Short Tubes by External Pressure. 53 



into which a tube divides in collapsing, but contains factors 

 for which a numerical value cannot at present be found. 

 It has been customary to assume that the strength is inversely 

 proportional to the length, the assumption being based solely 

 upon the early experiments of Fairbairn * and a few tests 

 on small seamless brass tubes by Carman f , who proposed 

 that the critical length should be regarded as the upper 

 limit of this relation, so that the strength of a shorter tube 

 would be given by the equation 



Pi=j.p, . , .... (2) 



where I is the length of the tube, p the collapsing pressure, 

 of an infinite tube, given (for solid drawn weldless steel 

 tubes) by the formula (1), and L, the critical length, = 6d. 



The inadequacy of the data in regard to short tubes sug- 

 gested to the author the experiments which are described in 

 this paper. It has not been found possible, however, to 

 represent the results accurately in any formula involving all 

 the variables, but it will be seen that the actual collapsing- 

 pressure is widely different from that obtained by calculation 

 from equation (2), if Carman's value of the critical length 

 be taken. Much more extensive experimental work, covering 

 a greater range of dimensions than has yet been undertaken, 

 would, however, be required before it would be desirable, or 

 even possible, to propose a new formula. 



The tests were carried out on solid drawn steel tubes 3 in. 

 internal diameter. A tensile test of a specimen cut longi- 

 tudinally from the tube gave the following results : — 



Stress at yield point 1S'4 tons per sq. in. 



Ultimate strength 25'9 „ ,, „ 



Elongation on G in 15 per cent. 



Elongation on 2 in 21 per cent. 



In order to ensure that the thickness should be as nearly 

 uniform as possible, the tubes were carefully machined to 

 the desired thickness after having been cut to the required 

 length. The cost of the preparation was very kindly defrayed 

 by the Vulcan Boiler and General Insurance Co., Ltd. The 

 thickness and length of the tubes were varied, but a constant 

 diameter of 3 in. was selected because a sufficiently low 



value of "7 could thereby be obtained without the thickness 



becoming undul}- small, and therefore liable to considerable 



* Phil. Trans. 1858, p. 389. 



t Physical Review, vol. xxi. Dec. 1905, pp. 381-387. 



