158 



Mr. A. Mallock on 



[June 19, 



appears in many problems relating to the flexure of solids, and has 

 besides a kind of historical interest in virtue of Poisson's erroneous 

 conclusion that it must be \ for all bodies. 



Various methods have been employed to measure the ratio. The 

 most obvious perhaps after direct measurement (which is obviously 

 only applicable to a very small class of bodies) is to compare the 

 times of longitudinal and torsional vibration of a wire or cylinder of 

 the substance. 



y 2 2V 2 



But as by this method /m= q - where Y q and V» are the velocities 



of the vibrations which depend on q and n respectively, it is easily 

 seen that large errors may appear in the value deduced for jx when 

 only comparatively small errors are made in the measurement of 

 Yq and V», and besides this it is not unlikely that the q and n deter- 

 mined by vibrations, when there is not time for the heat caused by the 

 strain to alter its distribution by conduction, may not be the same as 

 when determined by statical methods. Wertheim made use of tubes 

 closed at one end and filled with water, the surface of which appeared 

 in a capillary tube fixed at the other end. The necessary data were 

 obtained by subjecting the tubes to longitudinal strain, and observing 

 the extension produced by it and the depression of the water in the 

 capillary tube. Kirchhoff has employed an ingenious method in the 

 case of brass and steel rods. 



It depended on observing simultaneously the torsion and flexure 

 produced by hanging a weight on an arm attached in a horizontal 

 plane at right angles to one end of the rod, the other end of the rod 

 being fixed in a horizontal position. 



His experiments seem to have been made with every precaution 

 against error, and the values he deduces for /a are *294 for steel and 

 '387 for brass, both of which are larger than the values found in my 

 experiments on the same metals. 



This may be attributed in part, at any rate, to the fact that 

 Kirchhoff used hardened steel and drawn brass rods, whereas most of 

 my specimens were annealed. 



The method which I have employed has some advantages over these, 

 especially in this that it is applicable to almost every solid, no matter 

 how brittle it may be, or how narrow are its limits of elasticity. 



It depends on the proposition that when a rectangular bar with 

 plane sides is bent by opposing couples whose planes are parallel to 

 one pair of sides, the other pair become surfaces of uniform an ti- elastic 



curvature, with principal radii of curvature R and -~ provided 



R 



that R is large compared with the third proportional to the thickness 

 and breadth of the bar. (See Thomson and Tait "Nat. Phil.," § 716.) 

 If R-l and R 2 are the radii of curvature parallel to the length and 



