Collapse of Short lubes by External Pressure, 51 



specimens, and any results obtained will be given in due 

 course. 



In connexion with the small radium content of these rocks, 

 it is worthy o£ note that the temperature Gradient in the 

 Kolar mines is quite abnormally small ; and it is hoped that 

 a communication on this subject may be made at some future 

 date. 



Summary. 



1. The radium content of a number of similar schists from 

 different parts of the Kolar Gold Field has been examined 

 by means of a new method which involves the fusion of the 

 rock with potassium hydroxide under reduced pressure. 



2. The quantity of radium in these schists appeared to be 

 approximately constant, and has a mean value of 0'19 x 10~ 12 

 gram per gram of rock. 



3. A few other specimens of different rocks of later date 

 were found to contain larger quantities of radium varying 

 from 0"82 to 6'90x 10" 12 gram per gram. 



Indian Institute of Science, 

 Bangalore. 



VII. The Collapse of Short Tubes by External Pressure. 

 By Gilbert Cook, M.Sc, Assoc.M.Inst.C.E* 

 [Plate L] 

 npHE subject of the resistance of tubes to collapse by 

 JL external pressure is one in which, considering its 

 important practical applications, comparatively little experi- 

 mental work has been done ; moreover, the greater part of 

 this has referred to tubes whose length is verv great com- 

 pared with the diameter, and the most important researches 

 have included little, if any, reference to the strength of short 

 tubesf. 



The experimental work of Carman^ and Stewart § has 

 shown that the relation indicated by theory, namely, that the 

 collapsing pressure is proportional to the cube of the ratio of 

 thickness to diameter, is substantially true for long tubes, 



* Communicated by Prof. J. E. Petavel, F.R.S. 



t A full discussion, and bibliography, of the present state of know- 

 ledge in regard to tube collapse by external pressure, is given by the 

 author in a report to the British Association Committee on Complex 

 Stress Distribution. See British Association Report, Birmingham, 

 1913. 



X University of Illinois Bulletin, vol. hi. No. 17, June 1906. 



§ Transactions of the American Society of Mechanical Engineers, 

 1905-1906, vol. xxvii. pp. 730-822. 



E 2 



