AN INTERESTING TSEUDOSOLID 295 



the absolute value of the modulus of rigidity of the foam is ex- 

 tremely small. The ruptures took place at rather more than 

 45° to the direction of the compressive force, and in symmetri- 

 cal cases 4 systems of fissures were developed in 2 planes at 

 right angles to each other, as has been found by Mr. Adams in 

 his experiments on marble, as well as by man}- earlier observers.. 



According to a theory of elasticity published by one of us in 

 1S93, the continuity of a solid under linear compression should 

 be represented by the simple formula xy°' = constant, and the 

 attempt was made to determine the value of <t for this foam, with 

 the result that (t was found nearly or quite indistinguishable from 

 one half, a in this equation represents Poisson's ratio, which, 

 according to the molecular theory adopted by Cauch}- and him- 

 self, should in all cases be exactly one-fourth. On the other 

 hand, for a theoretically incompressible solid, Poisson's ratio is 

 necessarily one-half. Now, the mass of foam experimented 

 upon is certainly highly compressible, or in other words, its bulk 

 modulus is small, but the results of the experiments showed that 

 the modulus of rigidity is very much smaller than even the 

 modulus of compressibilit}', so that (t is nearly ^-. ^ 



Further experiments on this pseudosolid have been necessar- 

 ily postponed, but even the results which have been obtained 



' Poisson's ratio is ordinarily defined as the ratio of lateral contraction to axial 

 elongation. This definition should, however, be limited to the case of infinites- 

 imal strain. This may be shown by considering the case of an incompressible 

 mass of unit volume, when the equation of continuity must evidently be x'^y= i 

 or xy^= I. For infinitesimal strain in this case we have 



ff = — "^"^ / "'-^=i 

 X I y - 



while if the common definition is extended to finite deformation we should have 



y—\ i-t-.v 



which becomes J when 'a; differs infinitesimally from unity but is in general a 



variable. The theory of finite strain referred to in the text may be derived from 



the hypothesis that 



dx I dy 



X I y 

 is constant, or that 



^_ log .Vq — log.v 



log y — log Jo' 



