1902.] Approximate Solution for the Bending of a Beam. 491 



Appendix IV. — The following values have been obtained for the 

 vapour pressures of solid neon : — 



The vapour pressure of the neon did not change after successive 

 portions of it had been allowed to evaporate. This proved that neon 

 is a homogeneous substance. 



Appendix V. — From consideration of the periodic relationship be- 

 tween the critical and boiling points of the elements of the helium- 

 argon group it appears probable that the critical point of helium lies, 

 at about 10 o, 5 Abs. and the boiling point at 6° Abs.; Dewar fixes* 

 the former of these points at below 9° or 10°, and the latter at about 

 5°. In a series of experiments helium was compressed into a tube, one 

 end of which was cooled in liquid or solid hydrogen. At temperatures 

 down to that of solid hydrogen evaporating under a pressure of 5 mm. 

 of mercury (probably about 13° Abs.), the pressure on the helium was 

 slowly increased to 60 atmospheres. Under all conditions a change of 

 pressure accompanied a change of volume of the gas, and no evidence 

 that liquefaction had taken place could be obtained. 



" On an Approximate Solution for the Bending of a Beam of 

 Kectangular Cross-section under any System of Load, with 

 Special Eeference to Points of Concentrated or Discontinuous 

 Loading." By L. K G. Filon, B.A. (Cantab.), M.A., B.Sc. 

 (Lond.), King's College, Cambridge, Fellow of University 

 College, London, and 1851 Exhibition Science Besearch 

 Scholar. Communicated by Dr. C. Chkee, F.B.S. Beceived 

 June 12,— Bead June 19, 1902. 



The paper investigates the elastic equilibrium of a long bar of rect- 

 angular cross-section in those cases where the problem may be treated 

 as one of two dimensions, namely : — 



(a.) When the strain being in the plane of xy, the elastic solid 

 extends indefinitely in the direction of z, the applied stresses over the 

 bounding planes y = ±b, x = ±a being the same for any two sections 

 parallel to the plane of xy. We then have a strictly two-dimensional 

 strain. 



Temperature 

 (helium scale). 

 20°-4 

 15-65 



Pressure 

 (millimetres), 

 12-8 

 2-4 



(Abstract.) 



Loc. cit., p. 



364. 



