214 



Mr. C. Chree. 



[May 17, 



and sometimes has short blunt processes projecting from its outer 

 surface. These short processes apparently correspond to the long 

 complex projections which in R. batis give rise to an irregular net- 

 work, and they seem to indicate that the cortical layer of R. circularis 

 essentially agrees with the alveolar layer of R. batis, differing chiefly 

 in the amount of complexity. Surrounding the cortex there is a 

 thin layer of gelatinous tissue in which capillaries ramify. This 

 tissue evidently represents the thick gelatinous cushion which lies 

 behind the disk in R. batis, and fills up the alveoli. 



The stem of the cup is usually, if not always, longer than the 

 diameter of the cup. It consists of a core of altered muscular sub- 

 stance, which is surrounded by a thick layer of nucleated protoplasm 

 continuous with the cortical layer of the cup, and apparently also 

 identical with it. 



The cups are arranged in oblique rows to form a long, slightly- 

 flattened spindle, which occupies the posterior two-thirds of the tail, 

 being in a skate measuring 27 inches from tip to tip, slightly over 

 8 inches in length, and nearly a quarter of an inch in width at the 

 widest central portion, but only about 2 lines in thickness. 



The posterior three-fifths of the organ lies immediately beneath 

 the skin, and has in contact with its outer surface the nerve of the 

 lateral line. The anterior two-fifths is surrounded by fibres of the 

 outer caudal muscles. It is pointed out that while the organ in 

 R. circularis is larger than in R. radiata, it is relatively very much 

 smaller than the organ of R. batis. 



VII. " On .Eolotropic Elastic Solids." By C. Chree, M.A., Fellow 

 of King's College, Cambridge. Communicated by Professor 

 J. J. Thomson, F.RS. Received May 1, 1888. 



(Abstract.) 



This paper treats of elastic solids of various non-isotropic kinds. 

 Its object is to obtain solutions of the internal equations in ascending 

 integral powers of the variables, and apply them to problems of a 

 practical kind, some of them already solved, but in an entirely 

 different way, by Saint- Yenant. 



On the multi- constant theory of elasticity the equations connecting 

 the strains and stresses contain 21 constants. As shown by Saint - 

 Venant these reduce for one-plane symmetry to 13, for three-plane 

 symmetry to 9, and for symmetry round an axis perpendicular to a 

 plane of symmetry to 5. 



Part I of this paper deals with one-plane symmetry. A solution is 

 obtained of the internal equations of equilibrium complete so far as 



