THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



SEPTEMBER 1892. 



XXVI. On the Difficulties of Constructing a Theory of the 

 Collapse of Boiler-flues. By A.. B. Basset, M.A., F.R.S.* 



1. |~T has frequently happened in the history of mathe- 

 -■- matics that results which are substantially correct 

 have originally been obtained by processes which are in many 

 cases inadequate and sometimes erroneous. When a branch 

 of science is in its infancy, it is not surprising that many of 

 the methods adopted by the pioneers of the subject, in 

 attempting to discover the solutions of problems which have 

 never been previously attacked, are subsequently found to be 

 defective ; and after fulfilling their object by contributing to 

 the advancement of science, have ultimately to be consigned 

 to oblivion. The theory of elastic plates and shells affords a 

 striking illustration of these remarks ; for the investigations 

 of Clebsch and many of the earlier writers upon this subject 

 furnish numerous results which are substantially accurate, 

 although many of their arguments and methods are altogether 

 unsound. 



2. Clebsch and some of his followers have attempted to 

 construct a theory of plane plates upon the hypothesis that 

 the stresses R, S, T are accurately zero throughout the sub- 

 stance of the plate, where R is the normal traction, and S and T 

 are the two shearing-stresses tending to produce rotation about 

 two perpendicular lines which are parallel to the middle sur- 

 face of the plate. Clebsch then proceeds to integrate the 



* Communicated "by the Author. 

 Phil. Mag. S. 5. Vol. 34. No. 208. Sept. 1892. R 



