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Flp. 8. Soparotlon or the regions 

 the lobe numbers n equals 2 to 8, 



7. Comparison with Experiment. 



The comparison of our results with the accumulated observations of the 

 buckling pressure of boiler flues becomes very difficult for several reasons, 



a.-l 



First, the exact value of the 

 elastic modulus E is almost 

 never given for the experi- 

 ments. This is of particu- 

 lar importance If the aver- 

 age pressure lies near the 

 elastic limit, so that E 

 sinks far below the custom- 

 ary value. Second, the ex- 

 perimental arrangements pro- 

 vide no certainty that the ends of the tubes can be considered as fixed, in the 

 sense that w = is set for x = + //2. Analogous to the case of ordinary buck- 

 ling, we will, by not having sufficiently rigid ends, introduce e greater value 

 of /_ as the effective length ("Massgebende Lange"). Finally, the given wall 

 thicknesses are often to be regarded as the average for somewhat variable magni- 

 tudes while for the proposed problem it appears rather that the minimxim value 

 should be used. 



There are to be considered: Experiments by Fairbairn (I858), by Rich- 

 ards (1881, discussed by Wehage, referred to by Bach), the experiments of the 

 Danzig shipyards, (1887 to 1892) and those of A. P. Carman (1905). All those cases 

 were eliminated for which the average stress on the surface of the material of 

 the tube was above the proportional limit, that is, about 180O atmospheres. 

 (Translator's note: An atmosphere is slightly greater than a kg./cm^ ) .This cor- 

 responds in eq.(22) to the imposed upper limit on j_ of 3.19 ^ 10"^. The number 

 of experimental results to be compared, therefore is not very great. 



For the Carman experiments (Physical Review 21, I905, p.581) conducted 

 with very small, thick-walled brass tubes, this limitation permits only the tubes 

 of very great length to be considered: They give, as was noted by Carman himself 

 very good agreement with the formula (a) for I -co . 



For the experiments of the Danzig shipyards (Z.l894« p. 689), only two 

 lie within the valid region of our derivation, namely: 



2a = 100 cm, I = 106.2 cm, 2h = O.81 cm, P = 24 atm. 



