138 J. A. POLLOCK AND S. H. BARRACLOUGH. 



b. The above figures would apply if it were assumed that 

 the tube at the moment of collapse was at the ordinary 

 temperature. It is not probable that such was the case, 

 and the temperature may obviously have been anything up 

 to a limit just short of melting. The appearance of the 

 collapsed tube would not lead one to suppose that the metal 

 had reached the neighbourhood of its point of fusion, and 

 this view is confirmed by the fact that the solder connect- 

 ing the tube to the solid rod above does not appear to have 

 been melted to any marked degree, if at all. It is obvious 

 therefore that the temperature of the material at the time 

 of collapse is a matter of speculation. 



c. A large number of experiments have been made on 

 the pressures necessary to produce collapse in tubes, of 

 which the best known are those by Sir W. Fairbairn, 1 who 

 carried out an elaborate series on tubes and boiler flues. 

 None of the tubes were as small as that now under con- 

 sideration, but the results indicate generally the action of 

 the tubes when subject to external pressure. Professor 

 Unwin made a fresh analysis of the results obtained by 

 Fairbairn, and deduced several semi-empirical equations to 

 represent the collapsing pressure under various conditions. 2 

 He also demonstrated clearly that the number of lobes into 

 which the tube collapses depends on the ratio of the length 

 to the diameter, increasing in a definite fashion as this 

 ratio decreases. An illustration of this fact is seen in 

 the tube under consideration, where at the end near the 

 junction of the tube and the solid rod the conditions of a 

 tube of short length compared with its diameter are 

 approximated to, and where the number of lobes is large, 

 while further down where the long-tube conditions obtain, 

 the number of lobes is reduced to the minimum. The 

 conditions of the tube are so indeterminate that it is 

 unnecessary to discuss the formulae in detail. 



1 Phil. Trans , 1858. 2 Proc. Inst. C. E., Vol. xlvi. 



