410 



HYDRODYNAMICS. 



H ivory, larly directed to t])e doctrine of fluids; but his disco- 

 very of the uniform acceleration of gravity paved the 



Galileo. way for the rapid progress of this branch of science. 



Born 15(J4. [ n the Syxema Cosnticum of this great astronomer, we 

 "' find some occasional observations on the oscillation of 

 fluids, which are marked with his usual sagacity; and 

 in the first dialogue of iiis Mechanics, Sagredo enters in- 

 to a very interesting inquiry respecting the ascent of 

 water in pumps. Galileo had studied the operation of 

 a sucking pump, which had been erected to raise wa- 

 ter out of a cistern. He describes the pump as having 

 its piston raised high above the surface of the fluid, and 

 he remarks, that in this case the water ascends by the 

 attraction of the piston, whereas in pumps where the 

 piston is in the lower part of the tube, the water rises 

 by the impulse of the piston. He was surprised, how- 

 ever, to find, that, when the water descended to a cer- 

 tain point, the pump ceased to act, and continued to 

 lose its power, by any further subsidence of the fluid. 

 Being quite satisfied that the pump was broken, he im- 

 mediately sent for the pump maker, who, after exa- 

 mining the machine, assured him, " that the water 

 would not suffer itself to rise to a greater height than 

 1 8 cubits, whatever were the dimensions of the pump." 

 After reflecting upon this singular fact, Galileo satisfies 

 himself with the following explanation. When a rod 

 of any solid substance whatever is suspended by one 

 end, it may be made of such a length as to break by 

 its own weight ; and, in like manner, if a rod or column 

 of water is raised in a pump to the height of 18 cu- 

 bits, its weight overpowers the attraction of the piston 

 and the mutual conesion of the fluid particles. * 



Toricelli. This extraordinary explanation of the ascent of water 



Bor " 16 ' )8 - in pumps attracted, no doubt, the attention of his pupil 

 Evangelista Toricelli, by whom the fact was afterwards 

 completely explained ; and having learned from his 

 master that the air possessed weight like all other bo- 

 dies, f he entered upon the study of this branch of Hy- 

 drodynamics with very singular advantages. In the 

 year 1 64*3, the year after the death of his master, Tori- 

 celli being desirous of making an experiment on a small 

 scale in the vacuum left between the piston of a pump, 

 and the column of water which it raised, it occurred 

 to him, that, if he substituted in place of the wa- 

 ter a denser fluid, such as mercury, the same cause 

 which supported the water would support a column 

 of mercury of the same height. He communicated 

 this idea to his friend Viviani, who performed the expe- 

 riment with success, and Toricelli afterwards repeated 

 it with considerable modifications. He accordingly 

 provided a glass tube about three feet long, and her- 

 metically sealed at one end, and having filled it with 



mercury, he closed it at ihe open end with his fin- History, 

 gcr, and inverted it in a basin of mercury. Upon ^""""VT"*' 

 withdrawing his finger, the column of mercury de- loricc1 ''- 

 scended, and settled at the height of about 29 inches in 

 the tube. Toricelli was not immediately aware of the 

 cause of this singular result ; but a little reflection con- 

 vinced him that it was owing to the pressure of the ex- 

 ternal air, and that the weight of the atmospherical co- 

 lumn was balanced by the '2Q inches of mercury in the 

 tube, and by the 33 feet of water in the bore of the 

 sucking pump. When this explanation was fully im- 

 pressed upon his mind, Toricelli is said to have regret- 

 ted, with a feeling of generosity of which there is no 

 other example, that it had not fallen to the lot of his 

 master to complete a discovery of which he had the me- 

 rit of laying the foundation. 



The labours of Toricelli were not confined to Hydro- 

 statics. Having observed, that when a jet d'eau \vat 

 formed by the ascent of water through a small adju- 

 tage, it rose nearly to the same height as the reservoir 

 from which it came, he sagaciously conjectured, that it 

 ought to move with the velocity which it would have 

 acquired by falling through the same height. Hence 

 he deduced the fundamental proposition, that, abstract- 

 ing all resistances, the velocities of fluids in motion are 

 in the subduplicate ratio of the pressures. This result 

 was published in 16'43 at the end of his treatise De 

 Motu Graviitm naturaliter accelerate, and though true 

 only in small orifices, it was confirmed by the experi- 

 ments of Raphael Magiotti, and paved the way for the 

 discovery of the more complex law, which regulates 

 the motion of fluids, when the area of the orifice has a 

 considerable magnitude compared with the horizon- 

 tal section of the vessel. 



The subject of running water had been previously Castelli. 

 studied by Benedict Castelli, the disciple of Galileo, Born 157T. 

 and the first master of Toricelli. Pope Urban VIII. Died 16*4. 

 had requested him to devote his attention to this inte- 

 resting subject, when he was employed in teaching ma- 

 thematics at Rome ; and in order to discharge the duty 

 which was thus imposed upon him, he made numerous 

 experiments, of which he published a full account in a 

 small treatise Delia Mesura dell' acque correnli, which 

 appeared in 16'28. In this work he explains several 

 phenomena relative to the motion of fluids in rivers 

 and canals of any shape, and he shews, that when 

 the water has come to a state of permanent motion, 

 the velocities at different sections of the river or canal 

 are inversely as their areas. He applies these general 

 propositions to the course of some rivers, and he ex 

 plains several phenomena in a manner tolerably satis- 

 factory. The conclusions which he draws are gene- 



* As a very different account of this interesting anecdote is given in all the Histories of Hydrostatics and Pneumatics, we have subjoined 

 the account of it given by Galileo himself in his Discnrsus ct Demonttrationes Mathematicee. Dial. vol. i. p. IS. 



" SAGR. Et ego hujus discur&us ope causam invenio ciijusdam effectus, qui diutUsiine mcntem meam aclmiratione plenam, intellectu veo, 

 vacuum reliquit Observavi Cisternam, in qua ad extruhendain aquam conslructa erat Antlia cujus ope minori cum labore eandcm aut ma- 

 jorem aqua; quantitatem, quam urnis communibus, iorsan (sed fiustra) attolli posse credebam : Habetque hcec Antlia suum Epistomium 

 et lingulam in alto positam, ita ut per attractionem non vero per iinpul&um adscendat aqua, sicut isue Antlia faciunt, qua a parte inferior! 

 suum opus exercent. Hate autem magna copia aquara attrulu't, donee ea in cisterna ad determinatam quandam constiterit altitudinem ; 

 ultra quam si subsederit inutilis est Antlia. Ego, cum prima vice accidens istud observarem, instrumentum fractum esse crcdens, Fabrum 

 nccersivi, ut illud repararet ; qui nulli rei istum detectum adscribendum etse mihi respondebat, praterquam ipsi aquae, quse nimis depressa 

 ad tantam altitudinem attolli se non patiebatur ; subjungens ncc Antlia nee quavis allia machina, qua; aquam per attractionem elcvat, earn 

 nequidem pili lalitudine altius attolli quam octodecim cubitos ; et sive largior sive angustior sit Antlia, hanc maxime dtlinitam ejus esse 

 altitudinem. Et ego, licet jam pernoscam, chordam, massam ligneam et virgam ferream eousque prolongari posse, ut in ahum erecta pror 

 prin difftingatur pondere, ejus imprudcntia: hucusque reum me feci, ut idem in chorda aut virga aquae multo facilius evenire posse non 

 meminerim : et quid illud quod per Antliam attrahitur, est aliud, quam Cylindrus aqueus qui superne aflixus cum magis magisque pro- 

 longetur, ad eum tandem attingit terminum ultra qucm elevata, a pondere suo excessivo ad in star chorda; disrumpitur." 



+ This important doctrine is demonstrated by Galileo from two experiments, which he describes in his Discursus et Demonat. Malkcmat. 

 Dial. vol. i. p. 71, 72. 







