BORELLI ON SWIMMING. 385 



chine, and Torricellian tube, air is expanded to a remarkable rarity. 

 This being granted, that the same operation may be perceived more 

 clearly, first, in the same fluid, retaining the same degree of gravity, let 

 the syringe, AB, in which the piston, CD, being inserted, with its 

 stop -cock tightly pressing upon the smooth internal superficies, let 

 there remain a portion of air, DB, which may occupy the half of 

 the internal space of the syringe, and the spiracle, M, being stopped, 

 let the piston, cd, be drawn out, until the base, d, is brought near 

 the orifice, a, and is there violently retained by the handle, the internal 

 air, db, being rarefied, will fill double the space it did in its first natu- 

 ral expansion, DB. 



In the third place, let the same portion of air, BD, be compressed, by 

 violently pressing down the piston, K%, until it nearly touches the 

 bottom of the syringe, ftp,, and let it be firmly kept there by the handle, 

 in these three constitutions, the bulks or spaces occupied by the same 

 machines will be unequal ; for instance, CAB will be greater than Kafi, 

 and less than cab; but the absolute weights of the same bodies will be 

 equal to each other, as they consist of the same syringe, the same piston, 

 and the same portion of air. Hence it follows, that the gravities of the 

 same unequal bodies are very much altered in appearance in respect of 

 the water. For if the body of water, EF, be equal to the space CABM ; 

 and the body of water, He, be equal to the space Ka.fi/ji ; and in like 

 manner the body of the same water, eG, be equal to the space, cab ; 

 and the three bodies of water, ef, EF, and sH, are understood to be 

 equal to each other ; the body, EF, will be greater than tH, and 

 smaller than eG. Now if the absolute weights of the syringe, CABM, 

 and the bulk of the water be equal among themselves, they will also be 

 equally heavy ; and, therefore, the syringe, CABM, being sunk within 

 the water, will remain equipoised in it, since their bulks and weights 

 are equal*. But the elongate syringe, cabm, will be lighter than the 

 fluid body eG, which is equal to it ; because the weight of the water, 

 e&, is greater than the weight EF, or of the syringe itself, CB, or cb ; 

 and, thereforef, it does not remain sunk down within the fluid, but 

 ascends, until some portion of it, cs, rests on the surface, of the 

 water. And on the other hand, the syringe, /c/3, being compressed or 

 shortened, will be heavier than the fluid, tH, a body equal to it ; and 

 for the same reason, v/3 descends and rests, floating at the bottom of 

 the vessel. 



* In Arch. Auct. dc Ins. Flu. Prop. 2. f Jbid. Prop. 1. 



