On the Collapse of Short Thin Tubes, 559 



until they are more fully investigated, no definite conclusions 

 as to tbeir origin and significance are possible. 



Similarly, the variations in the hydrocarbon spectrum 

 with the changes in the conditions of its source and the 

 appearance of new lines with "the three " await further 

 research. 



The discovery of such variations and of new bands asso- 

 ciated with the spectra of carbon and its compounds may 

 be of importance in connexion with astrophysics, and 

 particularly in the study of comets. 



September 1, 1916. 



LXI. The Collapse of Short Thin Tubes. 

 By Albert P. Carman *. 



[Plate XIV.] 



THE problem of the collapse of tubes is to find an 

 equation to express the relation between the collapsing 

 pressure and the dimensions and elastic properties of the tube. 

 In this general form no solution has been found, and it is 

 probable that no simple solution is possible. We have 

 reached, however, from theory and from experiments, fairly 

 simple equations (1) for long thin tube*, and (2) for long 

 tubes of moderate thickness. The term "long" is used for 

 a tube the length of which is beyond a certain "critical 

 length," which is generally taken as about six diameters. 

 The thickness of the tube is expressed in terms of the ratio 

 of the wall thickness t to the mean diameter d. If t/d is 4 



not more than about "025, the tube is ordinarily called 

 "thin." By " moderately thick " we mean tubes for which 

 t/d has a value between *03 and '07. The equation for long 

 thin tubes was deduced first by G. H. Bryan f, from 

 theoretical considerations, and has the form p = c(tjd)' s , 



where c is a constant and equal theoretically to ■= r? (E is 



1 — s 

 Young's modulus, and s is Poisson's ratio for the material 

 of the tube). The form of this formula has been confirmed 

 by the experiments of Carman and Carr X on seamless steel, 

 lap-welded steel, and brass tubes, and by Stewart § for lap- 

 welded tubes. The values of the constants found by these 



* Communicated by the Author. 



t Proc. Camb. Phil. Soc. (1888). 



\ Univ. of Illinois Eng. Experiment Station Bulletin (1906), 



§ Trans. Am. Soc. Mech. Eng. (1900). 



