126 DOC.
1
MECHANICS LECTURE NOTES
[2]This
sentence is interlineated
in
the
original.
[3]In
the
following "m.
P."
is
often used
as an
abbreviation
for
"materieller
Punkt."
[4]Here
and
subsequently,
"K.
S."
stands for
"Koordinatensystem."
[5]MM1
should
be
MM'.
The
notation
is
the
same
as
that
used
in Violle
1892, §19.
At
At
[6]See
the
editorial
note,
"Einstein's Lecture
Notes,"
pp.
310,
for further discussion of
Einstein's
use
of
vectors.
[7]For
a
discussion of the
"Hodograph,"
a curve
whose radius
vector
represents
a
particle's
velocity, see e.g.,
Violle
1892, §22,
and Mach
1908, pp.
165166.
[8]The
a
in
the
diagram
is not
the
same as
the
a
in his
directioncosines for the normal
vector
N.
[9]The discussion of
inertia
given below,
and
in
particular
the introduction of the
concept
of
mass
(by means
of the accelerations of
bodies)
probably
reflect
Einstein's
reading
of Mach's
Mechanik;
see, e.g.,
Mach
1908,
pp.
230236. There
is
a
reference to
the Mechanik
in Einstein's
"Scratch Notebook"
(Appendix
A),
[p. 58].
In
his
lectures
on
electricity
and
magnetism
(Doc.
11),
Einstein takes
a
Machian
approach in
introducing
electric
charge.
See
also
[pp. 116117]
of
this
document for
a
"different derivation of
the
foundational
equations
of
the
material
point"
("Andere Herleitung
der
GrundGleichungen
des materiellen
Punktes").
[10]The
preceding
five words
are
interlineated
in
the
original.
[11]The
words
"erscheinende" and
"bzw.
aufrecht erhalten"
are
interlineated
in
the
original.
[12]A
similar calculation
is
found on [pp. 2122].
[13]Einstein's discussion of
cgs
units resembles the
corresponding
sections
in Violle
1892, §73,
and Mach
1908,
pp. 325330,
both of which mention
Gauss's contribution
to
the reform of
measurement
units.
[14]The
word
"phys[ikalischen]"
is
interlineated
in
the
original.
For
a
discussion of
the
possibility
that
gravity might depend on an object's "physical quality,"
see
Mach's
account
of
Newton's
experiments
related
to
this
subject (Mach 1908, pp. 207208).
The
possibility
that
gravity might depend on
the
speed
of
a body was
discussed
in
contemporary electromagnetic
theories of
gravity;
see
Jungnickel
and McCormmach
1986,
p.
237.
These
topics
are
not
men
tioned
in
contemporary
standard mechanics
texts
and
in
lectures such
as Voigt
1901
or
Helmholtz
1898.
[15]For
a
brief discussion of
the
role
played
by
the
assumption
of
equivalence
between inertial
and
gravitational
mass
in
Einstein's work
on
the
theory
of
relativity,
see
Vol.
2,
the editorial
note,
"Einstein
on
the
Theory
of
Relativity," pp.
273274.
[16]r

p
should
be
p

r;
the
following equation
for
Br
needs
a
minus
sign.
[17]For similar
treatments
of the
relationship
between
Kepler's
third law and the inverse
square
law
for the
force,
see
Violle
1892, §101,
and Mach
1908, pp.
193195.
[18]The
calculations and
diagrams following immediately
below refer
to
a
Cavendish
experi
ment to
measure
the
gravitational constant.
In
this
experiment
the
gravitational force is
mea
sured
by
a
torsion
balance
using spheres
of
radius 20
cm
and
density 13.6
gm/cm3,
correspond
ing
to
the
density
of
mercury.
[19]This
expression
starts
an
incomplete
calculation of the
force
exerted
by an
infinitely
thin
spherical
shell
on a
point mass
outside
it.
This calculation
closely
follows
Violle
1892, §102.
The
integration is performed
over
a
series
of
concentric, parallel rings
whose
planes
are
normal
to
the
line
joining
the
center
of
the shell to
the
point
mass.
R is
the radius of
the
shell,
and
r
is
the
distance between the
external
point
and the shell's
center.
Einstein
changes
notation
in
the
second
expression
denoting
by
p
the
mass density
on
the
shell.
[20]The
plus
sign
of the third term
on
the
right
should
be
a
minus
sign.
[21]A
factor of
1/2Rr2
has been
left
out
in
this
equation
and
in
the
following
one.
The
last
two terms
of
this
equation
should
be interchanged, giving
the
correct
result of
Kmp4nR2/r2
for
the attractive
force acting
on
the
mass
point.