On the Elastic Equilibrium of Circular Cylinders. 353 



4 Higher mammals depend principally upon variations in heat-loss, 

 in which rapid respiration plays an important part. 



5. Variation in production of heat is the ancestral method of homo- 

 thermic adjustment. During the evolution of the warm-blooded 

 animal it has, through developing a mechanism by means of which it 

 can vary production in accordance with heat lost, overcome one dis- 

 advantage of cold-blooded animals, viz., that activity is dependent on 

 external temperature. It has thereby increased its range in the 

 direction of low temperatures. Later, by developing a mechanism 

 controlling loss of heat, it has increased its range in the direction of 

 high temperatures, and also rendered body temperature largely inde- 

 pendent of activity ; these advantages have been gained by a greater 

 expenditure of energy. 



m On the Elastic Equilibrium of Circular Cylinders under certain 

 Practical Systems of Load." By L. X. G-. Eilon, M.A., B.Sc, 

 Research Student of King's College, Cambridge ; Fellow of 

 University College, London ; 1851 Exhibition Science Re- 

 search Scholar. Communicated by Professor EwiNG, F.E.S. 

 Received May 20,— Read June 6, 1901. 



(Abstract.) 



The paper investigates solutions "of the equations of elasticity in 

 cases of circular symmetry, and it applies them to discuss the elastic 

 equilibrium of the circular cylinder under systems of surface loading 

 which do not lead to the simple distributions of stress usually assumed 

 in practice. 



The analytical method employed has been to solve the equations of 

 elasticity in cylindrical co-ordinates, obtaining solutions in the typical 



cos I ~) 



form g - n «j Jcz x (function of r), r being the distance from the axis 



and z the distance measured along the axis. 



More general solutions, not necessarily symmetrical about the axis, 

 have been given by Professor L. Pochhammer* and by Mr. C. Chree.f 

 Professor Pochhammer has used his results to deduce approximate 

 solutions for the bending of beams. Neither Mr. Chree nor Professor 

 Pochhammer has, so far as I am aware, worked out his solutions in 

 detail for such problems as are discussed in the present paper. 



I found that solutions in trigonometrical series would be sufficient to 

 satisfy most conditions in the first of the three cases discussed, and all 



* ' Crelle's Journal,' vol. 81. 



t ' Cambridge Phil. Soc. Trans.,' vol. 14. 



