D O C . 1 2 R E L AT I V I T Y L E C T U R E N O T E S 9 9
[13]This argument, which goes as far as the bottom of this page of the manuscript, follows the cal-
culation on pp. 25–27 of Vol. 4, Doc. 1, of the Maxwell-Lorentz equations for a slowly moving par-
ticle. Note that q now, and throughout the rest of the document, refers to the velocity of a given mass
or object.
[14]The following derivation of the Fresnel coefficient follows the one given in Lorentz 1892a, pp.
524–526. See also Vol. 4, Doc. 1, pp. 27 –28, and Vol. 6, Doc. 7, pp. 47– 48.
[15]This insert should be “ ” if, as it appears, the term it is supposed to amend should read
“ .”
[16]The middle term in the top row of the matrix should be “ .”
[17]Einstein here writes down the right formula in this derivation, correcting the error in the matrix
highlighted in note 16. Presumably he corrects the error from memory, knowing that the cross term
does not cancel out as the matrix he has written down would have it. The deleted equation
immediately below the matrix also silently corrects the error. In this equation q, the speed of the run-
ning water (or other moving dielectric) in Fizeau’s experiment is treated as a quantity much smaller
than c.
[18]Here is the speed of light in water at rest and Δ is the correction to the velocity of light in a
frame in which the water is moving, where Δ is much smaller than .
[19]On 9 November 1918, mass demonstrations by armed workers in Berlin precipitated the resig-
nation of the imperial government. Soon after Einstein, Max Born (1882–1970), Extraordinary Pro-
fessor of Physics, and Max Wertheimer (1880–1943), Professor of Psychology, both at the University
of Berlin, made their journey through revolutionary Berlin to the Reichstag to appeal for the release
of some professors from the University of Berlin who had been incarcerated by revolutionary students
of the university (see Einstein to Pauline Einstein, 11 November 1918 [Vol. 8, Doc. 651], note 3 and
references therein, as well as Born 1975, pp. 257-259).
[20]This is the last date given in the notes and must have been the last lecture that Einstein intended
to deliver, since by 9 January 1919 he was already in Zurich, having left Berlin earlier than anticipated
“for pressing reasons” (“aus dringlichen Gründen”; Proclamation of Erziehungs-Direktion des Kan-
tons Zürich, 9 January 1920, SzZU, Rektorats-Archiv, No. 208-10). Einstein went to Zurich to give a
course of lectures at the University of Zurich on the same topic as these lectures (see Einstein to Hei-
nrich Mousson, 17 December 1918 [Vol. 8, Doc. 674]).
The remaining material in the notes covers the material of Vol. 4, Doc. 1, sec. 4, on the electrody-
namics of moving bodies, following it quite closely.
[21]This equation should be “ .”
[22]The third term “ ” should be “ .”
[23]Under the empty square root signs on this line and the one below it, there should be “ .”
[24]The two terms indicated by dashes here would read “ .”
[25]“ ” should be “ .” In this term and the one immediately above, the missing term is .
On both of these lines, Einstein has neglected to replace components of with the components of
the four-velocity .
[26]Beginning with (Vol. 4, Doc. 1, p. 12, eq. (8)) and taking , one obtains
rather than the result Einstein derives here.
[27]In full, this equation would read ,
c ⁄ –V
c
--
Vö
c
---ø –
æ
–è '
c
--
V
c
--- –
2-----
V
c2
-( ε 1) –
V0
V0
fμν pμν) + ∂(
∂xν
----------------------------- -
μ
=
∂xμ
∂fρμ
∂xν
∂fρμ
1 q2 –
z
y
1 q2 –
------------------
y
z
1 q2 –
------------------ –
1
x
1 q2 –
μ
uμ
μ 1) – ( = – =
μ–1
μ
--------- - =
pμνuρ pυρuμ pρμuν + +
μ 1 –
μ
-( –----------- fμνuρ fυρuμ fρμuν) + + =