[ i47 ] 
IV, On the Elastic EquUihrinm of Oircnlar Cylinders under Certain Practical 
Systems of Load. 
By L. N. G. Filon, Jf.."f., B.Sc., Research Siv.dent of Kings College, Cambridge; 
Fellow of University College, London ; 1851 Exhibition Science Research 
Scholar. 
Coimniinicated by Professor Ewing, F.R.S. 
Keceived May 20,—Read June 6, 1901. 
Table of Contents. 
Pages 
§ 1. Object and aims of the I3a2jer.148-150 
§ 2. Method of solution adopted. Historical references.150-151 
§ .3. General solution for a .symmetrical strain.152-153 
§ 4. Solution of the differential equation.153-155 
§ 5. Solution under given conditions of surface loading; lltr first prohlem .155-158 
§ 6. Consideration of the ajjproximate expressions to which the results of the last section lead, 
when the ratio of diameter to length is small.159-lGl 
§ 7. Numerical jrroblem. ExjDressions for .strains and stresses.lGl-165 
§ 8. Calculation of the stresses on the outer surface of the cylinder.1G5-168 
§ 9. Calculation of the displacemetits on the outer surface of the cylinder.1G8-170 
§ 10. Numerical values of the stresses and di.splacements ..170-173 
§ 11. Discussion of the re.sults.173-181 
§ 12. I'he second problem. Case of a cylinder under ^Jressure whose ends are not allowed to 
exjiand. (First method of constraint).182-18G 
§ 13. The second jH’oblem. Constraint effected by shear over the terminal cross-sections. 
Determination of the constants.18G-1S9 
§ 14. Determination of the coefficients so as to .satisfy the conditions at the curved surface . . 189-192 
§ 15. Determination of the constants E.192-195 
§ 16. Expre.ssions for the stresses.195-196 
§ 17. Numerical example.196-197 
§ 18. Tables of the constants for the special ca.se taken. 198-200 
§ 19. Methods of evaluation at the curved Ijoundary. 200-201 
§ 20. Calculation of the series in the j^receding section. 202-203 
§ 21. Numerical values of the stresses. 204-206 
§ 22. Princiijal stres.ses at each point; lines of jrrinciiral stress. 207-210 
§23. Application to rupture. Distrilmtion of maximum stress, strain, and stress-difference . 210-214 
§ 24. Distorted shape of the curved surface.214-216 
§ 25. Apparent Youxg’.S modulus and Poisson’.s ratio.216-217 
(303.) u 2 
28.2.1902 
