Scoped Notation Concordance

Universal molar gas constant, as printed

The value R = 8.31e7 erg/(mol·K) is an editorial input of the printed-historical constant set, not a concordance repair.

The printed group R beta / N, Planck's constant

The paper never writes h. Group rename only. h is not a printed symbol.

Energy per volume per frequency interval, not radiance

Binds frequencyEnergyDensity, never wavelengthEnergyDensity. Whether the edition also prints an un-subscripted rho is pending the facsimile; no un-subscripted rho entry is admitted without that check.

Reference radiation entropy

Reference entropy of a gas or dilute solution

Volume of the radiation or of the gas, as printed

Rename of the printed volume glyph to V. Whether the facsimile prints v or V is pending; this entry follows the bead's listed glyph.

Reference volume

Number of independent points or molecules in the kinetic-theory analogy

Relative probability of a volume configuration

Exciting frequency in Stokes fluorescence

Same quantity as nu (cyclic frequency); the subscript records the exciting-beam role.

Emitted frequency in Stokes fluorescence

Same quantity as nu (cyclic frequency); the subscript records the emitted-beam role.

Natural logarithm operator (base e), as printed throughout

Modern ISO 80000-2 (and DIN 1302) reads lg as log_10. In this paper lg is the natural logarithm.

Component of the radiation's electric force at a point

A vector component of radiationElectricField. The component is a term binding, not a second quantity id.

Fourier amplitude of one component of the radiation electric force

Time in the Fourier expansion of the §1 footnote

Probability density in the factorization of the §1 footnote

Probability density F_nu in the factorization of the §1 footnote

Probability density f_nu in the factorization of the §1 footnote

Probability element in the §1 footnote

Magnitude of the stopping potential

Never a signed collector potential. In the printed check Pi is in abvolts, and Pi · 10^{-8} is read as volts. This entry does not correct a printed number.

Elementary charge

Ionization work per gram-equivalent

Number of gram-molecules ionized, j = L / (R beta nu)

An amount of substance, never a rate.

Ionization work per molecule, the per-molecule form of J

Admitted as the per-molecule form named by the bead. Whether the facsimile prints J/N as a group is pending.

Mechanical CGS energy unit

1 erg = 10^{-7} J. The concordance never repairs a printed number.

Centimeter

Gram

Abvolt, electromagnetic CGS potential; Pi · 10^{-8} is read as volts

Conventional factor: 1 abV ↔ 10^{-8} V. exactness is conventional, not a 2019 SI identity. Follows the printed representation of the 4.3 V check.

Abcoulomb, electromagnetic CGS charge

Conventional factor: 1 abC ↔ 10 C. Printed E = 9.6e3 abC per gram-equivalent is 9.6e4 C/mol. This entry does not correct 9.6e3.

Statvolt, electrostatic CGS potential, documented modern restatement of the §8 check

Conventional factor 299.792458 V, not an exact 2019 SI identity. Historical calculations often use 300 V. Labeled a documented modern restatement, not a facsimile reading of an esu form of the check.

Total volume of the liquid solution

Partial volume containing suspended particles

Amount of solute in gram-molecules (moles)

Absolute thermodynamic temperature

Universal molar gas constant

Discrete index 1 ... l running over generalized state variables

Mean thermodynamic energy of the system

Energy of the system as a function of generalized state variables

Thermodynamic and statistical entropy

Product 2*kappa representing Boltzmann's constant k_B

Natural logarithm operator (base e)

ISO 80000-2 / DIN 1302 note: Einstein's 'lg' notation represents the natural logarithm (base e), rendered as \ln in modern standards.

Configuration integral over phase space

Spatial position-independent factor in the configuration integral

Virtual variation operator

Spatial coordinate along the 1D axis of diffusion

Diffusion coefficient of suspended particles

Drift velocity imparted by external force (K / (6*pi*k*P))

Ratio of molar gas constant to Avogadro constant (Boltzmann's constant k_B)

1D spatial displacement increment of a particle in interval tau

Particle number density per unit length (dn = f(x,t) dx, normalized to total count n)

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.

Elapsed observation time

Mean square root displacement (RMS displacement scale) along x-axis

Dynamic viscosity of water at 17 C in CGS poise converting to SI Pa*s

Printed unit word for micrometre (10^-6 m)

Printed abbreviation for second

Speed of the moving system k relative to the stationary system K

Spatial x-coordinate in the stationary system K

Spatial y-coordinate in the stationary system K

Spatial z-coordinate in the stationary system K

Time coordinate in the stationary system K

Clock reading at event A in K

Clock reading at event B in K

Spatial separation of the stations A and B

Length of the moving rod measured in the stationary system

Spatial y-coordinate in the moving system k

Spatial z-coordinate in the moving system k

Undetermined function of v in the §3 transformation, before it is fixed

Printed a is not the modern side-door ansatz a(v), which is a modernOnlySymbols record.

Velocity of a point relative to k

The composed velocity in K

Angle between w and the direction of motion

Speed by which v falls short of V, in v = V - kappa

A speed, not a ratio. Binding it as dimensionless makes the printed inequality fail a dimension check.

Speed by which w falls short of V, in w = V - lambda

A speed, not a ratio, and not wavelength.

x-component of the electric force in K (Gaussian)

Rename only. Gaussian-to-SI conversion E_G = sqrt(4 pi epsilon_0) E_SI is a unitConversion, not applied by the notation toggle. fromSystem gaussian-cgs, toSystem si.

y-component of the electric force in K (Gaussian)

Rename only. Gaussian-to-SI conversion is a separate unitConversion (gaussian-cgs to si). The SI transformation is E'_y = gamma (E_y - v B_z), not a string substitution on the Gaussian formula.

z-component of the electric force in K (Gaussian)

Rename only. Gaussian-to-SI is unitConversion, gaussian-cgs to si.

y-component of the magnetic force in K (Gaussian)

Rename only. SI form B'_y = gamma (B_y + v E_z / c^2) is not a string substitution on the Gaussian formula.

y-component of the electric force in k (Gaussian)

Rename of the printed glyph. Gaussian-to-SI conversion (fromSystem gaussian-cgs, toSystem si) is a unitConversion and is not applied by the notation toggle. The SI law is E'_y = gamma (E_y - v B_z).

Gaussian electric-field magnitude, for the unit-system conversion only

This entry records the unit-system conversion. It does not rename a printed glyph. The toggle must not apply it.

Common undetermined factor of the transformed fields, later shown to equal 1

A different record from §3's phi(v). Different argument, only later both equal to 1.

Phase of a plane wave

Angular frequency in K

Cyclic frequency in k

Direction cosine of the wave normal in K

Direction cosine of the wave normal in K

Amplitude of the light complex in K (Gaussian)

Gaussian amplitude. Energy density A^2/8pi is Gaussian; converting it is unitConversion, not a rename.

Amplitude of the light complex in k (Gaussian)

Energy of the light complex in k

Radiation pressure on a perfectly reflecting mirror

Printed 4-pi times the Gaussian electric-force divergence; not a plain charge density

The toggle must not display the printed rho as the modern SI charge density. Comparison witness: 4-pi-fache Dichte der Elektrizitat, pending facsimile.

The same printed density, in k

Charge-velocity component in k

The electron's charge (Gaussian)

Gaussian charge. Converting to SI is unitConversion, not this rename.

The electron's mass as printed

The printed transverse-mass coefficient under the paper's comoving-force convention

The notation toggle must not apply this entry. Glyph pending facsimile; expected form is the printed transverse-mass coefficient.

The printed longitudinal-mass coefficient

Glyph pending facsimile. Toggle must not apply this entry.

Work done on the electron

Coordinate axes of the stationary system K

Coordinate axes of the moving system k

Energy of a light complex in the moving system, as cited from paper 3 §8

Cosine of angle phi

Energy of each of the two emitted light pulses in the rest frame

Body energy in the stationary system after radiation emission

Body energy in the moving system after radiation emission

Body energy in the moving system, as printed in H - E = K + C

Kinetic energy of the body relative to the moving system after emission

Difference between kinetic energy before and after radiation emission

Second-order approximation of kinetic energy decrease to order (v/V)^2

Decrease in inertial mass of a body emitting radiation energy L

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).

Printed factor (3·10^10 cm/s)^2 in CGS converting energy in ergs to mass in grams

Unit-conversion entry for the paper's printed 9*10^20 factor. That is 0.14 percent above modern c^2 = 8.98755*10^20 cm^2/s^2 because the paper rounds V to 3*10^10 cm/s.

Effective viscosity of the dilute suspension, as printed

k-star is the suspension viscosity. The solvent viscosity is k. Neither is Boltzmann's constant.

Ratio of suspension viscosity to solvent viscosity

The ratio k-star/k. Distinct from the coefficient of phi.

Diffusion coefficient of the dissolved substance

Glyph pending facsimile. Used with Stokes drag and osmotic pressure to infer molecular size.

Absolute temperature

Universal molar gas constant