Сочинения. Том 3. История науки II

Г.К. Михайлов

Сочинения 

Товарищество научных изданий КМК
  Москва 2023

Том 3

История науки II

Товарищество научных изданий КМК
  Москва 2023

УДК [001:5](091)(081)
ББК 72.3я44+20г(0)я44
        М69

Михайлов Г.К. Сочинения. Том 3. История науки II. Москва: Товарищество 
научных изданий КМК. 2023. 346 с., портрет.

Третий том трудов историка науки Глеба Константиновича Михайлова (1929–2021) 
включает 15 работ по истории механики, гидравлики и ракетного дела, опубликованных 
в 1975–2008 гг. на русском, английском и немецком языках. Несколько работ посвящены 
трудам Даниила Бернулли (1700–1782) по гидродинамике. Дан очерк развития 
гидравлики в XVIII – первой половине XX века. Описаны некоторые аспекты развития 
истории механики. Другие исследования охватывают забытые работы ученого-
любителя Георга Букуа (1781–1851) по динамике систем с переменными массами, 
труды шотландского математика К. Макларена (1698–1746) по механике, историю 
изучения эффекта Робинса-Магнуса, ранние этапы развития теории реактивного 
движения и динамики систем переменного состава. Последняя работа посвящена 
зарождению и развитию механики в России и в особенности в Москве.
Для историков науки, физиков, математиков.

Ответственный редактор Кирилл Г. Михайлов

ISBN 978-5-907213-56-2
978-5-907533-81-3 (том 3)

© Г.К. Михайлов, текст, подбор 
иллюстраций, 1975–2021
© Товарищество научных изданий КМК, 
издание, 2023

СОДЕРЖАНИЕ

История науки II

Daniel Bernoulli, “Hydrodynamica” (1738)  ........................................................................ 9
Daniel Bernoulli und seine “Hydrodynamica”  .................................................................. 21
Die Werke von Daniel Bernoulli. Band 5. Hydrodynamik II. 
General preface ...............................................................................................................32 
General introduction ....................................................................................................... 36
Introduction to the additional texts 
on Geophysical Fluid Dynamics  ................................................................................. 100
Introduction to Daniel Bernulli‘s paper on Geophysical 
Fluid Dynamics and Barometrical studies .................................................................... 102
К истории изучения эффекта Робинса–Магнуса  ......................................................... 132
Colin Maclaurin und Newtons Bewegungsgesetz in der modernen 
Cartesischen Koordinatenform .. .................................................................................. 156
Hydrodynamics and Hydraulics  ....................................................................................... 167
Георг Букуа и начала динамики систем с переменными массами  ............................ 182
К истории динамики систем переменного состава  ..................................................... 231
Development of studies in the history of elasticity theory and structural mechanics  ...... 244
The Dynamics of Mechanical Systems with Variable Masses as Developed 
at Cambridge during the Second Half of the Nineteenth Century  .............................. 257
Ранние представления о природе реакции вытекающей струи 
и движения ракет  ....................................................................................................... 272
Ранние этапы развития теории реактивного движения и динамики ракет  ............... 284
Становление динамики систем с переменными массами в исследованиях 
по небесной механике  ............................................................................................... 301
Первые сто лет развития небесной механики тел переменного состава  .................. 323
Зарождение и развитие механики в России и в Москве .............................................. 332

Третий том сочинений Г.К. Михайлова включает труды по истории науки, не 
вошедшие в первые два тома. Как и в первых двух томах, порядок работ в основном 
соответствует общему содержанию проекта собрания сочинений, разработанному 
автором.
Более трети объема настоящего тома посвящены «Гидродинамике», одному из 
основных трудов Даниила Бернулли; ранее, во втором томе сочинений были опубликованы 
комментарии к первому тому трудов Д. Бернулли и его биографический 
очерк. Даны очерки развития гидравлики в XVIII – первой половине XX века 
и изучения истории некоторых аспектов механики (в т.ч. теории эластичности). 
В нескольких статьях подробно описаны незаслуженно забытые работы чешского 
ученого-любителя Георга Букуа первой половины XIX века по динамике систем 
переменного состава. Приведена история изучения эффекта Робинса-Магнуса. 
Дан очерк работ по Ньютоновой механике мало известного в России шотландского 
математика XVIII века Колина Макларена. Несколько работ посвящены ранним 
этапам развития теории реактивного движения, в т.ч. трудам У. Мура, давшего 
первую математическую теорию движения ракет, Ф.В. Бесселя, кембриджской математической 
школы XIX века, Х. Зеелигера, И.В. Мещерского, Т. Леви-Чивиты; 
рассказано о задаче Х. Гюльдена, формуле К.Э. Циолковского и многом другом. 
Справочный аппарат всех статей и очерков, за исключением очень сложно устроенных 
комментариев к пятому тому трудов Даниила Бернулли, полностью 
переработан и унифицирован. Написание всех формул выверено по исходным 
публикациям. Обозначения векторных величин унифицированы.
Работа над третьим томом шла гораздо труднее, чем над первыми двумя томами 
и затянулась на полтора года из-за особой сложности включенных в него текстов 
на пяти языках, русском, английском, немецком, французском и латыни, и 
множества формул. Работы Г.К. Михайлова, написанные в разные годы для разных 
журналов и сборников, содержат некоторые повторения, которые я не стал 
удалять, чтобы не нарушать логику и последовательность изложения материала.
Я особо благодарен моему брату, Кузьме Глебовичу Михайлову за предоставление 
фотографии, поддержку в работе и частичное финансирование издания 
этого тома.
Заключительный, четвертый том будет включать персоналии, публицистические 
работы Г.К. Михайлова, его воспоминания, семейные фотографии  и список 
публикаций.

Кирилл Г. Михайлов

От редактора

Besides introducing the fi rst hydraulic theory of the fl uid fl ow, this book is the 
most remarkable general work in theoretical and applied mechanics written in the 
pre-Lagrangean period of the 18th century, based on a deep physical understanding 
of mechanical phenomena and presenting many new ideas for the following scien-
tifi c progress.

First publication. Hydrodynamica, sive de viribus et motibus fl uidorum commentar-
ii. Opus academicum ab auctore, dum Petropoli ageret, congestum, Argentorati 
[= Strasbourg]: J.R. Dulsecker, printed by J.H. Decker, ‘Basiliensis’, 1738. 
[vi]+304 pages+12 tables with 86 fi gures.
New edition. In D. Bernoulli Werke, vol. 5 (ed. G.K. Mikhailov), Basel: Birkhäuser, 
2002.
Russian translation. Gidrodinamika, ili zapiski o silakh i dvizheniyakh zhidkostei 
(trans. V.S. Gokhman, with commentaries by A.I. Nekrasov and K.K. Baumgart), 
[Leningrad]: USSR Academy of Sciences, 1959. [Also many historical comments 
(including extracts from the draft manuscript of Hydrodynamica) and survey of 
Bernoulli’s life and work by V.I. Smirnov.]
German translation. Hydrodynamik oder Kommentare über die Kräfte und Be-
wegungen der Flüssigkeiten (trans. K. Flierl), Munich: Veröffentlichungen des 
Forschungsinstituts des Deutschen Museums für die Geschichte der Naturwissen-
schaften und der Technik, series C, Quellentexte und Übersetzungen, no. 1a, 1965. 
[Editor’s remarks, with mathematical misprints, in no. 1b.]
English translation. Hydrodynamics (trans. T. Carmody and H. Kobus), in D. Ber-
noulli Hydrodynamics and J. Bernoulli Hydraulics, New York: Dover, 1968, xvii–
xxii, 1–342. [Translation not always accurate [Binnie and Easterling, 1969].]
Manuscript. Draft in the Petersburg Archives of the Russian Academy of Sciences; 
to appear in Bernoulli Werke, vol. 4.
Related articles: Newton (§5), d’Alembert (§11), Lagrange on mechanics (§16).

Daniel Bernoulli, “Hydrodynamica” (1738)*

* Впервые опубликовано: Mikhailov G.K. 2005. Chapter 9. Daniel Bernoulli, “Hydrodynamica” 
(1738) // I. Grattan-Guinness (ed.). Landmark Writings in Western Mathematics, 1640–1940. Amster-
dam e.a.: Elsevier. P. 131–142.

Г.К. Михайлов Сочинения. Том 3. История науки II

1. Daniel Bernoulli’s life and work

Daniel Bernoulli (1700–1782) belonged to the well-known family of Swiss 
mathematicians; he was the second son of Johann I Bernoulli (1667–1748). Born 
in Groningen, he came as a child, with his father’s family, to Basel where he stud-
ied at the University. During almost two years the young Bernoulli tried to practice 
as a physician in Italy and was then invited, as a member of the illustrious family 
solely, to the Saint Petersburg Academy of Sciences that was organised in 1725. 
During over seven years of work in Russia he developed as a great scientist in the 
fi eld of pure and applied mathematics, confi rming the family’s fame. In 1733 he 
returned to Basel and lived there permanently thereafter, from 1733 as Professor 
of Anatomy and Botany, and from 1750 as Professor of Physics. He was gener-
ally recognised, honoured by election at the most prestigious European academies 
of Saint Petersburg, Berlin and Paris, as well as at the Royal Society of London. 
However, he never accepted fl attering invitations from the Berlin and Saint Peters-
burg sovereigns to leave Basel again.
Daniel Bernoulli published about 80 works, including 50 papers in the editions 
of the Petersburg Academy of Sciences and 10 prize-winningmemoirs of the Par-
is Academy. But there was only one large treatise — his famous Hydrodynamica, 
which had a complicated and partially dramatic fate.

2. General remarks

The contents of the Hydrodynamica are summarised in Table 1; its full title may 
be rendered ‘Hydrodynamics, or commentaries on the forces and motions of fl u-
ids’. In this book Bernoulli presented the earliest adequate theory of motion of an 
incompressible fl uid in tubes (vessels) and fl uid outfl ow through orifi ces, introduc-
ing the notion of the 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 fi rst model of the kinetic theory of gases, 
approaches the principle of conservation of energy, establishes a foundation for the 
analysis of effi ciency of machines, and he develops a theory of hydroreactive (water-
jet) ship propulsion, including a solution of the fi rst problem of motion of a variable-
mass system (see section 4 below).
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. Bernoulli’s treatise was to infl uence the entire development of me-
chanics and, especially, of applied mechanics, for at least a century. 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 immor-
tal Hydrodynamica’ in 1845, and Paul Du Bois-Reymond referred to ‘the enormous 
wealth of ideas which assures this work one of the fi rst places in the literature of 
Mathematical Physics of all ages’ in 1859.

Daniel Bernoulli, “Hydrodynamica” (1738)

Table 1. 
Summary by Sections of Bernoulli’s Hydrodynamica.

Sect.
Page
Topics
I
1
General introduction: historical survey, general principles of the theory.
II
17
Hydrostatics.
III
30
Fluid velocity at outfl ow from vessels.
IV
61
Duration of outfl ow.
V
90
Outfl ow from permanently full vessels.
VI
111
Fluid oscillation in tubes (vessels).
VII
124
Outfl ow from submerged vessels, and lost of living forces.
VIII
143
Flow through compound vessels with regard to loss of living forces.
IX
163
Hydraulic machines and their effi ciency; mechanical work.
X
200
Kinetic model of air, properties and motion of gases, cannon shooting.
XI
244
Rotational fl uid motion and fl uid fl ow in moving vessels.
XII
256
Pressure of moving fl uids on the tube (vessel) walls.
XIII
278
Reaction and impact of outfl owing jets, propelling ships by jet ejection. [End 304.]

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 de-
scent 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 ev-
erywhere 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 fl uid mo-
tion, reducing any fl ow 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 the fl uid fl ow by Bernoulli and Leonhard Euler also ear-
lier. Coincidence of their results presented independently in the Petersburg Academy 
of Sciences in 1727 forced Euler to change his scientifi c plans and to leave this fi eld 
for his elder colleague (Mikhailov, 2000). When Bernoulli developed his work, besides 
studying many special cases of fl ow, he achieved two new fundamental results. He 
succeeded in explaining the nature and determining the value of the hydrodynamic 
pressure of moving fl uids on the wall of tubes and he discovered the principal role of 
losses of living forces in the fl uid fl ow, especially at sudden changes of the fl ow 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 fi nal solution of the problem.
It should be recognized that the term hydrodynamics introduced by Daniel Ber-
noulli for the whole theory of fl uid motion is now applied only for the general fl uid 
dynamics, but is not used for the quasi-one-dimensional (hydraulic) theory of fl uid 
fl ow that was in fact developed by Bernoulli.