TOL. XLVII.] PHILOSOPHICAL TRANSACTIONS. 255 



after the discharge of the old one ; when and not before, the testaceous matter 

 has room for its secretion through its proper emunctories. It is in every circum- 

 stance analogous to all the other animals which annually cast their integuments ; 

 and, in its soft state, resembles that of a hen's egg before the testaceous matter 

 is secreted by the glands of the membrane ; being soft and flexible : for this 

 matter of all crustaceous animals, as well as of the eggs of fowls, is always suc- 

 cessive to the entire formation of the membrane under it ; nor are the glands ca- 

 pable of admitting the minima of the testaceous matter, till they have grown 

 into a state proper for that purpose. Hence it may be concluded that the crab, 

 the lobster, or other such animals, which had this property, are at first furnished 

 with this membrane entire, and sufficient to be a defence against the violence of 

 the agitated waves, and the rolling of sand, gravel, or other bodies, that might 

 prove hurtful even before it can grow hard. This seems to be the method or- 

 dained by the Creator for the preservation of every animal, however differing in 

 other little circumstances. The snake, adder, lizard, or any other kinds, which 

 we see endowed with this property, have the new skin entire under the shrivelled, 

 falling, old one ; and it is, no doubt, the case with crabs, lobsters, and other 

 crustaceous animals. 



In order to throw a little more light on this matter, it may not be disagreeable 

 to observe the manner of the induration of the surfaces of the shells of eggs. It 

 has been supposed that these consist of a nmcus indurated on the surface of the 

 membrane : but this is not the case. The particles of the shelly matter are 

 solid, though never so minute, and are carried with the fluids of the animal to 

 the membrane, now ready to receive them into the ducts of its glands ; and are 

 thence thrown into such order in the cellules of the external surface, as to ac- 

 quire a structure no less firm in proportion, than bricks laid on one another ; 

 and as capable of bearing any fair pressure, as a well built arch. 



When they are thus hardened and complete, they may be rendered as soft and 

 flexible, by being macerated in vinegar, as if the shelly particles had never been 

 placed on them. And this is not because the matter is quite dissolved; for a 

 vegetable acid is not capable of making a total dissolution of it ; but the minute 

 angles are destroyed, and the particles (which were before fixed like wedges to 

 each other, to which they were inevitably guided in the secretion by the very 

 structure of the receiving cellules of the membrane) are become round, by the 

 destruction of their angles, and admit of being rolled in some measure on one 

 another, so as in the whole to yield to the natural flexibility of the membrane. 



LXXjy. spherical Trigonometry reduced to Plane. By Francis Blake, Esq., 



F.R. S. p. 441. 



It is observable, that the analogies of spherical trigonometry, exclusive of the 



