Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt
Annalen der Physik, 1905 · paper · Physics
Proposes, as a heuristic viewpoint, that light energy is distributed discontinuously in space as localized energy quanta that are absorbed or emitted only whole. It argues this helps explain black-body radiation, photoluminescence and cathode-ray production by ultraviolet light.
Checked: PDF from myweb.rz.uni-augsburg.de, fetched 4 Oct 2026. Page numbers are those of that PDF.
3 findings
Substance Printed constant "α = 6,10 . 10^-56" does not reproduce "N = (β/α)(8πR/L³) = 6,17 . 10^23"; with the printed α the formula gives about 6,17·10^22, so the exponent of α appears to be −57.
- p. 5 §2, constants after Planck's formula
α = 6,10 . 10^-56
- p. 6 §2, formula for N
= 6,17 . 10^23
- p. 5 §2, constants of Planck's formula
α = 6,10 . 10-56
- p. 6 § 2, value of N
= 6,17 . 10²³
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the numerical values R = 8.31·10^7 erg/K and L = 3·10^10 cm/s, which the paper does not print. Viewed pages 5 and 6: the exponent −56 for α, β = 4,866·10^-11 and N = 6,17·10^23 are all as quoted. Mantissa: 4.866/6.10·8π·8.31/27 = 6.17; powers of ten: −11 + 56 + 7 − 30 = 22. The mantissa matches exactly and the result is a clean factor of 10 below the printed N, so only the power of ten in α is off. The printed N and 1/N = 1,62·10^-24 g are mutually consistent.
Second check: another model agreed
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Reference or label Conversion of Π to volts is printed two ways: "so ist Π.10^-8 das Potential in Volts" and, a few lines later, "Wir erhalten Π.10^7 = 4,3 Volt".
- p. 15 §8, sentence after footnote mark 1
so ist Π.10^-8 das Potential in Volts
- p. 15 §8, numerical estimate
Wir erhalten Π.10^7 = 4,3 Volt
- p. 15 §8, sentence after footnote mark 1
so ist Π.10-8 das Potential in Volts
- p. 15 § 8, after E = 9,6·10³
Π. 10−8 das Potential in Volts
Judge's note: Viewed page 15 image. Both exponents are printed as quoted (−8, then an unsigned 7) for the same quantity in consecutive sentences. Check with P' = 0, ν = 1,03·10^15, β = 4,866·10^-11, E = 9,6·10^3 from the page and R = 8.31·10^7 (not printed in the paper): mantissa 4.34, powers of ten 7 − 11 + 15 − 3 = 8, so Π ≈ 4.3·10^8 and Π·10^-8 = 4.3 V. The factor 10^7 is the odd one out; the 4,3 Volt result itself stands.
Second check: another model agreed
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Reference or label "Bei den von Hrn. Lenard untersuchten Substanzen ist P E stets bedeutend größer als R β ν, da die Spannung, welche die Kathodenstrahlen durchlaufen haben müssen ...": "PE" is printed where ΠE is meant.
- p. 16 §8, sentence after the cathodoluminescence inequality
ist PE stets bedeutend größer als Rβν
- p. 16 §8, sentence after the second inequality
ist P E stets bedeutend größer als R β ν, da die Spannung
Judge's note: Viewed page 16 image. An italic Latin P is printed, distinct from the Π in the inequality ΠE + P' ≧ Rβν directly above. The justification given is the voltage traversed, which is the potential Π throughout §8. P is defined on the previous page as the exit work of an electron, so P·E is not a quantity of the paper.
Second check: another model agreed
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8 minor (typos and the like; most checked by the judge only)
Wording Footnote equation "− d(E − TS) = p dv = T dS = R (n/N) dv/v ;" omits the factor T on the right, although the conclusion drawn from it is "p v = R (n/N) T".
- p. 11 footnote 1, first equation
− d(E − TS) = p dv = T dS = R n/N dv/v ;
- p. 11 footnote 1, conclusion
p v = R n/N T.
Only the authors can say what is right here.
Judge's note: Viewed page 11 image; the last member is printed without T. Reworking: from S − S0 = R(n/N) lg(v/v0), dS = R(n/N) dv/v, so T dS = R(n/N) T dv/v, and p dv = T dS gives pv = R(n/N)T. As printed the chain would give pv = R(n/N). The stated result is correct, so the step is faulty only by the dropped T.
Second check: another model agreed
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Typo Reflexive pronoun printed twice in one clause: "während sich die Energie eines von einer punktförmigen Lichtquelle ausgesandten Lichtstrahles ... auf ein stets wachsendes Volumen sich kontinuierlich verteilt".
- p. 1 first paragraph, last sentence
während sich die Energie eines von einer punktförmigen Lichtquelle ausgesandten Lichtstrahles
- p. 1 first paragraph, last sentence (continuation)
auf ein stets wachsendes Volumen sich kontinuierlich verteilt
Judge's note: Viewed page 1 image. Both "sich" are printed in the same subordinate clause governed by "verteilt"; one is redundant. Cosmetic.
Second check: none (judge only)
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Typo Wrong case: "In einem von vollkommen reflektierenden Wänden eingeschlossenen Raumes befinde sich" (dative "Raume" is required after "In einem").
- p. 2 §1, first paragraph
In einem von vollkommen reflektierenden Wänden eingeschlossenen Raumes befinde sich
Judge's note: Viewed page 2 image. "Raumes" with final s is clearly printed after "In einem ... eingeschlossenen". Grammatical slip, not OCR.
Second check: none (judge only)
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Typo Footnote 2 prints "welche die anderen Größen A bez. x besitzen" where the phase symbol α is meant (same sentence earlier: "der Größen A bez. α").
- p. 4 footnote 2, near the end
welche die anderen Größen A bez. x besitzen
Judge's note: Viewed page 4 image. At the end of the line the glyph after "A bez." is an italic x, visibly different from the α printed earlier in the same sentence. No quantity x is defined in the footnote. Scan resolution in the small footnote type leaves slight doubt, but the glyph reads as x.
Second check: none (judge only)
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Typo "aus welcher das Boyle-Gay-Lussacsche Gesetz und das gleichlautende Gesetz des osmotischen Druckes leicht thermodynamisch ableiten kann¹); keine Voraussetzung über das Gesetz zu machen braucht, nachdem sich die Moleküle bewegen": the relative clause lacks its subject ("man"), and "nachdem" stands for "nach dem".
- p. 11 §5, last paragraph
leicht thermodynamisch ableiten kann
- p. 11 §5, last paragraph
nachdem sich die Moleküle bewegen
- p. 11 end of §5
das Gesetz zu machen braucht, nachdem sich die Moleküle bewegen
- p. 11 end of §5
aus welcher das Boyle-Gay-Lussacsche Gesetz und das gleichlautende Gesetz des osmotischen Druckes leicht thermodynamisch ableiten kann
Judge's note: Viewed page 11 image. No "man" is printed in the relative clause, "nachdem" is set as one word, and a semicolon follows the footnote mark. The sense is "the law according to which the molecules move". Cosmetic; the meaning is recoverable.
Second check: none (judge only)
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Typo "es muß also die Bezeichnung gelten:" is followed by an inequality; "Beziehung" (relation) is meant.
- p. 13 §7, line before the Stokes inequality
es muß also die Bezeichnung gelten:
Judge's note: Viewed page 13 image. The word is printed "Be-/zeichnung" across the line break, directly before the inequality (R/N)βν2 ≦ (R/N)βν1. A relation "holds", a designation does not; wrong-word misprint.
Second check: none (judge only)
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Typo "die erzeugte Lichtmenge der erregenden unter sonst gleichen Umständen nach unserer Auffassung der erregenden Lichtstärke proportional sein muß": "der erregenden" appears twice, giving two competing dative complements.
- p. 13 §7, paragraph after "Stokessche Regel"
die erzeugte Lichtmenge der erregenden unter sonst gleichen Umständen nach unserer Auffassung der erregenden Lichtstärke proportional sein muß
Judge's note: Viewed page 13 image. The text is printed as quoted. The first "der erregenden" has no noun and the dative object recurs as "der erregenden Lichtstärke"; one of the two is redundant. The meaning is unaffected.
Second check: none (judge only)
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Typo Redundant wording: "daß jedes Elektron beim Verlassen des Körpers eine (für den Körper charakteristische) Arbeit P zu leisten hat, wenn es den Körper verläßt".
- p. 15 §8, top of page
daß jedes Elektron beim Verlassen des Körpers eine (für den Körper charakteristische) Arbeit P zu leisten hat, wenn es den Körper verläßt
Judge's note: Viewed page 15 image. The sentence is printed as quoted, with the same condition stated twice. It is a stylistic redundancy; the sentence is grammatical and its meaning is unaffected.
Second check: none (judge only)