V. On the General llieory of Elastic 

 I '.a R. V. SOUTH \VI-.M,. Ji.A., Fellow of Trinity College, Cambridge. 



Communicated by Prof. A. E. H. LOVE, f'./f.N. 







Received January 4, Read January 30, 1913. 



CONTENTS. 



Page 

 Introduction and summary of paper 187 



EQUATIONS OF NEUTRAL EQUILIBRIUM IN RECTANGULAR CO-ORDINATFA 



Method of derivation 190 



Example in rectangular co-ordinates. Stability of thin plating under edge thrust 198 



EQUATIONS OF NEUTRAL EQUILIBRIUM IN CYLINDRICAL CO-ORDINATES. 



Derivation of the equations 202 



Kxamplea in cylindrical co-ordinates. Stability of trailer flues and tubular struts 208 



Solution for boiler flue without end thrust 217 



Comparison with experimental results 222 



Validity of investigation by the theory of thin shells 224 



Comparison with existing formula! 225 



The " critical length " 226 



Solution for tubular strut. Special case 227 



Validity of investigation by the theory of thin shells 230 



Solution by the theory of thin shells. General case 231 



Comparison with existing formula 1 236 



Stability of tubes under combined end and surface pressure 236 



GENERAL THEORY OF INSTABILITY IN MATERIALS OF FINITE STRENGTH. 



The practical value of a theory of instability 237 



Stability of short struts 242 



Need for further research. Conclusion 244 



Introduction and Summary of Paper. 



PROBLEMS which deal with the stability of bodies in equilibrium under stress are so 

 distinct from the ordinary applications of the theory of elasticity that it is legitimate 

 to regard them as forming a special branch of the subject. In- every other case we 



VOL. COXIII. A 501. 2 B 2 Published Mpantcly, August 6, 1913. 



