UNIVERSITYOFASfRONOMY UBRARVJEr%ibrisL5 BR AR YOF THEASTRONOMICAL SOCIETYFACiFJC241.HYDEODYNAMICSSonton: C. J. CLAY AND SONS,CAMBRIDGE UNIVEKSITY PEESS WAREHOUSE,AVE MARIA LANE.STREET.laggoto: 263, ARGYLE: F. A. BROCKHAUS.ILetpjig: MACMILLAN AND CO.fo lorfcHYDRODYNAMICSBYF.R.S.HORACE M.A.,LAMB,PBOFESSOB OF MATHEMATICS IN THE OWENS COLLEGE,VICTORIA MANCHESTERUNIVERSITY, ;CAMBRIDGE.FORMERLY FELLOW OF TRINITY COLLEGE,CAMBRIDGE :AT THE UNIVERSITY PRESS.1895[All Rights reserved.]ASffiONOMY LIBRARYCambridge:& C. F.PRINTED BY J. CLAY,THE UNIVERSITY PRESS.ATASTRONOMYPREFACE."rilHIS a abook be as second edition of Treatisemay regarded-- on the Mathematical of the Motion of Fluids,"Theoryin but the additions and alterations are so ex1879,publishedtensive that it has been to make a in thethought proper changetitle.I have to frame a connected account of theattempted principaltheorems and methods of the and of such of the morescience,aas admit of withinimportant applications being presentedmoderate It is that all of fundacompass. hoped investigationsmental will be found to have been with sufficientimportance givenbut in matters of or illustrative interest I havedetail, secondaryoften condensed the or stated results,argument, merely leavingthe full out to the reader.workingIn a selection of the to be treated I havemaking subjectsbeen considerations of interest.guided by physical Long analyticalbeto results which ...
UNIVERSITY
OF
ASfRONOMY UBRARV
JEr%ibrisL5 BR AR Y
OF THE
ASTRONOMICAL SOCIETY
FACiFJC
241.HYDEODYNAMICSSonton: C. J. CLAY AND SONS,
CAMBRIDGE UNIVEKSITY PEESS WAREHOUSE,
AVE MARIA LANE.
STREET.laggoto: 263, ARGYLE
: F. A. BROCKHAUS.ILetpjig
: MACMILLAN AND CO.fo lorfcHYDRODYNAMICS
BY
F.R.S.HORACE M.A.,LAMB,
PBOFESSOB OF MATHEMATICS IN THE OWENS COLLEGE,
VICTORIA MANCHESTERUNIVERSITY, ;
CAMBRIDGE.FORMERLY FELLOW OF TRINITY COLLEGE,
CAMBRIDGE :
AT THE UNIVERSITY PRESS.
1895
[All Rights reserved.]ASffiONOMY LIBRARY
Cambridge:
& C. F.PRINTED BY J. CLAY,
THE UNIVERSITY PRESS.ATASTRONOMY
PREFACE.
"rilHIS a abook be as second edition of Treatisemay regarded
-- on the Mathematical of the Motion of Fluids,"Theory
in but the additions and alterations are so ex1879,published
tensive that it has been to make a in thethought proper change
title.
I have to frame a connected account of theattempted principal
theorems and methods of the and of such of the morescience,
aas admit of withinimportant applications being presented
moderate It is that all of fundacompass. hoped investigations
mental will be found to have been with sufficientimportance given
but in matters of or illustrative interest I havedetail, secondary
often condensed the or stated results,argument, merely leaving
the full out to the reader.working
In a selection of the to be treated I havemaking subjects
been considerations of interest.guided by physical Long analytical
beto results which cannotinvestigations, leading interpreted,
have as far as been avoided. Considerable itbut,possible
is not excessive has been devoted to the ofhoped, space theory
waves of various theand to the of Onkinds, subject viscosity.
other some readers be to find that thehand, may disappointed
of isolated vortices is still much in the form in whichtheory given
it was. left the and Lordearlier researches of von Helrnholtzby
and that little reference is made to theKelvin, subsequent
of J. J. W. M. and in thisothers,investigations Thomson, Hicks,
field. The omission has been made with and can bereluctance,
on the inthat thejustified only ground investigations question
L. b
M6772O1VI PREFACE.
derive most of their interest from their on kinetic theoriesbearing
of which lie outside the of a treatise likeseem tomatter, province
the
present.
I in to make a serioushave oneventured, important particular,
innovation in the established notation of the reversingsubject, by
the of This taken notthe has beensign velocity-potential. step
without and was decided when I foundhesitation, upononly finally
that it had the countenance of friends whose I couldjudgment
trust and thebut the of the
; function,physical interpretation
with the are both so much
far-reaching analogy magnetic potential,
the its to soonerthat be,improved by change adoption appeared
or inevitable.later,
I have the to attribute to theirendeavoured, book,throughout
authors the more in the ofproper important steps development
the That this is not an matter is shewnsubject. easy byalways
the fact that it has found tobeenoccasionally necessary modify
asreferences in the former andtreatise,given generally accepted
correct. I that errors of whichtrust, therefore, any ascription
beremain will be viewed with It well,indulgence. may
to warn the once for that I have allowedmoreover, reader, all,
a free hand in with the materials atmyself dealing my disposal,
and that the reference in the footnote must not be takenalways
to that the method of the author has beenimply original
thatfollowed in the text. I will confess, indeed,closely my
ambition has a text-book abeen not tomerely produce giving
with itsfaithful record of the state of the science,present
achievements and its if to it abut,imperfections, possible, carry
the due coordinafurther here and and at all eventsthere,step by
tion of results obtained to in some thedegreealready lighten
labours of future I be if I have at leastshallinvestigators. glad
succeeded in of the fascinationto readers someconveying my
which the has exerted on so a line of distinguishedsubject long
writers.
in otherIn the more thanpresent subject, perhaps any depart
ment of mathematical there is room for Poinsot s warningphysics,