444 



I. Any surface may (without being wholly inextensible) 

 have at each point one or two inextensible directions. 



II. If a surface have at each point three or more inextensible 

 directions, the surface is wholly inextensible. 



III. If the curves of flexure be inextensible, the extension of 

 an indefinitely small arc of a curve, divided by the arc itself, will 

 at each point, and for a given law of displacement, vary inversely 

 as the radius of curvature of the normal section passing through 

 the tangent to the curve. 



Professor Allman read a paper on the structure of hydra. 



The substance of hydra consists of two perfectly distinct 

 strata, — an external, which may be called the ectoderm ; and 

 an internal, to which the name of endoderm may be given. 

 The ectoderm is composed of cells of a more or less spherical 

 figure ; the greater number of these cells possess the power of 

 developing, in their interior, thread-cells. Only one thread- 

 cell is generally developed in each cell of the ectoderm. 



The endoderm is composed of elongated pyriform or cla- 

 vate cells, with their long axes perpendicular to the surface, 

 and developing free, spherical, distinctly nucleated cells within 

 them ; several of these free cells being developed in each cell 

 of the endoderm. Of the free cells thus developed in the in- 

 terior of the endodermal cells, some are filled with colourless 

 and transparent contents, while others contain a deep-brown 

 granular matter. In this structure we cannot avoid recog- 

 nising a true glandular system ; the free cells being true se- 

 creting cells developed in the interior of mother-cells, and 

 producing, by a process of genuine secretion, the brown gra- 

 nular matter, which may be viewed as representing the biliary 

 secretion of the higher animals. 



The endoderm and ectoderm are closely united to one ano- 

 ther immediately round the mouth ; in other parts of the body 

 they are very easily separable. The cavity of each tentacle is 



