



Conclusions (added by translator). 



Equation (6) gives a solution for the collapsing pressure of a circular 

 cylindrical vessel closed at the ends by flat heads and subjected to uniform hy- 

 drostatic pressure on both shell and heads. As will be observed, the determination 

 of the correct collapsing pressure depends not only upon the length, diameter and 

 thickness, but also upon the number of lobes, n, into which a circumferential belt 

 of the vessel, between stiffening rings, divides itself at collapse. Equation (6) 

 gives a different value of p for each assumed value of n and collapse occurs in 

 that number of lobes for which p is a minimum. The use of Eq. (6), therefore, 

 involves the determination of the value of n which gives a minimum value of p, 

 either by actual substitution in that equation or by the use of curves previously 

 prepared, such as given in Fig. 4. However, the determination of n by Fig. 4 is 

 not always accurate, as was shown in the solution of example 1, page 15, where the 

 author by using n = 8 instead of the correct value n = 9 obtained a collapsing 

 pressure which was considerably too high. Fig. 8 on page 18 is drawn to a differ- 

 ent scale and gives a very accurate determination of n. 



Equation (7) is simpler than Eq. (6) and the collapsing pressures calculated 

 by it differ from those calculated by Eq. (6) by less than 1 per cent for all values 

 of 1/d below 0.5, as shown by Tables II and III, page 19. However, Eq. (7) like- 

 wise requires the determination of that value of n which gives the minimum collaps- 

 ing pressure and hence is somewhat cumbersome and indirect. 



Equation (a) presents a striking contrast to equations (6) and (7). It is 

 very simple and gives the collapsing pressure directly without the use of n. More- 

 over, Eq. (a) checks Eq. (6) even more closely than does Eq. (7), and can replace 

 Eq. (6) in all practical calculations. 



