Keep every explanation and worked example on the page. Nothing moves or plays by itself, and the larger instruments load only when you ask.
Notation
One letter, several meanings
Einstein reused letters. In the relativity paper β is the factor a modern reader writes γ; in the light-quanta paper it is Wien’s constant, the modern h/kB. In the Brownian paper k is the viscosity of the liquid, not Boltzmann’s constant. Each entry below gives a symbol as it was printed, what it means in the sections where it appears, the symbol a modern reader would use where that differs, and the first place the paper uses it.
Avogadro's number here and in paper 2; a magnetic-field component in paper 3. The printed 6.17 · 10²³ is kept as printed, as one of Einstein's constants, not corrected.
Modern notation writes the ratio R/N as Boltzmann's constant, a symbol the paper never prints. The C of §5 is identified with R/N later in the argument; until then the two are kept apart.
The paper never writes h. It prints this group only with ν attached, as Rβν/N (first on page 143) and as (R/N)βν. Modern notation writes the whole group Rβ/N as Planck's constant h.
β
Wien's constant in the exponential; in modern terms, Planck's constant over Boltzmann's
The third meaning of β. In paper 3 it is the factor a modern reader writes γ. It is not v/c: read as v/c, every later formula looks plausible and is wrong.
Reading β as h/k, Planck's constant over Boltzmann's, is Planck's identification of Wien's constant. It changes the argument, and it is not a new name for the letter. § 2 finds N = (β/α)·8πR/L³ by comparing coefficients. With β = h/k and α = 8πh/c³ written in, that becomes N = R/k, a molecular number drawn from a constant that already contains it. The modern notation keeps a letter.
This page never carries or corrects a printed value.
Reading α as 8πh/c³ is Planck's identification of Wien's prefactor. It changes the argument, and it is not a new name for the letter. With it and β = h/k written in, § 2's N = (β/α)·8πR/L³ becomes N = R/k, a molecular number drawn from a constant that already contains it. The modern notation keeps a letter.
L
Speed of light in empty space, as printed in §§1–2
The speed of light here; a magnetic-field component in paper 3 §6; emitted energy in paper 4. The L of §9 is a different quantity. The value 3 · 10¹⁰ cm/s is an input this edition supplies.
ϱν
Energy per volume per frequency interval, not radiance
Energy density per unit frequency, never per unit wavelength. In §§3 and 4 the paper also prints ρ without the subscript (pages 137 to 139): lq.rho.frequencyEnergyDensity.
ϱ
Radiation density at each frequency: energy per volume per frequency interval, printed without its subscript
The same quantity as ρ with subscript ν in §§1 and 2, energy density per unit frequency. §§3 and 4 write it as ρ(ν), a function of the frequency, and as ρ alone.
E
Mean energy of one rectilinear oscillation of a resonator electron, from the kinetic theory of gases
The mean energy the kinetic theory of gases assigns to each of a resonator electron's three perpendicular oscillations, (R/N)T. Not the radiation energy E of §§3, 4 and 6.
Eν
Mean energy of a resonator of eigenfrequency ν, per component of oscillation, in Planck's condition
Spectral entropy density here; the transition probability density in paper 2; an angle in paper 3; a volume fraction in the dissertation. The φ(W) of §5 is a different quantity.
Radiation energy in §§3–4 and §6. Not the §5-footnote system energy and not the §8 gram-equivalent charge. An electric field in paper 3. A body's rest-frame energy in paper 4.
A cyclic frequency, the exciting frequency in Stokes's rule. The rule compares it with the emitted frequency, so the two must not read as one quantity.
A cyclic frequency, the emitted frequency in Stokes's rule. The rule compares it with the exciting frequency, so the two must not read as one quantity.
ν3
Frequency of a further light quantum that the absorption of one exciting quantum may also produce
A frequency of light produced in photoluminescence, as ν₂ is: besides the quantum of frequency ν₂, the absorption may also produce quanta of frequencies ν₃, ν₄ and so on.
ν4
Frequency of a further light quantum that the absorption of one exciting quantum may also produce
A frequency of light produced in photoluminescence, as ν₂ is: besides the quantum of frequency ν₂, the absorption may also produce quanta of frequencies ν₃, ν₄ and so on.
lg
Natural logarithm operator (base e), as printed throughout
Always a magnitude, never a signed potential. In the printed check Π is in abvolts, and Π · 10⁻⁸ is read as volts. This page does not correct the printed number.
Not an energy. Modern notation writes F, the Faraday constant. The printed 9.6 · 10³ abcoulombs per gram-equivalent is 9.6 · 10⁴ C/mol, beside the modern 96485.33 C/mol. The printed value is kept as printed.
The paper's last formula runs the relation backwards to determine N, so this N is an estimate the paper infers from an observed displacement, not the constant of §§ 1-5.
pν
Generalized state variable (phase-space coordinate) of the system
One of the state variables §2 names p₁ p₂ … p_l, such as the coordinates and velocity components of all the system's atoms; p_ν stands for any of them.
p2
The second of the state variables p₁ … p_l that fix the system's momentary state
One of the state variables §2 names p₁ p₂ … p_l, such as the coordinates and velocity components of all the system's atoms; p_ν stands for any of them.
pl
The last, the l-th of the state variables p₁ … p_l that fix the system's momentary state
One of the state variables §2 names p₁ p₂ … p_l, such as the coordinates and velocity components of all the system's atoms; p_ν stands for any of them.
ν
Discrete index 1 ... l running over generalized state variables
B taken over the primed regions dx′₁ … dz′_n, which differ from the first only in their position; dB/B and dB′/B are the probabilities of the two placements.
J
Spatial position-independent factor in the configuration integral
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
y1
The y-coordinate of the centre of gravity of the first particle, in the first system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
z1
The z-coordinate of the centre of gravity of the first particle, in the first system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
x2
The x-coordinate of the centre of gravity of the second particle, in the first system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
y2
The y-coordinate of the centre of gravity of the second particle, in the first system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
z2
The z-coordinate of the centre of gravity of the second particle, in the first system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
xn
The x-coordinate of the centre of gravity of the last particle, in the first system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
yn
The y-coordinate of the centre of gravity of the last particle, in the first system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
zn
The z-coordinate of the centre of gravity of the last particle, in the first system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
x1′
The x-coordinate of the centre of gravity of the first particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
y1′
The y-coordinate of the centre of gravity of the first particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
z1′
The z-coordinate of the centre of gravity of the first particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
x2′
The x-coordinate of the centre of gravity of the second particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
y2′
The y-coordinate of the centre of gravity of the second particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
z2′
The z-coordinate of the centre of gravity of the second particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
xn′
The x-coordinate of the centre of gravity of the last particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
yn′
The y-coordinate of the centre of gravity of the last particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
zn′
The z-coordinate of the centre of gravity of the last particle, in the second system of regions
One of the rectangular coordinates §2 gives each particle's centre of gravity; the primed coordinates place the same particles in a second system of regions of the same size.
The walk's short step: a time interval very small beside the intervals one can observe, yet long enough that a particle's motions in successive intervals are independent
Einstein's f(x,t) represents number density with integral over space equaling total particle count n. Renaming to probability density p(x,t) is an argument modernization.
t
Time, the variable of the equations of motion of the state variables p_ν
Plain time in § 4, the time in the diffusion equation. In §4, paragraph 11, the same letter is the time over which the displacements occur, listed separately.
The time over which a displacement is observed, as λ_x = √(2Dt) uses t at the end of §4 and in §5 (p. 559). In § 2 and the rest of § 4 the same letter is plain time.
λx
Mean square root displacement (RMS displacement scale) along x-axis
λ_x is first printed at the head of p. 559, the end of §4, before §5 prints it again. The modern view keeps Einstein's own λ_x, the letter this edition's formulas print; written out, it is the square root of the mean squared displacement, √⟨x²⟩.
1,35.10−2
Viscosity of water at 17 °C, printed as a bare number; in CGS units it is in poise, and SI uses Pa·s
The printed x′ = x − vt is an auxiliary coordinate. In modern notation x′ means the moving-frame coordinate the paper writes ξ, so a modern rendering of §3 gives the two different symbols.
t′
The time t' of the third system K' (p. 901)
Easily misread§3, paragraph 18in the stationary systemtoday tˉfirst used on p. 901
Notes
In the paragraph that tests the transformation, K' is a third system moving with -v relative to k, so it rests relative to K, and p. 902 shows the transformation from K to K' is the identity. Not the Galilean auxiliary x' = x - vt that this section's other paragraphs print, and not the moving system's coordinate.
x′
The coordinate x' measured in the third system K' (p. 901)
Easily misread§3, paragraph 18 and §3, paragraph 22in the stationary systemtoday xˉfirst used on p. 901
In the paragraph that tests the transformation, K' is a third system moving with -v relative to k, so it rests relative to K, and p. 902 shows the transformation from K to K' is the identity. Not the Galilean auxiliary x' = x - vt that this section's other paragraphs print, and not the moving system's coordinate.
y′
The coordinate y' measured in the third system K' (p. 901)
Easily misread§3, paragraph 18 and §3, paragraph 22in the stationary systemtoday yˉfirst used on p. 901
Notes
In the paragraph that tests the transformation, K' is a third system moving with -v relative to k, so it rests relative to K, and p. 902 shows the transformation from K to K' is the identity. Not the Galilean auxiliary x' = x - vt that this section's other paragraphs print, and not the moving system's coordinate.
z′
The coordinate z' measured in the third system K' (p. 901)
Easily misread§3, paragraph 18 and §3, paragraph 22in the stationary systemtoday zˉfirst used on p. 901
Notes
In the paragraph that tests the transformation, K' is a third system moving with -v relative to k, so it rests relative to K, and p. 902 shows the transformation from K to K' is the identity. Not the Galilean auxiliary x' = x - vt that this section's other paragraphs print, and not the moving system's coordinate.
K′
A third coordinate system K′, moving with −v relative to k, so at rest relative to K
The printed a is not the a(v) that some modern derivations introduce; that one is listed under Symbols this edition adds. In §§7–8 the letter a is a direction cosine of the wave normal.
φ
Unknown scale function φ(v), later shown to equal 1
Printed in Gaussian units; the conversion to SI is separate, and the modern-notation view does not apply it. In SI this component transforms by a different formula, not the Gaussian one with its letters changed.
A magnetic-field component. Not the speed of light (paper 1) and not emitted energy (paper 4). Printed in Gaussian units; the Gaussian field is c√(4πε₀) times the SI field, a conversion kept separate.
Printed in Gaussian units; the conversion to SI is separate, and the modern-notation view does not apply it. In SI this component transforms by a different formula.
Not the φ(v) of §3: a different argument, though both later turn out to equal 1. On p. 909 the paper itself writes this factor as φ, in φ(v)·φ(−v) = 1 and φ(v) = 1.
The paper prints the direction cosines of the wave normal as a, b, c (pp. 910 and 913), not l, m, n. In §3 the letter a is a different quantity, the undetermined coefficient of the transformation.
In §3, phi is the unknown scale function. Spectral entropy density in paper 1; transition kernel in paper 2. The modern view keeps φ, the letter this edition's formulas and prose use for the angle, where many modern texts write θ.
φ′
Angle between the wave normal and the line from the source to the observer, in k
Energy of a light complex here. Electric-field components in this paper are X, Y, Z, not E. The modern view keeps E, the letter this edition's formulas use: no field stands beside it in the formulas of §8.
The modern-notation view does not show the printed ρ as the modern SI charge density. The paper defines ρ as the divergence of the electric force and calls it „die 4π-fache Dichte der Elektrizität“ (p. 916).
Printed in Gaussian units. In SI units the quantity takes a different form, not a simple rescaling.
The modern-notation view leaves this as printed. Page 919 prints μβ² as the coefficient in the transverse equation of motion, and the transverse mass as μ/(1 − (v/V)²).
The source's transverse coefficient is m gamma^2 under its comoving-force convention. The laboratory convention gives m gamma (transverseMassLaboratory). That is a change of force convention, not a rename of beta and not a Gaussian-to-SI conversion.
The modern-notation view leaves this as printed. Page 919 prints μβ³ as the coefficient in the longitudinal equation of motion, and the longitudinal mass as μ/(√(1 − (v/V)²))³.
The printed longitudinal coefficient is tied to the paper's force convention. Modern invariant-mass dynamics does not keep a direction-dependent mass as a primitive.
W
The electron's energy of motion (Bewegungsenergie), set equal to the work the field does on it
Einstein names W the electron's energy of motion and sets it equal to the work the field does on it, the integral of εX dx. The formulas of this edition call that energy K.
Scoped to the first of the two X's this paragraph prints, not to the paragraph: the second is the electrostatic force, and so is the X of the integral that follows it. The entry for §10, paragraph 4 does the same work for a paragraph where the letter only names the axis.
Symbols this edition adds
These appear in the modern explanations and worked examples for Special relativity. The paper itself does not print them.
χ
Rapidity, whose tanh is the speed ratio. Not printed.
Not printed in the paper§3 and §5
aans(v)
Modern ansatz spatial scale. Distinct from printed §3 a.
Not printed in the paper§3
bans(v)
Modern ansatz time scale.
Not printed in the paper§3
dans(v)
Modern ansatz time-space coefficient.
Not printed in the paper§3
a⊥
Modern ansatz transverse coefficient. NEVER written k; k is the moving system.
Not printed in the paper§3
q
The charge carried through the magnetic field in the explanation of § 6; the paper names no charge there
Not printed in the paper§6
q
The electron's charge, which § 10 prints as ε, as the explanation writes it
Not printed in the paper§10
u
The electron's speed, the variable of the explanation's integral in § 10
Not printed in the paper§10
u
The speed of a transported clock on one leg of its path, in the explanation of § 4
Not printed in the paper§4
u
The velocity of the moving charges, whose components § 9 prints as u_x, u_y, u_z, as the explanation writes it undivided
Propagation angle in the §8 transformation formula the paper cites. Scoped strictly to that citation, in paragraph 1, and distinct from the emission angle φ of paragraphs 2 to 6.
The factor is printed as an explicit radical every time, six times (p. 639 once, p. 640 four times, p. 641 once). β is not printed anywhere in this paper, although the relativity paper uses β for the same factor. Modern notation writes the whole radical as γ.
L
Total energy emitted by the body as light radiation, measured in the body's rest frame
The total energy emitted, measured in the body's rest frame. Not the speed of light (paper 1) and not a magnetic-field component (paper 3 §6): a reader who carries paper 1's L into this paper reads the central result as being about the speed of light when it is about radiated energy. Modern notation writes it as an E with a subscript, not a bare E, because the paper also prints a plain E.
L/2
Energy of each of the two emitted light pulses in the rest frame
Kinetic energy of the body in the moving system before emission. K has only this meaning in paper 4; the stationary-system K belongs to paper 3 and the force K to paper 2.
K1
Kinetic energy of the body relative to the moving system after emission
Kinetic energy relative to the moving system. K has only this meaning in paper 4; it collides across papers with the stationary system K of paper 3 and the force K of paper 2.
K0−K1
Difference between kinetic energy before and after radiation emission
Additive constant in H - E = K + C. Cancels in differences H0 - H1 and E0 - E1 because C depends on v and arbitrary energy baseline, which are unchanged by emission.
21V2Lv2
Decrease in kinetic energy, to second order in v/V
The central result: if a body gives off energy L in radiation, its mass decreases by L/V^2 (in modern notation, Delta m = L/c^2).
The paper names the decrease only by its value, L/V². The explanation gives it a letter of its own. Written in that letter's place, L/c² would turn the paper's conclusion into the identity L/c² = L/c², so the modern notation keeps the letter.
9⋅1020
Printed factor (3 · 10¹⁰ cm/s)², which turns an energy in ergs into a mass in grams
A coordinate of the stationary system (x, y, z). The paper uses the three letters together to name the system, as in the Koordinatensystem (x, y, z), and paper 3 binds the same letters to the same coordinates.
y
Second of the three coordinates that name the stationary system (x, y, z)
A coordinate of the stationary system (x, y, z). The paper uses the three letters together to name the system, as in the Koordinatensystem (x, y, z), and paper 3 binds the same letters to the same coordinates.
z
Third of the three coordinates that name the stationary system (x, y, z)
A coordinate of the stationary system (x, y, z). The paper uses the three letters together to name the system, as in the Koordinatensystem (x, y, z), and paper 3 binds the same letters to the same coordinates.
ξ
First of the three coordinates that name the moving system (ξ, η, ζ), along the x-axis of the stationary one
A coordinate of the moving system (ξ, η, ζ). The paper uses the three letters together to name the system, as in the Koordinatensystem (ξ, η, ζ), and paper 3 binds the same letters to the same coordinates.
η
Second of the three coordinates that name the moving system (ξ, η, ζ)
A coordinate of the moving system (ξ, η, ζ). The paper uses the three letters together to name the system, as in the Koordinatensystem (ξ, η, ζ), and paper 3 binds the same letters to the same coordinates.
ζ
Third of the three coordinates that name the moving system (ξ, η, ζ)
A coordinate of the moving system (ξ, η, ζ). The paper uses the three letters together to name the system, as in the Koordinatensystem (ξ, η, ζ), and paper 3 binds the same letters to the same coordinates.
Symbols this edition adds
These appear in the modern explanations and worked examples for Mass and energy. The paper itself does not print them.
minv
Invariant mass of a system of particles or radiation. A modern-lens quantity, not printed in 1905.
Not printed in the paperthroughout
Δm
Signed change in mass accompanying energy exchange. Modern notation for Einstein's L/V^2.
Not printed in the paperthroughout
Mbox
Mass of the box in the 1906 thought experiment extension.
Not printed in the paperthroughout
The dissertation · 1906
Molecular dimensions
Ann. Phys. (4) 19, 289–306 (1906)
k
Solvent viscosity in the dilute-suspension law, as printed
Easily misread§1, §2, §3, §4, the 1906 text and the 1911 correctiontoday ηfirst used on p. 289
The same danger collision as paper 2: Einstein's k is viscosity, never Boltzmann's constant. The coefficient of phi in the viscosity law is never called k.
k∗
Effective viscosity of the dilute suspension, as printed
§1, §2, the 1906 text and the 1911 correctiontoday η∗first used on p. 300
Notes
k-star is the suspension viscosity. The solvent viscosity is k. Neither is Boltzmann's constant.
φ
Volume fraction of suspended spheres in the dilute-suspension viscosity law
§1, §2, §3, the 1906 text and the 1911 correctiontoday φfirst used on p. 298
Volume fraction here. Spectral entropy density in paper 1, transition kernel in paper 2, an angle in paper 3.
1
Coefficient of φ in the 1906 viscosity law k* = k(1 + φ), printed as 1
Easily misreadthe 1906 texttoday 1first used on p. 289
Notes
The 1906 printing, not k. The 1911 correction prints 2,5 for the same coefficient (modern 5/2), listed separately. The modern value for rigid spheres, 5/2, is not substituted here, or the 1906 error would be hidden.
2,5
Coefficient of φ after the 1911 correction, printed as 2,5 (modern 5/2)
Easily misreadthe 1911 correctiontoday 25first used on p. 592
Notes
Ann. Phys. (4) 34, 591-592. Not k. N scales as the square root of this coefficient. This value is not silently back-ported onto the 1906 printing. The 1911 correction prints this coefficient as the decimal 2,5, in k* = k(1 + 2,5 φ) on page 592, not as the fraction 5/2.
k∗/k
Ratio of suspension viscosity to solvent viscosity
§1, the 1906 text and the 1911 correctiontoday η∗/ηfirst used on p. 301
Notes
The ratio k-star/k. Distinct from the coefficient of phi.
Used with Stokes drag and osmotic pressure to infer the size of a molecule. Printed as italic D, first as the diffusion coefficient on page 303, in §4. On pages 293 and 294, in §1, the same letter names an auxiliary function.
These appear in the modern explanations and worked examples for Molecular dimensions. The paper itself does not print them.
[η]
Modern intrinsic viscosity. Equal to 5/2 for rigid spheres; never substituted for the 1906 printed 1, and never called k.
Not printed in the paperthe 1911 correction
In the printed equations, without an entry of their own
These quantities appear in the papers' displayed equations but have no symbol entry above. Each line gives the letters as printed, the paper, the quantity, and what it is.
x2Mean-square displacement (one dimension) (Brownian motion): The average of the squares of the particles' displacements along one axis.
A′′Reflected light amplitude (moving system) (Special relativity): The amplitude of the light reflected by the mirror, as measured in the moving system k, in which the mirror is at rest.
φ′′Reflected propagation angle (moving system) (Special relativity): The angle between the reflected light's direction of travel and the direction of motion, as measured in the moving system k.
ν′′Reflected light frequency (moving system) (Special relativity): The frequency of the light reflected by the mirror, as measured in the moving system k, in which the mirror is at rest.
ν′′′Reflected light frequency (stationary system) (Special relativity): The frequency of the light reflected by the moving mirror, as measured in the stationary system K.
PAccelerating potential (Special relativity): The potential difference, the voltage, through which an electron has been accelerated from rest.