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557 



THURSDAY, JANUARY 29, 1920. 



THE WORKS OF TORRICELLI. 



Opere di Evangelista Torricelli. Edite da Gino 

 Loria e Giuseppe Vassura. Vol. i. Parte i. 

 Pp. xxxviii + 407. Vol. i. Parte 2. Pp. 482. 

 Vol. ii. Pp.320. Vol. iii. Pp.521. (Faenza : 

 G. Montanari, 1919.) Price 60 franchi the 3 

 vols. 



THIS work consists nominally of three volumes, 

 of which the first contains mathematical 

 papers, the second papers on mechanics, and the 

 third the correspondence of Torricelli. In reality 

 there are four volumes. It is to be hoped that 

 this inconvenient way of describing- the volumes 

 of a work will soon go out of fashion. This is 

 the first complete edition of the collected writings 

 of Evangelista Torricelli ; it is published under the 

 auspices of the municipality of his native town, 

 Faenza, who have in this way raised a lasting 

 memorial to their celebrated townsman. 



Torricelli was born in 1608, and died in 

 1647. In the introduction to vol. i., Signor 

 Loria has given the few particulars about his life 

 which it has been possible to gather. In 1627 Torri- 

 celli went to Rome to study under Benedetto 

 Castelli, a disciple of Galileo, who in the previous 

 year had been appointed professor of mathematics 

 there. He seems to have remained at Rome until 

 October, 1641, when Galileo, who had heard from 

 Castelli of the valuable work in dynamics done by 

 his pupil, invited him to Arcetri. Torricelli gladly 

 accepted the invitation, but was only for a few 

 months able to benefit by the instruction thus 

 offered, as Galileo died on January 6, 1642. 

 Soon after, Torricelli was appointed to the post 

 of mathematician to the Grand Duke of Tuscany 

 held by Galileo, and spent the few remaining years 

 of his life at Florence until his death on October 

 25, 1647. The subsequent fate of his unpublished 

 papers and letters is told in the introduction; they 

 had a narrow escape from total destruction in 

 1733, when they were sold as waste paper to a 

 pork butcher. Fortunately, the first customer to 

 whom one of the papers was handed, wrapped 

 round a sausage, was Nelli, the biographer of 

 Galileo, who to his horror recognised the hand- 

 writing of the great man, and at once secured the 

 whole pile of papers. 



It was the study of Galileo's " Discorsi e dimon- 

 strazioni matematiche intorno a due nuove 

 scienze " which led Torricelli to make further in- 

 vestigations in dynamics and hydrodynamics. His 

 principal results appeared in two books, " De motu 

 gravium naturaliter descendentium '" and " De 

 NO. 2622, VOL. 104] 



motu projectorum," which appeared in a volume 

 of tracts, "Opera geometrica," published in 1644. 

 It is the second of these which contains his experi- 

 ments on the flow of fluids from vessels through 

 a small orifice. These experiments had been com- 

 menced by Castelli, whose erroneous result, that 

 the velocity of outflow was proportional to the 

 depth from the surface, was corrected by Torri- 

 celli. He showed that the quantity of water flow- 

 ing from a hole in the horizontal bottom of a vessel 

 in equal times was proportional to the series of 

 odd numbers, if the quantity flowing out in the 

 last unit of time was put equal to one. A particle 

 from the surface flows out with a velocity equal 

 to that which it would have acquired by falling 

 from its original height over the opening. There- 

 fore the outflowing velocity is proportional to the 

 square root of the height. From this it followed 

 that the figure of a jet issuing from a small hole 

 in the side of a vessel is a parabola. Among Torri- 

 celli 's discoveries is also the mechanical principle 

 that if two or more bodies are so connected that 

 their motion will neither make their centre of 

 gravity rise nor fall : they are in equilibrium. 



The fame of Torricelli rests, however, mainly 

 on his discovery of air-pressure. He knew from 

 Galileo that water would not rise in a tube closed 

 at the top more than 33 ft., which was supposed 

 to indicate that Nature's dislike to empty space 

 [horror vacui) had a limit. Torricelli thought that 

 this was nonsense and that it would be interesting 

 to experiment with a heavier fluid. He anticipated 

 that mercury would rise only to one-thirteenth of 

 the height to which water would rise. At his in- 

 stigation Viviani made the experiment in 1643, and 

 found that the column of mercury in a tube closed 

 at one end and inverted in a vessel containing 

 mercury sank to about 30 in. and remained there. 

 Torricelli found, however, by repeated measures 

 that the height of the column of mercury was 

 always changing, and he rightly interpreted this 

 as indicating changes in the pressure exercised 

 by the air on the open surface of the mercury. In 

 a letter to his friend Ricci of June 11, 1644 

 (vol. iii., p. 186), he says that he has made these 

 experiments, not to produce a vacuum, but chiefly 

 to make an instrument for measuring changes in 

 the density of the air. He explains that we live 

 at the bottom of an ocean of air, the weight of 

 which at the surface of the earth is about equal to 

 one-four-hundredth of the weight of an equal 

 volume of water. During the remaining three 

 years of his life Torricelli does not seem to have 

 pursued these researches further, and the new 

 doctrine was not universally accepted until Pascal 

 in 1648 had proved the connection of barometric 

 height with the height of the observer above the 



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