176, 177] ELASTIC MODULI. 463 



is called Poisson's ratio. According to Poisson and the older writers 

 A = ^, so that t] = - We must certainly have 



- 1< <YI < 1, 

 for if ij > y ^ < 0, making the rigidity negative. If 17 < 1, 



making the bulk -modulus negative. No known bodies have 77 < 0, 

 and in experiments on isotropic bodies 77 has generally been found 



nearly equal to > the value assumed by Poisson, the value being 



found to approach more nearly to Poisson's value the more pains 

 were taken the secure isotropic specimens. 



The bulk-, shear- and stretch -moduli and Poisson's ratio are the 

 important elastic constants for an isotropic body, any two of which 

 being known, all are known. 



CHAPTER X. 



STATICS OF DEFORMABLE BODIES. 



177. Hydrostatics. Let us now consider the statics of a perfect 

 fluid, that is, a body for which p = 0. If each element of the fluid 

 is subjected to forces whose components are X, Y f Z per unit mass, 

 equations 144), 175 reduce to 



while the equations for the surface forces 145) become 



X n = (JL6 P) cos (nx), 

 2) r n 



The surface force is accordingly normal and equal to 

 3) l<s-P = -p. 



