276 LECTURE XXX. 



conical and conoidal solids will be stable, and in what cases unstable. 

 Archimedes was the inventor of the mode of measuring the bulk of a solid 

 by immersing it in a fluid : to us, indeed, there appears to have beef\ little 

 difficulty in the discovery, but the ancients thought otherwise. Vitruvius 

 observes that this invention indicates a degree of ingenuity almost in- 

 credible. The philosopher himself is said to have valued it so highly, 

 that when it first occurred to him, in a public bath, he hastened home in 

 an ecstasy without recollecting to clothe himself, in order to apply it to 

 the determination of the specific gravity of Hiero's crown and to the 

 detection of the fraud of the maker, who had returned the crown 'equal 

 in weight to the gold that was given him, but had adulterated it with 

 silver, and imagined that on account of the complicated form of the work, 

 which rendered it almost impossible to determine its bulk by calculation, 

 he must infallibly escape conviction. The hydrometer, which has some- 

 times been attributed to Hypatia, a learned Greek lady of Constantinople, 

 is mentioned by Fannius,* an early writer on weights and measures, and 

 is ascribed by him to Archimedes. 



The forcing pump, or rather the fire engine, was the invention of 

 Ctesibius of Alexandria, the greatest mechanic of antiquity after Archi- 

 medes. He is also said to have invented the clepsydra, for the hydraulic 

 measurement of time, and Philot informs us that he constructed an air 

 gun, for propelling a stone, or rather a ball, by means of air previously 

 condensed by a syringe. The ball was not immediately exposed to the 

 action of the air, but was impelled by the longer end of a lever, while the 

 air acted on the shorter. Ctesibius is said to have been the son of a barber, 

 and to have had his attention turned to mechanics and pneumatics, by 

 being employed to fit a shutter, with a counterpoise sliding in a wooden 

 pipe, for his father's shop window.^ 



Hero was a cotemporary, and a scholar of Ctesibius ; he describes, in 

 his treatise on pneumatics, a number of very ingenious inventions, a few 

 of which are calculated for utility, but the greater part for amusement 

 only ; they are principally siphons variously concealed and combined, 

 fountains, and water organs, besides the syringe and the fire engine. The 

 description of this engine agrees precisely with the construction which is 

 at this day the most usual ; it consists of two barrels, discharging the 

 water alternately into an air vessel ; and it appears from Vitruvius, that 

 this was the original form in which Ctesibius invented the pump. Hero 

 supposes the possibility of a vacuum in the intervals of the particles of 

 bodies, observing that without it no body could be compressible ; but he 

 imagines that a vacuum cannot exist throughout a perceptible space, and 

 thence derives the principle of suction. The air contained in a given 

 cavity may be rarefied, he says, by sucking out a part of it, and he 

 describes a cupping instrument, which approaches very nearly to the 

 nature of an imperfect air pump. (Plate XXIV. Fig. 324.) 



After the time of Ctesibius and Hero, the science of hydraulics made 



* Rhemnius Fannius Palsemon de Ponderibus et Mensuris. 



f Duten's Inquiry into the Origin of the Discoveries attributed to the Moderns, 

 Lond. 1769, p. 186. 



I Vitruvius, ix. 9. A figure of tbe clepsydra is given in Perrault's translation. 



