For thin-layer chromatography, define the TLC retardation factor using distances along the development direction:The origin coordinate is $y_0$; use the centre of a resolved spot and a front marked at the end of development. Both distances begin at the origin, never at the plate bottom. The ratio is dimensionless. An immobile spot has $R_f=0$; a spot at the front has $R_f=1$, where separation from other fast components may be poor. This distance ratio is distinct from the chromatographic partition coefficient and from a column retention time.

For an original stylized plate, choose absolute vertical coordinates $y_0=1\mathrm{cm}$, $y_{\mathrm{front}}=11\mathrm{cm}$, $y_A=4\mathrm{cm}$ and $y_B=8\mathrm{cm}$ above the plate bottom. The solvent distance is therefore $10\mathrm{cm}$, while the spot distances are $3\mathrm{cm}$ and $7\mathrm{cm}$:Using $4/11$ or $8/11$ would wrongly include the unused centimetre below the origin. These chosen positions do not represent measured pigments or the protocol's plate dimensions.

The TLC retardation factor depends on the sample, chromatographic stationary phase, eluent composition, and temperature; plate handling and development conditions must also match when comparing runs. The moving wet front and possible surface adsorption require their own transport assumptions. The equilibrium mobile fraction $f_m$ in the chromatographic partition coefficient model is not unconditionally equal to $R_f$; even that model depends on the phase volume ratio. Coincident TLC retardation factors alone never prove chemical identity.

Chapter 7 by Michael Edidin in The Legacy of Cell Fusion, pp. 101–114, published 8 August 1996 by Oxford University Press. This is a chapter authorship credit.

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Paper 9 by James Joseph Sylvester, reprinted on pp. 54–57 in The Collected Mathematical Papers of James Joseph Sylvester, Volume I. The reprint identifies the original publication as Philosophical Magazine XVI (1840), 132–135. Henry Frederick Baker edited the collection; he is not credited as author of this paper.

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Cited passages: The Cell: A Molecular Approach, 2nd edition by Geoffrey M. Cooper, The Golgi Apparatus: Indexed official section text: opening paragraphs and Organization of the Golgi, Figures 9.22–9.23; Indexed official section text: Protein Sorting and Export from the Golgi Apparatus, Figure 9.27 and targeting discussion; Official indexed citation header: Cooper GM, second edition, Sinauer Associates, 2000.

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Section of The Cell: A Molecular Approach, 2nd edition by Geoffrey M. Cooper. The 2000 publication date and author credits belong to the whole book; no separate chapter byline is established. Sinauer Associates publishes the book; NCBI Bookshelf at the National Library of Medicine hosts the text.

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Cited passages: Mobility of Membrane Proteins, lateral movement, cytoskeletal restriction and junction barriers.

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Section of The Cell: A Molecular Approach, 2nd edition by Geoffrey M. Cooper. Whole-book author: Geoffrey M. Cooper; no separate chapter byline is established. Sinauer Associates publishes the book; NCBI Bookshelf at the National Library of Medicine hosts the text. The year 2000 belongs to the second edition; no separate section revision date is established.

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