560 Mr. A. P. Carman on the 



experiments are, however, about 25 per cent, less than those 

 indicated by theory, probably in consequence of the material 

 being beyond the elastic limits. The formula for moderately 



thick tubes has the form p = a-. — b, where a and b are 



constants. This formula is purely empirical both in its form 

 and its constants. 



Carman concluded from his early experiments on small 

 brass tubes (Phys. Ptev. vol. xxi., 1905) "that there is a 

 minimum length for each tube, beyond which the collapsing 

 pressure is constant, and further, that this minimum length 

 is quite definite. Again, for lengths less than this critical 

 minimum length, the collapsing pressures rise rapidly. As 

 definitely as can be determined from these small tubes, the 

 collapsing pressure varies inversely as the length for lengths 

 less than the critical length." This last law is stated by 

 Gilbert Cook in what he has called "Carman's equation" 



(Phil. Mag. July 1914, p. 53). p' — yp, where p is the 



collapsing pressure of an infinitely long tube, L is the 

 critical length, I the length of the given tube, and p' the 

 corresponding collapsing pressure. A curve drawn with 

 lengths as abscissae and collapsing pressures as ordinates, 

 would thus consist, as P. V. Southwell has noted (Phil. Mag. 

 Jan. 1915) of two discontinuous branches, a straight line 

 parallel to the axis of abscissae and a rectangular hyperbola 

 intersecting the straight line at the point corresponding to 

 the critical length. For both theoretical and practical 

 reasons, the form of this pressure-length curve at and within 

 the critical length has recently aroused much interest and 

 discussion. The practical interest came first from the 

 problem of spacing el collapse rings " in boiler-flues. Another 

 practical problem comes from the collapse of steel flumes by 

 atmospheric pressure, when accidents have suddenly let out 

 the water and reduced the pressure almost to the zero on 

 the inside. The theoretical interest comes from a formula 

 deduced by P. V. Southwell in a very important papf-r on 

 u Elastic Stability," read in 1912 before the Poyal Society 

 of London. In this paper Professor Southwell has deduced 

 the formula 



— 91? f z d ^ ■ - m * n.2 i\* 2 



where p is the collapsing pressure, E the Young's modulus, 

 — is Poisson's ratio, z is a constant depending upon the 



