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I. Any surface may (without being wholly inextensible) 
have at each point one or two inextensible directions. 
Il. Ifa surface have at each point three or more inextensible 
directions, the surface is wholly inextensible. 
III. Jf the curves of flecure be inextensible, the extension of 
an indefinitely small are 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 
