Table Of ContentUNIVERSITY
OF
ASfRONOMYUBRARV
JEr %ibris
L5 BR AR Y
OF THE
ASTRONOMICAL
SOCIETY
FACiFJC
241
HYDEODYNAMIC
S
.
Sonton: C. J. CLAY AND SONS,
CAMBRIDGE UNIVEKSITY PEESS WAREHOUSE,
AVE MARIA LANE.
laggoto: 263, ARGYLE STREET.
ILetpjig: F. A. BROCKHAUS.
fo lorfc: MACMILLAN AND CO.
HYDRODYNAMICS
BY
HORACE LAMB, M.A., F.R.S.
PBOFESSOB OF MATHEMATICS IN THE OWENS COLLEGE,
VICTORIA UNIVERSITY, MANCHESTER;
FORMERLY FELLOW OF TRINITY COLLEGE, CAMBRIDGE.
CAMBRIDGE
:
AT THE UNIVERSITY PRESS.
1895
[All Rights reserved.]
ASffiONOMYLIBRARY
Cambridge:
PRINTED BY J. & C. F. CLAY,
AT THE UNIVERSITY PRESS.
ASTRONOMY
PREFACE.
rilHIS book may be regarded as a second edition of a "Treatise
--
on the Mathematical Theory of the Motion of Fluids,"
published in 1879, but the additions and alterations are so ex
tensive that it has been thought proper to make a change in the
title.
I haveattempted toframe a connected accountofthe principal
theorems and methods of the science, and of such of the more
important applications as admit of being presented within a
moderate compass. It is hoped that all investigations of funda
mental importance will be found to have been given with sufficient
detail, but in matters of secondary or illustrative interest I have
often condensed the argument, or merely stated results, leaving
the full working out to the reader.
In making a selection of the subjects to be treated I have
been guided by considerations ofphysical interest. Longanalytical
investigations, leading to results which cannot be interpreted,
have as far as possible been avoided. Considerable but, it
is hoped, not excessive space has been devoted to the theory of
waves of various kinds, and to the subject of viscosity. On the
other hand, some readers may be disappointed to find that the
theory ofisolated vortices is still given much in the form in which
it was. left by the earlier researches of von Helrnholtz and Lord
Kelvin, and that little reference is made to the subsequent
investigations of J. J. Thomson, W. M. Hicks, and others, in this
field. The omission has been made with reluctance, and can be
justified only on the ground that the investigations in question
L. b
M6772O1
VI PREFACE.
derive most oftheir interest from their bearing on kinetic theories
of matter, which seem to lie outside the province ofa treatise like
the
present.
I have ventured,in one important particular,to make a serious
innovation in the established notation of the subject, by reversing
the sign of the velocity-potential. This step has been taken not
without hesitation, andwas only finallydecided upon when I found
that it had the countenance of friends whose judgment I could
trust but the physical interpretation of the function, and the
;
far-reachinganalogywith the magnetic potential, are both so much
improved by the change that its adoption appeared to be, sooner
or later, inevitable.
I have endeavoured, throughout the book, to attribute to their
proper authors the more important steps in the development of
the subject. That this is not always an easy matter is shewn by
the fact that it has occasionally been found necessary to modify
references given in the former treatise, and generally accepted as
correct. I trust, therefore, that any errors of ascription which
remain will be viewed with indulgence. It may be well,
moreover, to warn the reader, once for all, that I have allowed
myself a free hand in dealing with the materials at my disposal,
and that the reference in the footnote must not always be taken
to imply that the method of the original author has been
closely followed in the text. I will confess, indeed, that my
ambition has been not merely to produce a text-book giving a
faithful record of the present state of the science, with its
achievements and its imperfections, but, if possible, to carry it a
step further here and there, and at all events bythe due coordina
tion of results already obtained to lighten in some degree the
labours of future investigators. I shall be glad if I have at least
succeeded in conveying to my readers some of the fascination
which the subject has exerted on so long a line of distinguished
writers.
In the present subject, perhaps more than in anyother depart
ment of mathematical physics, there is room for Poinsots warning
