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Tables numériques des équations de lagrange
.\farch,
BOOK REVIEWS.
~
concerning
the
and value. The text
adulterants
found
of the book
in illicit
is carefully
liquors
and clearly
will
be
written
of
much
intert>t
and the publisher
has
It is a book that will bc very it in a convenient and attractive form. to the student and equally so to the practising physician and toxicologist. HER’RV LEFFMANN.
issued useful
DES EQUATIONS no LAGRANLIS.Par
T.WI.ES N~X~RIQ~XS fesseur
a 1’Universite
Sciences.
xviii-Jo0
Boghandel
; Paris,
The Unlike
theory other
modern Until
of
progress
this
unknown.
there
leaders
of
modern
school
of number
and
rational Only
to
the
one
noted.
of Fermat’s
Fermat
Euler equations, notable
theorems
presented
in his
with
algebra
applicable additions
announced
Euler
fell has
dealt
It was
the fifth development
of these
century
dominated
of
fully
theory
in researches
investigators
method,
various
expressions
forms
obviously
an
which invaluable
of the II. u and
aid.
with
quadratic
but
the
solution were
that
are eleven
tables
of
the their
subject.
one, of
it may
be
indeterminate
edition
of this work
supplied
author
states,
by Lagrange. that
a theory
of Lagrange
:
tables
laws
led Gauss
which
by a prodigal
of integers
in dealing
with
work
is such
present
the argument
which
number
n in the above
for
a.
of which
Table
theorems
formula
the explanatory
I and
applicasatisfy
a collection
with each table. The only explanatory notes occur in the preface pages which indeed contains a surprising amount of information ITI pages. The bases greater
Fermat,
demonstra-
refractory
forms.
related values in the same or in transformed formulas. There is no text in the body of the work except
There compass. formula occupy Table II-Certain
of
initiator
(_I)&
assume The
true,
to seek general
and adequate
w under
for
science,
in supplying
that
devices
on the equation
are inclined
tion of the statistical
not
share of
the present of
TL?-&= Modern
names without
and in the French
of these
supplements, the
important
proved
theorems
and amplifications
to the
an
of
to bring about a In the days of the
the
his theorems
was
exclusively
the was
of
research
branches
areas.
who
genius.
the result
reservation.
very
to number
in
has done much
difficulties
due
cooperation
thought,
its early
individual were
establishments
Fermat.
disentangling
of
in general
separated
mathematical
outstand.
of
Pro-
history.
development,
in special
times
in widely
analysis,
and
no great
of modern
Gauss
genius
derivation
systematic
to-day
modern
and
Nielsen,
in mathematical
contributions
to Foundations
workers
Lagrange
tion,
are
place
by gradual
in science
effort;
in publication
Euler,
a unique
spectacular
kindred
among
paper.
advanced
advances
and
research
great
by
times,
It is true
but the freedom
have
been
Niels
de 1’Academie Royale des Copenhagen, Gyldendalske
1925.
occupies
which
has
cluasi-coiiperation
Membre
6 x g inches,
numbers
initiative
mathematical
early
pages,
recent
individual
de Copenhague,
Gauthier-Villars,
branches
relatively
values
.;~,(I
Table
of
the are the
and other captions of thirteen in its small
II of the above
list is as follows : Table I-Bases a = 2 to 102. than 102. III-Bases of the first kind, IV-
370
ROOK
REVIEWS.
[J. F. I.
Simultaneous equations. V-Non-elemental bases of Tables I and II. VI-Prime numbers less than 5600 (with a = 8n + I, 3, 5 and 7; and some primes greater than 5600). VII-Certain sums of two squares. VIII-Bases of the second kind. IX-Non-elemental bases. X-Summary of certain sums of two squares. XI-Summary of products of two prime numbers. The work is evidently intended for mathematical investigators rather than for those who utilize the results of mathematical research and do not primarily deal with the fundamentals of the subjects. The former type of users will find adequate information in the captions of the tables, but a larger class not so well qualified in the subject, yet deeply interested, would welcome a text on the subject. However, the tables occupy a fairly large volume and a text might require one as large or larger. The tables, which the author states have been duly checked, represent an immense amount of skilfully directed labor and constitute a valudble addition to the equipment of investigators in the theory of numbers. The press-work is of a high order of excellence. LUCIEN E. PICOLET. NATIONAL ADVISORYCOMMITTEEFOR AERONAUTICS.. Report No. 225, The Air Forces on a Model of the Sperry Messenger Airplane without Propeller. By Max M. Munk and Walter S. Diehl. 12 pages, illustrations, quarto. Washington, Government Printing Office, 1925. Price, five cents. This is a report on a scale-effect research which was made in the variable density wind&mnel of the National Advisory Committee for Aeronautics aL the request of the Army Air Service. A I/IO scale model of the S&rry Messenger airplane with USA-5 wings was tested without a propeller at various Reynolds numbers up to the full scale value. Two series of tests were made: The first on the original model which was of the usual simplified construction, and the second on a modified model embodying a great amount of detail. While the present report is of a preliminary nature, the work has progressed far enough to show that the scale effect is almost entirely confined to the drag. In the tests so far conducted, the drag at any given angle of attack within the normal flying range is found to vary as
. The exponent n is constant for
any one angle of attack, and ranges from -0.045 at large angles of attack to -o.r7 gi,. at small angles. It was also found that the model should be geometrically similar to the fullscale airplane if the test data are to ~)t directly applicable to full scale. If the condition of geometric similarity be fulfilled, the data obtained at a full scale value of Reynolds number agree very closely with free-flight data. The variable density wind-tunnel therefore appears to be a very promising instrument for It is also admirably suited for procuring test data free from scale effect. studying the scale effect and obtaining information which is necessary in an interpretation of the results obtained in atmospheric wind-tunnels at low values of the Reynolds number. Report No. 228, A Study of the Effect of a Diving Start on Airplane 9 pages, illustrations, quarto. Washington, By Walter S. Diehl. Speed. Government Printing Office, 1925. Price, five cents.
BOOK REVIEWS.
~
concerning
the
and value. The text
adulterants
found
of the book
in illicit
is carefully
liquors
and clearly
will
be
written
of
much
intert>t
and the publisher
has
It is a book that will bc very it in a convenient and attractive form. to the student and equally so to the practising physician and toxicologist. HER’RV LEFFMANN.
issued useful
DES EQUATIONS no LAGRANLIS.Par
T.WI.ES N~X~RIQ~XS fesseur
a 1’Universite
Sciences.
xviii-Jo0
Boghandel
; Paris,
The Unlike
theory other
modern Until
of
progress
this
unknown.
there
leaders
of
modern
school
of number
and
rational Only
to
the
one
noted.
of Fermat’s
Fermat
Euler equations, notable
theorems
presented
in his
with
algebra
applicable additions
announced
Euler
fell has
dealt
It was
the fifth development
of these
century
dominated
of
fully
theory
in researches
investigators
method,
various
expressions
forms
obviously
an
which invaluable
of the II. u and
aid.
with
quadratic
but
the
solution were
that
are eleven
tables
of
the their
subject.
one, of
it may
be
indeterminate
edition
of this work
supplied
author
states,
by Lagrange. that
a theory
of Lagrange
:
tables
laws
led Gauss
which
by a prodigal
of integers
in dealing
with
work
is such
present
the argument
which
number
n in the above
for
a.
of which
Table
theorems
formula
the explanatory
I and
applicasatisfy
a collection
with each table. The only explanatory notes occur in the preface pages which indeed contains a surprising amount of information ITI pages. The bases greater
Fermat,
demonstra-
refractory
forms.
related values in the same or in transformed formulas. There is no text in the body of the work except
There compass. formula occupy Table II-Certain
of
initiator
(_I)&
assume The
true,
to seek general
and adequate
w under
for
science,
in supplying
that
devices
on the equation
are inclined
tion of the statistical
not
share of
the present of
TL?-&= Modern
names without
and in the French
of these
supplements, the
important
proved
theorems
and amplifications
to the
an
of
to bring about a In the days of the
the
his theorems
was
exclusively
the was
of
research
branches
areas.
who
genius.
the result
reservation.
very
to number
in
has done much
difficulties
due
cooperation
thought,
its early
individual were
establishments
Fermat.
disentangling
of
in general
separated
mathematical
outstand.
of
Pro-
history.
development,
in special
times
in widely
analysis,
and
no great
of modern
Gauss
genius
derivation
systematic
to-day
modern
and
Nielsen,
in mathematical
contributions
to Foundations
workers
Lagrange
tion,
are
place
by gradual
in science
effort;
in publication
Euler,
a unique
spectacular
kindred
among
paper.
advanced
advances
and
research
great
by
times,
It is true
but the freedom
have
been
Niels
de 1’Academie Royale des Copenhagen, Gyldendalske
1925.
occupies
which
has
cluasi-coiiperation
Membre
6 x g inches,
numbers
initiative
mathematical
early
pages,
recent
individual
de Copenhague,
Gauthier-Villars,
branches
relatively
values
.;~,(I
Table
of
the are the
and other captions of thirteen in its small
II of the above
list is as follows : Table I-Bases a = 2 to 102. than 102. III-Bases of the first kind, IV-
370
ROOK
REVIEWS.
[J. F. I.
Simultaneous equations. V-Non-elemental bases of Tables I and II. VI-Prime numbers less than 5600 (with a = 8n + I, 3, 5 and 7; and some primes greater than 5600). VII-Certain sums of two squares. VIII-Bases of the second kind. IX-Non-elemental bases. X-Summary of certain sums of two squares. XI-Summary of products of two prime numbers. The work is evidently intended for mathematical investigators rather than for those who utilize the results of mathematical research and do not primarily deal with the fundamentals of the subjects. The former type of users will find adequate information in the captions of the tables, but a larger class not so well qualified in the subject, yet deeply interested, would welcome a text on the subject. However, the tables occupy a fairly large volume and a text might require one as large or larger. The tables, which the author states have been duly checked, represent an immense amount of skilfully directed labor and constitute a valudble addition to the equipment of investigators in the theory of numbers. The press-work is of a high order of excellence. LUCIEN E. PICOLET. NATIONAL ADVISORYCOMMITTEEFOR AERONAUTICS.. Report No. 225, The Air Forces on a Model of the Sperry Messenger Airplane without Propeller. By Max M. Munk and Walter S. Diehl. 12 pages, illustrations, quarto. Washington, Government Printing Office, 1925. Price, five cents. This is a report on a scale-effect research which was made in the variable density wind&mnel of the National Advisory Committee for Aeronautics aL the request of the Army Air Service. A I/IO scale model of the S&rry Messenger airplane with USA-5 wings was tested without a propeller at various Reynolds numbers up to the full scale value. Two series of tests were made: The first on the original model which was of the usual simplified construction, and the second on a modified model embodying a great amount of detail. While the present report is of a preliminary nature, the work has progressed far enough to show that the scale effect is almost entirely confined to the drag. In the tests so far conducted, the drag at any given angle of attack within the normal flying range is found to vary as
. The exponent n is constant for
any one angle of attack, and ranges from -0.045 at large angles of attack to -o.r7 gi,. at small angles. It was also found that the model should be geometrically similar to the fullscale airplane if the test data are to ~)t directly applicable to full scale. If the condition of geometric similarity be fulfilled, the data obtained at a full scale value of Reynolds number agree very closely with free-flight data. The variable density wind-tunnel therefore appears to be a very promising instrument for It is also admirably suited for procuring test data free from scale effect. studying the scale effect and obtaining information which is necessary in an interpretation of the results obtained in atmospheric wind-tunnels at low values of the Reynolds number. Report No. 228, A Study of the Effect of a Diving Start on Airplane 9 pages, illustrations, quarto. Washington, By Walter S. Diehl. Speed. Government Printing Office, 1925. Price, five cents.