PEOCEEDINGS 



OF THE 



Cmfoidgc Hljilnsnpljkal Sflflrfff. 



February 7, 1881. 

 Professor Newton, President, in the Chair. 



Horace Darwin, M.A., Trinity College, was balloted for and 

 duly elected a Fellow of the Society. 



The following communication was made to the Society : 



Determination of the greatest height consistent with stability 

 that a vertical pole or mast can be made, and of the greatest 

 height to ivhich a tree of given proportions can grow. By A. G. 

 Greenhill, M.A. 



I. Suppose a uniform cylindrical pole or wire fixed in a 

 vertical direction at its lowest point, and carried to such a height 

 that the vertical position becomes unstable and flexure begins ; it 

 is required to determine this height. 



Let 2a be the diameter in inches, and A the sectional area of 

 the pole in square inches: and E be Young's modulus of elasticity 

 of the substance, expressed in gravitation measure of lb to the 

 square inch. 



Then, if p be the radius of curvature of the central fibre of the 

 pole, the bending moment of resilience (the unit being the inch-lb.) 



= EI 1 = EA7^-. 



P P 



VOL. IV. PT. II. 5 



