430 Mr. J. H. Michell on the 



ject to the law of uniformity in the assemblage, act between 

 the points of our primary assemblage : and, if we please, also 

 between all the points of our second assemblage ; and between 

 all the points of the two assemblages. Let these forces fulfil 

 the conditions of equilibrium ; of which the principle is de- 

 scribed in § 16 and applied to find the equations of equilibrium 

 for the simpler case of a single homogeneous assemblage there 

 considered. Thus we have an incompressible elastic solid ; 

 and, as in § 17 above, we see that there are fifteen indepen- 

 dent coefficients in the quadratic function of the strain- 

 components expressing the work required to produce an 

 infinitesimal strain. Thus we realize the result described in 

 § 7 above. 



§ 35. Suppose now each of the four tie-struts to be not 

 infinitely resistant against change of length, and to have a 

 given modulus of longitudinal rigidity, which, for brevity, we 

 shall call its stiffness. By assigning proper values to these 

 four stiffnesses, and by supposing the tetrahedron to be freed 

 from the two conditions making it our special tetrahedron, 

 we have six quantities arbitrarily assignable, by which, adding 

 these six to the former fifteen, we may give arbitrary values 

 to each of the twenty-one coefficients in the quadratic function 

 of the six strain-components with which we have to deal when 

 change of bulk is allowed. Thus, in strictest Boscovichian 

 doctrine, we provide for twenty- one independent coefficients 

 in Green's energy-function. The dynamical details of the 

 consideration of the equilibrium of two homogeneous assem- 

 blages with mutual attraction between them, and of the 

 extension of §§ 9-17 to the larger problem now before us, are 

 full of purely scientific and engineering interest, but must be 

 reserved for what I hope is a future communication. 



XLIV. The Highest Waves in Water. By J. H. MiCHELL, 

 M.A., Fellow of Trinity College, Cambridge*. 



THE waves contemplated are those in which the motion is 

 parallel to one plane and which advance without change 

 of form. Most of the work already done on irrotational waves 

 applies only to those of small height and unbroken outline. 

 Stokesf has, however, long since expressed the opinion that 

 the height of the wave could be increased until the summit 

 became pointed, and showed that the angle at the summit 

 would be 120°. The object of this communication is to make 

 known a method of investigating such maximum waves. 



* Communicated by the Author. 

 t Collected Papers, vol. i. p. 227. 



