## Hydrodynamica, sive De Viribus et Motibus Fluidorum Commentarii. Opus Academicum.

Strasbourg: Johann Reinhold Dulsseker, 1738.

First edition, a very fine copy from the library of Michel Chasles, of Bernoulli’s epochal work on fluid dynamics and the kinetic theory of gases, containing the famous ‘Bernoulli equation’ for fluid flow. “Bernoulli's *Hydrodynamica *[was] one of the major works initiating the mathematical study of fluid flow. Bernoulli presents the following equation for steady, non-viscous, incompressible flow: *p *+ ½*ρv*^{2} + *ρgy *= *A*, where *p *symbolizes pressure, *ρ* density, *v *velocity, *g *the acceleration of gravity, *y *height, and *A *a constant. He also examines the equilibrium oscillation of an inertialess ocean, and explicitly states that the flow equations are appropriate not only for the more common applications of fluid dynamics but also for the flow of blood in veins and arteries. Bernoulli, like Galileo Galilei in 1638 and Christiaan Huygens, assumes conservation of *mv*^{2} rather than conservation of momentum *mv, m *and *v *symbolizing a body’s mass and velocity respectively” (Parkinson, *Breakthroughs*)*. *The *Hydrodynamica *also “initiates the mathematical study of the kinetic theory of gases … and analytically deduces Boyle’s Law that the volume and pressure of a gas are inversely related, a law originally obtained empirically. To establish the analytical derivation, Bernoulli follows Robert Hooke in visualizing the pressure of a gas as resulting from huge numbers of impacts on the walls of the container by hard, fast-moving gas particles. Bernoulli’s explanation, based on random motions of the gas particles, is more modern than an earlier attempt by Isaac Newton to explain Boyle’s Law by assuming relatively motionless particles which repel each other with a force inversely proportional to the distance between them” (*ibid*.)*. *“Besides introducing the first hydraulic theory of fluid flow, this book is the most remarkable general work in theoretical and applied mechanics written in the pre-Lagrangian period of the 18th century, based on a deep physical understanding of mechanical phenomena and presenting many new ideas … Bernoulli’s treatise was to influence the entire development of mechanics and, especially, of applied mechanics, for at least a century” (*Landmark Writings*, pp. 131-2). “In 1738 Bernoulli published *Hydrodynamica.* In this treatise, which was far in advance of his time in many ways, is his famous equation governing the flow of fluids in terms of speed, pressure, and potential energy, upon which much modern technology is based, especially aerodynamics” (DSB).

*Provenance*: Michel Chasles (1793-1880), French mathematician and historian of mathematics (bookplate); initials ‘M R’ (unidentified) on covers; Latin inscription from a student to professor (or professor to student) dated 1773 on first flyleaf.

“In this book Bernoulli presented the earliest adequate theory of motion of an incompressible fluid in tubes (vessels) and fluid outflow through orifices, introducing the notion of hydrodynamic pressure. However, the treatise is not restricted to theoretical hydraulics. In the subsequent sections, he opens up new branches of physics and mechanics. He develops the first model of the kinetic theory of gases, approaches the principle of conservation of energy, establishes a foundation for the analysis of efficiency of machines, and develops a theory of hydroreactive (water-jet) ship propulsion, including a solution of the first problem of motion of a variable-mass system.

“*Hydrodynamica *contains many profound remarks on the physical background of a wide range of mechanical effects, and its study remains most edifying also to the modern reader … However, many of his advanced ideas were far ahead of his time and met an adequate understanding only later. In the 19th century, J.-V. Poncelet called Bernoulli’s treatise ‘the immortal *Hydrodynamica*’ in 1845, and Paul Du Bois-Reymond referred to ‘the enormous wealth of ideas which assures this work one of the first places in the literature of Mathematical Physics of all ages’ in 1859.

“*Hydrodynamica *is founded mainly on the *principle of conservation of ‘living forces’ *(that is, kinetic energy). Bernoulli preferred to use this principle not in its traditional form, received with hostility by Newtonians, but in Christiaan Huygens’s formulation that Bernoulli named the *principle of equality between the actual descent and potential ascent*: ‘If any number of weights begin to move in any way by the force of their own gravity, the velocities of the individual weights will be everywhere such that the products of the squares of these velocities multiplied by the appropriate masses, gathered together, are proportional to the vertical height through which the centre of gravity of the composite of the bodies descends, multiplied by the masses of all of them’.

“As to hydraulics proper, Bernoulli’s considers only quasi-one-dimensional fluid motion, reducing any flow to this case by means of the *hypothesis of plane sections*: he does not distinguish between tubes and vessels. The principle of conservation of living forces was used for studying fluid flow by Bernoulli and also by Leonhard Euler. Coincidence of their results presented independently in the Petersburg Academy of Sciences in 1727 forced Euler to change his scientific plans and to leave this field for his elder colleague. When Bernoulli developed his work, besides studying many special cases of flow, he achieved two new fundamental results. He succeeded in explaining the nature and determining the value of the hydrodynamic pressure of moving fluids on the wall of tubes and he discovered the principal role of losses of living forces in the fluid flow, especially at sudden changes of the flow cross-sections. The former gave an instrument to engineers for calculation of tube strength and the latter served, in addition, a step to the general *principle of conservation of energy*. Bernoulli concluded also the sharp discussion of many years on the impact and reaction of emitting jets, giving the final solution of the problem” (*Landmark Writings*, pp. 132-3).

Bernoulli composed the first version of this work at St. Petersburg in the early 1730s; its forthcoming publication was announced in the September 1734 issue of the journal *Mercure Suisse*. The following December Bernoulli, now in Basel, wrote to Euler: ‘My *Hydrodynamica *is now really being printed by Mr. Dulsecker, and he gives me, besides 30 copies, even 100 thalers of royalty’. However, the actual printing of the book seems to have begun only in 1737, and it finally appeared at the end of April or the beginning of May 1738. In May, Bernoulli sent the first copies of his treatise to St. Petersburg and asked Euler for his comments, but the parcel was lost on the way and it was not until spring 1739 that Euler saw a copy of the book and warmly congratulated its author: “I have read through your incomparable Treatise with full attention and have drawn immense gain from it. I congratulate you, Sir, from all my heart on the felicitous execution of such a difficult and obscure topic, as well as on the immortal fame thus gained. The entire execution of the project deserves all conceivable attention, and all the more so as it is not accessible to rigorous mathematics, but demands the help of several important physical principles, which you have known to employ to indescribable advantage.”

In contrast to Euler’s appreciation, *Hydrodynamica *became the focus of a bitter dispute between Daniel and his father Johann I. Although the details are disputed, it seems that Johann saw a copy of Daniel’s book and used it to compose his own work on the subject, *Hydraulica*, keeping this secret from his son. Johann published *Hydraulica* at the beginning of 1743 in his *Opera Omnia*, adding the subtitle *now for the first time disclosed and directly shown from purely mathematical foundations, 1732*. Daniel was incensed by Johann’s pretence that his *Hydraulica* had been composed some six years before his own work had been published, and the resulting rift between father and son was never completely healed.

“Daniel Bernoulli (1700-1782) was the second son of Johann Bernoulli, who first taught him mathematics. After studying philosophy, logic, and medicine at the universities of Heidelberg, Strasbourg, and Basel, he received an M.D. degree (1721). In 1723–24 he wrote *Exercitationes quaedam Mathematicae *on differential equations and the physics of flowing water, which won him a position at the influential Academy of Sciences in St. Petersburg, Russia. Bernoulli lectured there until 1732 in medicine, mechanics, and physics, and he researched the properties of vibrating and rotating bodies and contributed to probability theory. In that same year he returned to the University of Basel to accept the post in anatomy and botany. By then he was widely esteemed by scholars and also admired by the public throughout Europe.

“Between 1725 and 1749 Daniel won 10 prizes from the Paris Academy of Sciences for work on astronomy, gravity, tides, magnetism, ocean currents, and the behaviour of ships at sea. He also made substantial contributions in probability. He shared the 1735 prize for work on planetary orbits with his father, who, it is said, threw him out of the house for thus obtaining a prize he felt should be his alone. Daniel’s prizewinning papers reflected his success on the research frontiers of science and his ability to set forth clearly before an interested public the scientific problems of the day. In 1732 he accepted a post in botany and anatomy at Basel; in 1743, one in physiology; and in 1750, one in physics” (Britannica).

Barchas 175; Norman 215; Parkinson pp. 155-6; Roberts and Trent pp. 34-5. Mikhailov, ‘Daniel Bernoulli, *Hydrodynamica *(1738),’ Chapter 9 in *Landmark Writings in Western Mathematics 1640-1940*, Grattan-Guinness (ed.), 2005. For a detailed analysis of the work, see Truesdell, ‘Rational fluid mechanics, 1687-1765,’ in Euler *Opera Omnia*, Ser. 2, Vol. 12 (1954), pp. vii–cxxv (especially pp. xxiii–xxxviii).

4to (243 x 190 mm), pp. [viii] 304, title in red and black, with engraved vignette and 12 folding engraved plates by Johann Martin Weis. Contemporary sheep panelled in silver-gilt, with monogram 'M R' on covers, edges gauffered and gilt (binding a bit worn at corners and foot of spine).

Item #5219

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Price:
$25,000.00
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