Physics and Mathematics to Geology. 235 



may be reduced in bulk, but, smaller than which no degree of 

 pressure, however great, can condense it, is a question which 

 cannot be answered in the present state of science." 



Maxwell, by denying the existence of a perfectly rigid body, 

 maintains that every solid can sustain stress or transmit 

 force only by suffering strain. Thus on depositing a feather 

 on the most solid block of iron we produce in the iron a 

 system of strains, infinitesimally small it is true, but whose 

 existence can no more be questioned than the existence across 

 the surface separating the iron and the feather of forces 

 balancing the portion of the feather's weight left uncom- 

 pensated by the air-pressure. The hypothesis quoted above 

 from Sir W. Thomson, that there may be a limit beyond 

 which no body can be compressed, is not inconsistent with 

 Maxwell's statement. The hypothesis regards the ratio of 

 the increment of strain to the increment of pressure as 

 ultimately becoming infinitesimally small, but it in no way 

 implies that this ratio ever becomes absolutely zero. 



In a solid bar, supposed perfectly elastic, exposed to longi- 

 tudinal stress, the ratio of the stress to the strain is styled 

 Young's Modulus. In many materials Young's modulus varies 

 in magnitude according to the direction in which tlie axis of 

 the bar is taken. Thus, in ordinary woods, there is a marked 

 difference between the value of Young's modulus in the 

 direction of the pith of the tree and in any perpendicular 

 direction-. Materials in which Young's modulus is independent 

 of the direction in which the axis of the experimental bar is 

 taken are termed isotropic, all others are termed seolotropic. 



In an isotropic elastic solid it is supposed, on the ordinary 

 British or biconstant theory, that the value of Young's modulus, 

 E, alone is insufficient to define the elastic structure, and that 

 some other elastic constant must be known. For many 

 purposes the most convenient additional constant is the ratio 

 of the lateral contraction to the longitudinal extension — each 

 measured per unit of length — in a bar exposed to simple 

 longitudinal traction. For instance, if the diameter of a bar 

 under uniform longitudinal stress change from 10 to 9*9997 

 inches the lateral contraction is '00003, and if the longitudinal 

 strain be '0001, the ratio of lateral contraction to longitudinal 

 extension is '3. This ratio is termed Poisson's Ratio, and is 

 represented here by tj. 



On the uniconstant theory of isotropy t) must have the value 

 *25, which certainly accords well with experiments on glass 

 and some of the more common metals, especially iron and 

 steel under certain conditions. 



On the biconstant theorv V ma 7 have any value within 

 *R 2 



