tot. XVir.] PHILOSOPHICAL TRANSACTIONS. 465 



acid austere matter, and the coagulum made by such a matter is not so easily 

 dissolved as when it is made by an acid only. This coagulum therefore being 

 imprisoned, and the more gross and earthy parts being incapable of evapora- 

 tion, or being otherwise spent, are concentrated and indurated by the evapora- 

 tion or flowing off of the moist particles, and so produce a hard and chalky 

 substance. 



The last discourse is on the cartilages, which approach near to the nature of 

 bones, but differ from them in their formation and in their flexibility ; this 

 flexibility is from the figure and order of their parts, which are such that the 

 particles, as they must slide one way or other in the inflexion of a body, may 

 move without interrupting the continuity of the whole, even when they recede 

 from one another, unless they are forced too far. The cartilages have a mem- 

 brane every way like to the periosteum, and is a continuation of it, where they 

 are joined to any bones. They have also a great number of blood vessels. 



The use of the cartilages in general is to give a strength to some parts, 

 which did stand in need of such bodies as are both flexible and rigid. Those of 

 the ribs are designed to make them capable of an elongation, that so they may 

 protrude the sternum one way, and drive back the vertebrae of the breast the 

 other, so making an addition to the capacity of the breast. These gristles 

 serve likewise in the contraction of the breast ; for having their natural figure 

 altered in the elevation of the ribs, and the ampliation of the cavity of the 

 thorax, they naturally endeavour to regain their first figure, and to return into 

 their proper position. 



0/ the several Species of Infinite Quantity, and of the Proportions they bear t9 v 

 one another. By Mr. E. Halley. N° IQS, p. 556. 



That all magnitudes infinitely great, or such as exceed any assignable quan- 

 tity, are equal among themselves, though it be vulgarly received for a maxim, 

 is not yet so common as it is erroneous ; and the reason of the mistake seems 

 to be, that the mind of man coming to contemplate the extensions of what ex- 

 ceeds the bounds of its capacity, and of which the very idea includes a negation 

 of limits ; it comes to pass that we acquiesce generally, and it suffices to say, 

 Buch a quantity is infinite. But if we come more nearly to examine this notion, 

 we shall find, that there are really, besides infinite length and infinite area, no 

 less than three several sorts of infinite solidity ; all which are quantities sui ge- 

 tieris, having no more relation or proportion to one another than a line to a 

 plane, or a plane to a solid, or a finite to an infinite ; but that among them- 

 selves, each of those species of infinites are in given proportions, is what I 

 now intend to make plain, if possible. 



VOL. HI. 3 O 



