Avogadro's Hypothesis, and the Number That Came Later
Covers Avogadro's 1811 paper, the subsequent measurement of the constant by later chemists, and how 6.022 × 10²³ became the figure against which homeopathic dilutions are compared. Attributed throughout to the named publications.
Labelled by remedy and by potency; what is inside each vial is sugar.Photo: cottonbro studio / Pexels
The constant was measured long after the hypothesis, and fixed exactly in 2019.Photo: Lighten Up / Pexels
A 1811 paper on molecular volumes, a constant measured decades later, and the arithmetic that sets a ceiling on any dilution series
The Hypothesis Itself
Amedeo Avogadro published his molecular hypothesis in 1811 in the Journal de Physique, de Chimie et d'Histoire Naturelle. The core claim was that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules ↗ — a statement about proportion, not about any absolute count. Avogadro was a physicist from Turin, and his paper was largely ignored for roughly half a century. The hypothesis was not widely adopted until Stanislao Cannizzaro, at the Karlsruhe Congress of 1860, used it as the foundation for a consistent system of atomic weights. By that point, Avogadro had been dead for four years.
Sixty zeros, written out.Photo: https://kaboompics.com/ / Pexels
The constant that now bears his name — 6.022 × 10²³ entities per mole — is not a figure Avogadro himself calculated. The path to a measured value ran through the work of Josef Loschmidt, who in 1865 published the first credible estimate of the number of molecules in a cubic centimetre of gas at standard conditions. That figure, sometimes called the Loschmidt constant in continental Europe, gave chemists a quantitative handle on what Avogadro had described qualitatively. Jean Perrin, in experimental work published between 1908 and 1913 on Brownian motion, converged on a value close to 6 × 10²³ and proposed the name nombre d'Avogadro — Avogadro's number — for the constant. Perrin received the Nobel Prize in Physics in 1926, in part for this determination.
The International System of Units defines the mole as exactly 6.02214076 × 10²³ elementary entities, a value fixed by the 2019 redefinition of SI base units ↗. The constant is no longer a measurement with experimental uncertainty; it is a definition.
- 1811Avogadro publishes molecular hypothesis in Journal de Physique
- 1860Cannizzaro revives the hypothesis at the Karlsruhe Congress
- 1865Loschmidt estimates the number of molecules per cubic centimetre of gas
- 19081913 — Jean Perrin measures the constant via Brownian motion; proposes the name nombre d'Avogadro
- 1926Perrin awarded the Nobel Prize in Physics
- 2019SI redefines the mole: 6.02214076 × 10²³ is now a fixed definition, not a measurement
Where Dilution Meets the Constant
Homeopathic dilution scales were codified before Perrin's measurement and long before the SI definition. Samuel Hahnemann's centesimal scale, described in successive editions of the Organon beginning in 1810, specifies a 1-in-100 dilution at each step, with vigorous shaking — succussion — applied between steps. On that scale, a preparation labelled 12C has been diluted by a factor of 10⁻²⁴, which, starting from one mole of material, leaves roughly one molecule in the final volume. Above 12C, the arithmetic crosses the threshold set by Avogadro's number: statistically, no molecule of the original substance is likely to remain.
The threshold is not a sharp line — it depends on the starting concentration and the volume of the final preparation — but the order of magnitude is consistent. A 30C preparation carries a dilution factor of 10⁻⁶⁰, a figure worked out as straightforward repeated multiplication of the centesimal ratio. For context, 10⁻⁶⁰ is larger than the ratio of a single proton's volume to the estimated volume of the observable universe (roughly 10⁻¹²⁵). At 200C, the exponent is 10⁻⁴⁰⁰. In none of these cases does the arithmetic allow for the presence of a single molecule of solute in any physically realistic volume of solvent.
This relationship between the Avogadro constant and dilution scale is presented in evaluations of homeopathy by scientific and government bodies as a matter of chemistry, not of therapeutic assessment. The Australian National Health and Medical Research Council's 2015 systematic review notes the molecular implausibility of high-potency preparations as part of its framing. The European Academies Science Advisory Council's 2017 statement on homeopathic products made the same arithmetic point, citing the Avogadro limit explicitly.
The Number as a Reference Point
Avogadro's number entered homeopathic discourse not as a rebuttal but as a reference point: it is the figure against which the dilution arithmetic is compared in pharmacopoeial, regulatory and scientific documents that address the question of what high-potency preparations can contain. The Homeopathic Pharmacopoeia of the United States acknowledges the dilution scales it governs without commenting on molecular content. Regulatory bodies, including the US Federal Trade Commission in its 2016 enforcement policy statement, have cited the Avogadro constant when addressing the factual basis of product claims.
Avogadro published a hypothesis about molecular volumes. It took fifty years for chemistry to accept it, another fifty for Perrin to measure the implied constant, and a further century for SI to fix it by definition. The number arrived; the dilution arithmetic did not change.