1889.] Mr C Chree, On Elastic Solids. 31 



are no crucial experiments, that I am acquainted with, -which 

 definitely and finally contradict it, and until such experiments are 

 made it may be well to bear in mind the possibility of such 

 explanations as the theory affords. 



(2) The finite deformation of a thin elastic plate. By A. E. H. 

 Love, M.A., St John's College. 



(3) A solution of the equations for the equilibrium of elastic 

 solids having an axis of material symmetry, and its application to 

 rotating spheroids. By C. Chree, M.A., King's College. 



[Abstract] 



A solution is obtained of that type of the elastic solid equations 

 which contains five elastic constants, answering to those bodies in 

 which the structure is symmetrical round an axis. The solution 

 proceeds in ascending powers of the variables x, y, z. In the 

 expressions for the displacements terms containing powers of the 

 variables below the fourth are retained. Thus the solution, while 

 complete so far as it goes, can solve exactly only certain classes of 

 problems. One of the problems which it can completely solve is 

 that of a spheroid of any eccentricity rotating uniformly about 

 the axis of revolution, this axis being in the direction of the axis • 

 of symmetry of the material; and it is to this problem that atten- 

 tion is mainly directed. 



The solution obtained for the general case of a rotating sphe- 

 roid being somewhat complicated, certain special cases are first 

 considered. The first of these cases, that of a very flat oblate 

 spheroid, applies approximately to a thin plate rotating about 

 the normal to its plane through the centre. The second case, that 

 of a very elongated prolate spheroid, applies even more satis- 

 factorily to the non-terminal portions of a rotating cylinder of 

 length great compared to its diameter. In these two cases the 

 material is of the 5-constant type. The third special case is that 

 of uniconstaut isotropy in spheroids of every form. 



From the light thrown on the question by the results obtained 

 in the third special case it becomes possible to dissolve out of the 

 complicated mathematical expressions for the general case a very 

 considerable amount of information as to the state both of stress 

 and strain throughout the spheroid. The key to this information 

 is supplied by the recognition in every material whether of the 

 5-constant or of the isotropic type of a "critical" spheroid. The 

 ratio of the "polar" to the "equatorial" diameter of this spheroid 

 depends only on the elastic constants of the material, and is given 

 by a simple expression. The following, which are only a few of 



