Reciprocity Failure and the Life of the Latent Image

Point a light meter at a subject and it hands you a pair of numbers. It does not care which pair: it assumes that a hundredth of a second at one brightness and a hundred seconds at a ten-thousandth of that brightness are the same exposure, because the product is the same. For most of the range of ordinary photography that assumption is good enough to build an industry on. At the two ends it fails, and it fails in opposite directions for opposite reasons — both of which come straight out of the four-atom cluster of the previous page.

This page is about what happens to that cluster when the light arrives too slowly, too fast, or a long time ago.

The law, and who stated it

The claim is simple enough to write on one line. Equal products of intensity and time produce equal photochemical effect. Schwarzschild states it in exactly that form at the head of his 1900 paper: the so-called law of reciprocity states that sources of light of different intensity I produce an equal degree of blackening in their photographic images under different exposures t if the product I × t has the same value in the different cases.

E = I × t

The reciprocity law, as Schwarzschild states it

Here E is exposure, I is the illumination falling on the material, and t is the time it falls for. Everything a light meter does rests on that equation, and so does every exposure table in every manual since the 1850s.

⁇Bunsen and Roscoe: 1855–1859, and where 1862 comes from

The law carries the names of Robert Bunsen and Henry Enfield Roscoe, who did not state it about photographic plates at all. They stated it about a mixture of chlorine and hydrogen, which they used to build the first instrument capable of measuring the chemical action of light absolutely rather than relatively.

Eder dates the work 1855–1859. He records that Bunsen and Roscoe began their investigations of chlorine detonating gas in 1854, that the dissertations appeared under the title Photochemische Untersuchungen in Poggendorff’s Annalen across 1855 to 1859, and that within the field where photochemical induction has disappeared, the amount of substance changed per unit time is in direct proportion to the incident light intensity — which he labels, in so many words, the Bunsen and Roscoe Reziprozitäts-Gesetz.

Mike Ware dates it 1862, citing Annalen der Physikalische Chemie volume 117 — a later paper in the same series.

Part I settled this course on 1855–1859, on Eder’s evidence, and this page keeps that. The disagreement is not about who or what, only about which paper in a five-year run of papers to name; and 1862 is the date you will most often meet, so it is worth knowing why this course does not use it.

Schwarzschild’s exponent, and what he actually measured

By the 1890s astronomers had a problem the law could not explain. Scheiner had shown in 1891 that prolonging an exposure did not bring in the number of faint stars the law predicted. Karl Schwarzschild, working at the von Kuffner Observatory in Vienna, confirmed the deviation on stellar plates, then went to Eder’s k. k. graphische Lehr- und Versuchsanstalt to reproduce it under laboratory control — same plate, cut up; same developing bath; same time; only the lamp distance changed.

His result is one number. Equal blackening is produced when

I × t^p = constant

Schwarzschild's rule

with p = 0.86 for the Schleussner gelatine plates he tested. I is intensity, t is time, and p is an exponent applied to time alone. Because p is less than one, time is worth less than the law says it is: doubling the time buys less than doubling the intensity would.

His own worked pair makes the size of the effect concrete.

🧮Schwarzschild's two exposures, checked

For the same degree of blackening he found these two combinations:

Intensity I	Time t	I × t	I × t0.86
81	4.8 s	389	312
1	785 s	785	309

Read the third column first. The reciprocity law says those two numbers should be equal; they differ by a factor of two. Schwarzschild’s own summary of it is the sentence to remember: on diminishing the intensity to 1/81, twice the amount of light is necessary to produce the same blackening.

Now read the fourth column. With time raised to the power 0.86 instead of 1, the two agree to within one per cent — 312 against 309, which he calls equal within the limits of the errors of observation. Check it yourself: 4.8^0.86 = 3.85, and 81 × 3.85 = 312; 785^0.86 = 309.

Two things follow. The exponent is not a fudge: it collapses a factor-of-two discrepancy to one per cent across an eighty-fold range of intensity. And it is not a law of nature either, because it is a property of that plate — which the next section is about.

Schwarzschild also reported the related effect that a chopped exposure is worth less than a continuous one of the same total duration. Using Scheiner’s sensitometer, continuous exposures of 96, 72, 48, 24 and 12 seconds matched intermittent exposures of 99, 80, 54, 30 and 16.5 seconds, with the open fraction falling from 1 in 2.5 to 1 in 15 down the series. The shorter the flashes and the longer the gaps, the worse the loss. Hold on to that: it is the same phenomenon as low-intensity failure seen from another angle, and it is the reason the mechanism below is about timing rather than about brightness as such.

Where the law breaks, and the two different reasons

Reciprocity failure is not one effect. It is two, at opposite ends of the intensity scale, with opposite mechanisms and opposite consequences, and the course’s own experiment and its pinhole work will meet both.

What reciprocity failure looks like: the exposure needed for one fixed density

• Exposure needed for a fixed density

Show the numbers behind this plot

A shallow U-shaped curve plotted against illumination. Across the middle three or four decades of illumination the curve is flat: the same total exposure, intensity multiplied by time, produces the same density however that product is made up, which is the reciprocity law holding. At the left-hand end, at very low illumination, the curve turns upwards steeply: much more total exposure is needed to reach the same density, and this arm is labelled low-intensity reciprocity failure, the arm that matters for pinhole photography, night exposures and printing-out in dull weather. At the right-hand end, at very high illumination, the curve turns upwards again, less steeply, and this arm is labelled high-intensity reciprocity failure, the arm that matters for electronic flash and for printing out in direct sun. A horizontal guide line marks the level the reciprocity law predicts everywhere. A note records that the shape is drawn to teach and was not measured from any material, and that the width of the flat region and the steepness of each arm differ from material to material.

Series	log illumination (dim on the left, bright on the right)	log exposure needed for a fixed density
Exposure needed for a fixed density	-4.00	0.62
Exposure needed for a fixed density	-3.50	0.42
Exposure needed for a fixed density	-3.00	0.26
Exposure needed for a fixed density	-2.50	0.14
Exposure needed for a fixed density	-2.00	0.06
Exposure needed for a fixed density	-1.50	0.01
Exposure needed for a fixed density	-1.00	0.00
Exposure needed for a fixed density	0.00	0.00
Exposure needed for a fixed density	1.00	0.00
Exposure needed for a fixed density	1.50	0.01
Exposure needed for a fixed density	2.00	0.05
Exposure needed for a fixed density	2.50	0.13
Exposure needed for a fixed density	3.00	0.24

Drawn to teach, not measured. Only the shape is general: where the flat region begins and ends, and how steep each arm is, are properties of a particular emulsion, and the manufacturer's sheet is the only place to get them. The curve is drawn to show the shape, not measured from a real material. Your own materials will differ, and measuring them is what the sensitometry part of the course is for.

Low-intensity failure: the first atom does not wait

The mechanism follows directly from the Gurney–Mott alternation. A latent image is built one silver atom at a time, and about four atoms are needed. The steps are separated in time: an electron is trapped, then a silver ion has to travel through the lattice and arrive.

A single silver atom on a crystal surface is not a stable object. It can lose its electron again and revert to a silver ion, and if it does, the crystal is back where it started. So the whole business is a race between two clocks: the lifetime of a one-atom speck, and the interval between photon arrivals at that crystal.

At ordinary intensities the second photon arrives long before the first atom decays, and the cluster grows. Dim the light enough and the interval between arrivals grows past the lifetime of the speck. The crystal can then absorb photons all day and never accumulate four atoms at once, because it keeps losing the first one before the second arrives.

ILFORD states the cause in one sentence on its own reciprocity sheet: low-intensity reciprocity failure is caused by a reduced efficiency in forming stable development centres with lower levels of light. Note the word stable. That is the whole mechanism in a manufacturer’s phrasing.

A race between two clocks, at two intensities

1. 1A photon is absorbed and a silver atom forms — one electronic step followed by one ionic step
2. 2The lifetime of a one-atom speck — it can lose its electron again and revert to a silver ion
3. 3The developable threshold — about four atoms, on Ware's figure and with his hedge
4. 4Decay before the next arrival — the count returns to zero and the crystal starts again

Drawn, not measured: the course has read no source giving the lifetime of a one-atom speck, and the spacing here carries no timescale. What the drawing claims is only the relation between two intervals, which is what the mechanism turns on.

Sheppard and Mees measured the low-intensity arm in 1907, and their table is the only measurement of it this course holds. They found the exposure needed to reach a density of 1.0 on a Wratten Ordinary plate developed in ferrous oxalate, at intensities spanning four decades.

Sheppard and Mees, 1907: the exposure product needed for density 1.0

• Wratten Ordinary plate, ferrous oxalate, density 1.0

Show the numbers behind this plot

Six measured points from Sheppard and Mees's Table 110, plotted as the product of intensity and time needed to reach a density of one against the logarithm of intensity. From the brightest intensity, 84.5 candle-metres requiring 0.204 seconds, down through 0.452, 0.130 and 0.0198 candle-metres, the product stays between about 15.5 and 18.4 candle-metre-seconds, which is the reciprocity law holding across nearly four decades of intensity. At the two dimmest intensities, 0.0074 candle-metres requiring 4760 seconds and 0.0056 candle-metres requiring 6460 seconds, the product jumps to about 35 and 36, roughly double. The plot therefore shows a flat region and then a sharp upturn at the low-intensity end, and does not extend to high enough intensities to show the other arm at all.

Series	log intensity, in candle-metres	I × t needed, in candle-metre-seconds
Wratten Ordinary plate, ferrous oxalate, density 1.0	-2.25	36.20
Wratten Ordinary plate, ferrous oxalate, density 1.0	-2.13	35.20
Wratten Ordinary plate, ferrous oxalate, density 1.0	-1.70	18.40
Wratten Ordinary plate, ferrous oxalate, density 1.0	-0.89	15.60
Wratten Ordinary plate, ferrous oxalate, density 1.0	-0.34	15.55
Wratten Ordinary plate, ferrous oxalate, density 1.0	1.93	17.20

Measured, from Table 110 of Sheppard and Mees's Investigations on the Theory of the Photographic Process (1907); products recomputed from the intensities and times as printed. A seventh row in that table is omitted here because, in the scanned copy this course holds, its printed logarithm does not agree with its printed intensity. Note also what the data do not show: the intensities never go high enough to reach the other arm.

Two of their conclusions matter more than the numbers. First, the failure is not a simple function of time. Second — and this is the one people get wrong — they tested whether the size of the failure depends on the total exposure and found that it does not: two series at intensities differing by six hundredfold, matched for total exposure, deviated by the same amount. Reciprocity failure is caused by the rate at which light arrives, not by how much of it arrives.

High-intensity failure: too many electrons, in too many places

At the other end the loss has the opposite cause. Very bright light frees electrons in a crystal faster than the ionic step can keep up with them. Instead of one trap collecting four atoms in sequence, electrons are caught at many separate sites, and the crystal ends up carrying a scatter of sub-developable specks — several one- and two-atom clusters where a single four-atom cluster would have made it developable. Some of the image also ends up inside the crystal rather than on its surface, where an ordinary developer cannot reach it, which the previous page called the internal latent image.

Ware confirms that the high-intensity arm is real, that it is rarely of consequence in ordinary film photography, and that it matters a great deal in the early printing-out processes that used direct sunlight. He also draws out the practical consequence that nineteenth-century printers exploited without being able to explain it: bright sun gives a lower-contrast printed-out image than a proportionally longer exposure to a clear north sky, because the shadows suffer the failure more than the highlights. Burton and Towler both recommended the choice of illumination as a method of contrast control, decades before anyone could say why it worked.

!How much of that mechanism is sourced

The existence of both arms is thoroughly sourced: Schwarzschild, Sheppard and Mees, Ware and three current manufacturers all state it, and two of them publish correction factors for it. The mechanisms above are the standard account, and this course has read them stated only in outline — ILFORD’s one sentence about stable development centres for the low-intensity arm, and nothing at all from a Tier-1 source for the high-intensity arm. What is offered here is what the Gurney–Mott mechanism and the four-atom threshold require, set out as an argument you can check, rather than a quotation. Treat the sub-developable-speck account of high-intensity failure as the course’s reading, not as a measured result.

Reading a reciprocity correction on a data sheet

Every manufacturer that sells film for long exposures publishes a correction, and no two publish it in the same form. Here are three, and they are the same law wearing different clothes.

ILFORD publishes an exponent. Their sheet gives one factor P per film and this equation:

T_c = T_m^P

ILFORD's correction

where T_m is the metered (indicated) time in seconds and T_c is the corrected time. Their own worked example is HP5 Plus at a metered 10 seconds: 10^1.31 = 20.4 s, rounded to 20 seconds. They state that exposures of one second or less need no compensation, that the factor differs from film to film, and that very long exposures may also need less development because the shadows suffer the failure more than the highlights, which raises contrast.

BERGGER publishes a table in stops. For Pancro 400: nothing below one second, +0.5 stop at one second, +1 stop at ten seconds, +2 stops at sixty seconds.

FOMA publishes a multiplication table, and calls the effect by Schwarzschild’s name. For Fomapan 100 Classic: ×1 from a thousandth to half a second, ×2 at one second, ×8 at ten seconds, ×16 at a hundred seconds, with the equivalent aperture corrections of 0, −1, −3 and −4 stops.

🧮Deriving ILFORD's factor from Schwarzschild's exponent

The two look unrelated. They are not. This derivation is the course’s own; neither sheet states it.

Your meter assumes reciprocity, so the time it indicates satisfies I × T_m = K′ for some constant. The material actually obeys Schwarzschild, so the time it really needs satisfies I × T_c^p = K. Substitute I = K′/T_m into the second:

T_c^p = (K / K′) × T_m

Substituting

so T_c is proportional to T_m^1/p. ILFORD anchors the fit at one second — a metered second needs no correction — which forces the constant of proportionality to one when time is measured in seconds, and leaves

P = 1 / p

ILFORD's P is the reciprocal of Schwarzschild's p

Run the films through it. HP5 Plus at P = 1.31 is p = 0.76. FP4 Plus at P = 1.26 is p = 0.79. Ortho Plus at P = 1.25 is p = 0.80 — and ILFORD’s own Ortho Plus sheet prints the same relation in the other notation, T_a = T_m^1.25, which is a useful confirmation that the two forms really are one form. Schwarzschild’s 1899 plate, at p = 0.86, would take P = 1.16.

Now check BERGGER against it. Their +1 stop at ten seconds means 10 → 20 s, so P = log 20 / log 10 = 1.30; their +2 stops at sixty seconds means 60 → 240 s, so P = log 240 / log 60 = 1.34. One table, one exponent, near enough. But their +0.5 stop at one metered second cannot be produced by any exponent at all, because one raised to any power is one — so at the short end the two makers genuinely disagree about where the failure starts.

FOMA disagree by much more. Their ×8 at ten seconds implies P = log 80 / log 10 = 1.90, and their ×16 at a hundred seconds implies P = log 1600 / log 100 = 1.60. Neither the exponent nor its value matches ILFORD’s films, and the correction is several times larger. That is not an error in anybody’s sheet. It is the point: the exponent is a property of the emulsion, exactly as Sheppard and Mees said in 1907 when they noted that Abney and Englisch both found p variable while Schwarzschild treated it as fixed.

The practical rule that follows is short. Use the sheet for the film that is in the camera, and no other. Part VI (pinhole-exposure-and-reciprocity-correction) is where these corrections stop being a table and become the difference between a negative and a blank, because a pinhole at f/200 makes long exposures the normal case rather than the exception; that page owns the values and the field arithmetic, and this one owns the reason they exist.

The life of the latent image

A latent image is a few atoms of a reactive metal sitting on the surface of a crystal, in a moist organic colloid, in air. It is not obvious that it should survive at all, and the interesting fact is how well it does.

Manufacturers state the keeping they will stand behind, and the statements are narrow. ILFORD’s Multigrade RC sheet says that no significant change in picture quality will be seen when the papers are left for a period of 24 hours after exposure and before processing — twenty-four hours, not a week, and not a claim about anything longer. For films, ILFORD’s instruction is to process exposed film as soon as practical and store it meanwhile in cool, dry conditions; Kodak’s is to store exposed film in a cool, dry place and process it promptly. HARMAN’s direct positive paper sheet names the mechanism outright: process as soon as possible after exposure to minimise any risk of latent image regression.

The most useful description of what regression actually does is a century old. Sheppard and Mees quote Baekeland’s conclusions, and they are a list of the variables:

• it happens to all halide emulsions, and more to under-exposed than to over-exposed material;
• it may become apparent in forty-eight hours under some conditions, and can go on until the image has entirely vanished;
• it is faster at high temperatures;
• it is worse in a damp atmosphere than a dry one;
• an acid film favours it; a neutral or slightly alkaline one suffers less.

Heat, humidity, and the chemistry of the layer. Every one of those is something you control by where you put the exposed material, which is why “cool and dry” is not a platitude on a data sheet but the whole of the available treatment.

The fourth agent is oxidation. Sheppard and Mees list what destroys a latent image outright — free halogen first, then chromic acid, persulfate, nitric acid, ammoniacal copper compounds and mercury(II) chloride — a roll-call of oxidisers, which is what you would expect of an image made of a few atoms of metal. The most practically alarming entry is not in that list but in the Encyclopaedia Britannica of 1911, reporting W. J. Russell’s experiments: contact with substances such as wood makes a plate fog on development, the probable agent being hydrogen peroxide, and the same substance will destroy the effect light has already had. Russell’s conclusion, quoted there, is the practical one: it gives a warning to store exposed plates only for brief periods.

⁇Does the latent image fade or not?

The evidence genuinely conflicts, and it conflicted from the start.

C. H. Bothamley reported plates exposed two and a quarter and four years before development that gave negatives in no wise different from those developed immediately.

Gaedicke stated that the latent image gradually loses tone and intensity.

Baekeland concluded that it happens to everything, and can go to total loss in some conditions.

Sheppard and Mees, who report all three, add the methodological warning that resolves much of it and which nobody should skip: photographers confuse a change in the plate with a change in the latent image. They had already shown that plates stored in an unfavourable atmosphere changed their rate of development, the velocity coefficient falling to as much as a third of its former value in six months. A thin negative from an old exposed plate might be a decayed latent image or a lazier emulsion, and without a control you cannot tell which.

That is not an academic point. It is the reason Station 2 of this part’s darkroom session develops three strips and not two: one exposed and developed today, one exposed today and developed in a week, and one exposed and developed in a week. The third strip is what separates the two explanations, and it costs one sheet of paper.

☠Latensification and hypersensitisation — Level D, described and not instructed

This box, and only this box, carries the Level D marking. The page as a whole is an unclassified lesson. Level D means the course studies a practice as chemistry and history and gives no procedure: no quantities, no times, no apparatus.

If a latent image can be pushed down below the threshold by decay, it can be pushed up over it by a small uniform dose of something. Two families of practice did exactly that, and both have modern names that ILFORD still uses on its safelight sheet.

Hypersensitisation treats the material before exposure to make it faster. Latensification treats it after exposure to push sub-developable specks over the threshold. ILFORD’s safelight test turns on the distinction: the strip given a safelight exposure after the enlarger exposure is, in their words, checking for latensification, and the strip given it before is checking for hypersensitisation. They also note which matters more — paper is more sensitive to safelight fogging after it has been exposed in the enlarger than before. Kodak’s guide says the same in different words, calling a low-level overall exposure before or after the printing exposure a super-additive exposure. (That is Kodak’s term for an exposure effect and has nothing to do with the superadditivity of two developing agents, which is a different phenomenon taught in Part VIII.)

The historical methods, named without detail. A dye bath was the common hypersensitiser: Wall’s 1924 manual gives one built from pinaverdol, pinachrome and pinacyanol in alcohol, and records its governing defect, which is that treated plates will not keep more than about 36 hours. Beyond the dye baths, three families are regularly named in the literature: exposure to mercury vapour, treatment with hydrogen (a practice associated with long-exposure astronomical plates), and a uniform faint pre- or post-exposure to light.

What this course could not verify, and says so rather than filling the gap. The corpus behind this course contains no source describing the mercury-vapour or hydrogen procedures. It therefore names them as practices that existed and gives no method, no concentration, no temperature and no timing — not as a safety flourish, but because it does not know them and will not guess.

Why they are Level D regardless. Mercury vapour is invisible, odourless and released from a liquid at ordinary room temperature; HSE’s EH40 sets a long-term workplace exposure limit for mercury and its divalent inorganic compounds of 0.02 mg per cubic metre, a figure a domestic room has no way of measuring, let alone holding. Hydrogen work is flammable-gas work. Neither belongs in a home darkroom, and the modern answer to “my material is not fast enough” is to buy a faster material, which the nineteenth century could not do and we can.

What survives, and is not Level D at all, is the measurement: the safelight test in Station 4 of this part’s darkroom session is a latensification experiment run for a defensive purpose. You are looking for the effect precisely so that you can get rid of it.

Reversal: solarisation, Herschel and Clayden

Keep going past the shoulder of the characteristic curve and something strange happens: more exposure gives less density. Hurter and Driffield named the region for what it does — the period of reversal — and described the arithmetic of it plainly. While the deep shadows are still gaining density the highlights have passed their maximum and are losing it, so that with enough exposure the shadows overtake the highlights and the negative becomes a positive.

Sheppard and Mees classify the varieties, and the classification is worth having because these things are constantly confused with one another. Setting aside the forms that are merely a second exposure printing through, three are real:

Solarisation proper: reversal under continuous exposure to light or X-rays, at enormous exposures.

The Clayden effect: a very short exposure — a thousandth of a second or less — to intense light, followed by diffuse light, after which the intensely exposed region develops less. Sheppard and Mees suggest it is probably an exaggerated case of the departures from the Bunsen–Roscoe law, which puts it in the same family as the high-intensity failure two sections above; they credit R. W. Wood’s investigation of it, and Hurter and Driffield’s bibliography records A. W. Clayden’s own paper, “Experiments on Reversal and Clayden Effect”, in the British Journal of Photography volume 58. The example the effect is usually explained by is a lightning flash recording as a dark streak against a lighter sky, but this course has read the definition and not that history.

The Herschel effect: long-wavelength light bleaching an image that short-wavelength light has already made.

⁇What causes solarisation

There is no settled account in the sources this course holds, and the disagreement is old and substantive. Sheppard and Mees list the positions:

• Abney, and Englisch independently, held that two actions run in parallel, the second producing a less reducible product that eventually predominates; Abney tied it to oxygen.
• Hurter and Driffield, and Sterry, held that the released halogen destroys the latent image — a straightforward extension of the halogen-acceptor argument of the previous page.
• Precht held that it is largely a development phenomenon, and had the strongest single piece of evidence: soaking a plate in developer before exposure pushed the onset of reversal from about 9,000 units to some 400,000, a factor of about forty-four.
• Sheppard and Mees’s own evidence for the halogen account is that bathing the film in sulfite or nitrite solution retards reversal.

The modern account you will most often meet — that the halogen re-forms silver halide over the cluster, and that the image is driven inside the crystal where a surface developer cannot find it — is consistent with several of those positions at once, and this course has read no Tier-1 source stating it, so it is reported here as the common modern explanation and not as settled.

What is not in doubt: reversal is real, it is reached only at exposures far beyond anything ordinary photography uses, and where the reversal point sits depends on how the material is developed as much as on how it was exposed.

The Herschel effect, and what Herschel actually saw

On 27 August 1839, working with a concentrated solar spectrum on chloride-sensitised paper, Herschel noticed something he had not expected. Where the full red of the spectrum had fallen, the paper was whiter than the surrounding sheet, which had been discolouring under stray daylight from the sky. The red rays, he wrote in the paper the Royal Society read in 1840, are by no means to be regarded as inactive, but rather as exciting an action of an opposite nature to that of the blue, violet and lavender rays.

He then found the limit of it. On paper already darkened, red light did not restore whiteness but turned the darkening a fiery red, and no amount of further red exposure would take it further. His attempt to make a positive copy of an engraving this way produced shadows in black and highlights “eaten out in red, the colour of venous blood”. A powerful red ray could neutralise a feeble white one at the moment of action, but could not undo an effect already fully produced.

The name attached later, and it attached to something slightly different. Eder records that Draper (1842), Lerebours (1846) and Claudet (1847) found the same red-light action on the latent image of the iodised daguerreotype plate, and that the work was extended to collodion and to gelatine silver bromide. That is the modern definition: Ware describes the Herschel effect as the ability of long-wavelength light to quench the latent image in an exposed but undeveloped silver halide emulsion, and notes that it is the basis of the one direct-positive process still in limited commercial use.

So Herschel’s own observation was about visible print-out silver, and the effect named after him is about the invisible latent image. They are the same physics — long-wavelength light acting on silver that short-wavelength light has already made — applied at two very different scales, and it is worth knowing that the name travelled.

!The Sabattier effect is not on this page, and this is why

Every effect above happens during exposure, or between exposure and development. Nothing has touched a tray.

The Sabattier effect — the partial reversal and the black Mackie line you get by re-exposing a print or a film part-way through development — is a development phenomenon. Its mechanism involves the developer, the bromide released by the grains already developing, and the fogging of the remaining halide, none of which exists in the dark box where reciprocity failure and the Herschel effect happen. It is taught in the printing and experiment parts, where there is a tray to do it in.

Three tests to keep them apart. Solarisation needs no second light and no developer: it is one very long exposure. The Herschel effect needs a second exposure of a different colour, before development. The Sabattier effect needs a second exposure during development. A page that calls the third one “solarisation” — and a great many do — has merged two effects that share nothing but an appearance.

Recap

• The reciprocity law says equal products of intensity and time give equal effect. It is Bunsen and Roscoe’s, from the photochemical investigations of 1855–1859, and it was stated about chlorine and hydrogen, not about plates.
• Schwarzschild’s rule replaces it with I × t^p = constant, and he measured p = 0.86 on one 1899 plate. The exponent collapsed a factor-of-two error to one per cent — but it is a property of the emulsion, not a constant of nature.
• Low-intensity failure is a race: a one-atom speck decays before the next photon arrives, so the four-atom threshold is never reached. ILFORD calls it a reduced efficiency in forming stable development centres.
• High-intensity failure is the opposite crowding: too many electrons at once, trapped at too many sites, giving sub-developable specks and internal image. It matters most for printing out in direct sun, where it was used as a contrast control long before it was understood.
• The failure depends on the rate, not the total. Sheppard and Mees proved that in 1907.
• Data sheets give the correction in three different forms — an exponent, a table of stops, a table of multipliers — and they are the same law. ILFORD’s P is the reciprocal of Schwarzschild’s p. The values differ from film to film by more than a factor of two, so use the sheet for the film you have.
• The latent image decays, faster when hot, damp, acid or under-exposed, and oxidisers destroy it outright. ILFORD stands behind 24 hours on paper; everyone says process promptly. Whether it fades measurably in a week is exactly what Station 2 will tell you — provided you develop the control.
• Solarisation, Clayden and Herschel are three different reversals, all of them before development, and none of them is the Sabattier effect.

Check your understanding

Question 1. Two exposures are given to the same film. One is 1/100 s at a bright subject; the other is 100 s at a subject 10,000 times dimmer. The metered exposure is identical. What do you expect on the developed negative, and why?

• Identical densities, because exposure is intensity times time
• The long exposure gives noticeably less density, because at low intensity a one-atom speck decays before the next photon arrives
• The long exposure gives more density, because the crystals have longer to respond
• The short exposure gives less density, because the shutter is inaccurate

Show the answer and why

Answer: The long exposure gives noticeably less density, because at low intensity a one-atom speck decays before the next photon arrives

This is low-intensity reciprocity failure, the arm that every long-exposure photographer meets. The mechanism is a race between two clocks: the lifetime of a single silver atom on the crystal, and the interval between photon arrivals. Dim the light enough and the interval wins, so the crystal keeps losing its first atom before the second arrives and never reaches the four-atom threshold. ILFORD states the cause as a reduced efficiency in forming stable development centres at low light levels, and publishes a per-film correction factor precisely because the size of the loss differs between emulsions.

Question 2. ILFORD gives HP5 Plus a reciprocity factor P = 1.31, used as corrected time equals metered time raised to the power P. Your meter indicates 30 s. What exposure should you give, to the nearest useful value?

• About 39 s
• About 60 s
• About 90 s
• About 300 s

Show the answer and why

Answer: About 90 s

30 raised to the power 1.31 is about 86 seconds, so 90 s is the answer to give in the field. Two things are worth noticing about the arithmetic. It is an exponent, not a multiplier, so the correction grows with the metered time: at 10 s the sheet gives 20 s, a factor of 2, while at 30 s the factor has risen to about 2.9. And ILFORD anchors the fit at one second, which is what makes P the reciprocal of Schwarzschild's exponent p; here p works out at about 0.76, appreciably further from unity than the 0.86 Schwarzschild measured in 1899.

Question 3. A student develops paper negatives exposed a month ago and finds them thinner than fresh ones exposed and developed the same day. Which conclusion is justified by that evidence alone?

• The latent image has faded over the month
• The developer is exhausted
• Nothing yet: a change in the paper itself would look the same, and a control exposed today and developed today has not separated the two
• The paper was fogged by the safelight

Show the answer and why

Answer: Nothing yet: a change in the paper itself would look the same, and a control exposed today and developed today has not separated the two

Sheppard and Mees raise exactly this objection and it is still the right one: photographers confuse the developing properties of a material with the survival of the latent image. They had measured plates whose velocity coefficient of development fell to a third of its value in six months of poor storage, which would thin a negative without any latent-image decay at all. The experiment needs three strips, not two: exposed and developed today, exposed today and developed later, and exposed and developed later. Only the third separates a decayed image from a lazier emulsion. Storage conditions still matter either way, because heat, damp and an acid layer accelerate both.

Question 4. Which of these is the Sabattier effect?

• A negative that reverses to a positive after an enormously long exposure in the camera
• A lightning flash recorded as a black streak against a lighter sky
• A print re-exposed to white light part-way through development, showing partial reversal and a black line along strong tonal boundaries
• An exposed but undeveloped film bleached by exposure to red light

Show the answer and why

Answer: A print re-exposed to white light part-way through development, showing partial reversal and a black line along strong tonal boundaries

The three wrong answers are solarisation, the Clayden effect and the Herschel effect, in that order, and all three happen before any developer is involved. The Sabattier effect requires the developer to be present and working when the second exposure is given: the bromide released by the grains already developing restrains the freshly fogged halide next to them, which is where the Mackie line comes from. The course keeps these four apart deliberately, because calling a Sabattier print solarised is the single most common terminology error in darkroom writing.

Question 5. FOMA give Fomapan 100 a correction of eight times at a metered 10 s, while ILFORD give FP4 Plus a factor of 1.26, which is about 1.8 times at 10 s. What does that difference tell you?

• One of the two sheets contains an error
• FOMA measure at a different temperature
• The reciprocity exponent is a property of the particular emulsion, so a correction can only be taken from the sheet for the film in the camera
• Fomapan 100 is a slower film, and slower films always fail more

Show the answer and why

Answer: The reciprocity exponent is a property of the particular emulsion, so a correction can only be taken from the sheet for the film in the camera

Both sheets are correct for their own product. Schwarzschild measured p = 0.86 on one plate and treated it as fixed; Abney and Englisch found it variable within a few years; Sheppard and Mees reported that disagreement in 1907; and a century later three manufacturers publish factors that differ by more than a factor of two for the same metered time. Grain size, halide composition, sensitisation and the depth of the electron traps all bear on how long a one-atom speck survives, so there is no reason to expect a universal exponent. The fourth option is a tempting generalisation with nothing behind it: nothing here links nominal speed to the exponent.

Question 6. Why does a darkroom safelight test give a paper an enlarger exposure first, rather than simply covering half a sheet and timing the safelight?

• Because the enlarger exposure makes the fog easier to see against a grey tone
• Because paper is more sensitive to safelight fogging after it has been exposed, so a fog-only test misses the effect that actually damages prints
• Because the safelight is brighter near the enlarger
• Because the enlarger exposure warms the paper

Show the answer and why

Answer: Because paper is more sensitive to safelight fogging after it has been exposed, so a fog-only test misses the effect that actually damages prints

ILFORD calls the after-exposure strip a check for latensification, and states plainly that paper is more sensitive to safelight fogging after the enlarger exposure than before. Kodak makes the same point and warns explicitly that a test which merely covers part of a sheet with a coin checks only for fog, not for the added effect of safelight plus enlarger exposure, so a questionable safelight can pass it. The underlying physics is this page: a sub-developable cluster left by the enlarger needs only a little more to cross the threshold, and the safelight supplies it. What ruins the print is not black borders but degraded highlights and lost contrast in the image area.

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