Experiment: Four Curve Families, Measured

Sixteen strips are already in the file. They were exposed in one sitting from one lamp at one distance through one wedge, developed in Part IX at seven pH and bromide levels and six sulfite and dilution levels, fixed, washed, dried, sleeved and labelled — and read by eye, because when they were made there was no instrument to read them with. There is now. This session does not develop them again. It measures them.

That is a pedagogic argument and also an arithmetic one. Re-running both Part IX sessions would cost about ten hours of darkroom work to establish a second time that pH matters, and would introduce a new film batch, a new exposure batch and a new week’s water into a comparison whose whole value is that none of those changed. What the archive cannot give you is a record better than the one you wrote months ago, and the largest part of this page is the accounting for that: an uncertainty budget whose terms are your densitometer’s certificate, your wedge’s provenance, and a set of Part IX notebook pages written by somebody who did not yet know what they would be used for.

Purpose

To read every step of sixteen archived Part IX strips on the densitometer built in Part XV, plot the pH, bromide, sulfite and dilution arms as four curve families, extract base plus fog, a relative speed point, a contrast index and a shape ratio from each, and — the actual subject of the page — build the uncertainty budget that says how large a difference between two of those numbers has to be before it may be called a difference at all. The design is set out below in the usual three parts — the hypothesis, the control, and the one variable that changes — and on this page all three say something slightly unexpected, because the objects being measured were made months ago by somebody who did not yet own an instrument.

Hypothesis. This page’s hypothesis is not about developers. Part IX already put a hypothesis on each arm and this page does not restate them as though they were findings. The hypothesis under test here is about the apparatus: that the combined uncertainty of a contrast index measured off an archived Part IX strip, on a home-built densitometer through an uncalibrated wedge, is small enough that at least one of the four arms shows a difference between its extreme cells larger than twice that uncertainty. It can fail. If every arm’s spread lands inside the budget, the finding of the session is that this apparatus cannot resolve what Part IX set out to measure, and that is a result worth more than a plot of noise.

The control. Two shared reference strips, one from each Part IX session — the standard condition of D-76 at 1+1 for 11 minutes at 20 °C set by the test-negative lab. They control nothing inside either session. Their job here is to be the same thing measured twice, months apart, through two different developments: any difference between them is a bound on everything this session cannot separate — bottle-to-bottle variation, session-to-session process drift, and whatever the archive has done to silver density since. If they agree, the four families may be read across the two sessions. If they do not, they may only be read within one.

The one variable that changes. Within this session, nothing. That is the point of reading in one sitting: the instrument, its zero, its lamp, its temperature and the person reading are held constant across all sixteen strips, so that every difference the plots show was put there in Part IX and not here. The variables being studied — added alkali, bromide, sulfite, dilution — were set months ago and are now fixed properties of the objects on the stage.

!What this page is not

It is not a repeat of Part IX. Part IX asked which way does it move, and answered by eye, from a threshold step and a scale length. This page asks how far, how reproducibly, and is the difference bigger than the apparatus, and answers in density and log exposure.

It is also not a licence to develop a second set. One bounded top-up run is specified below, for arms with a strip missing, spoiled, unlabelled or short of its record. Everything else on this page is instrument work on dry film.

Learning objectives

By the end of the session you will be able to:

• audit an archived strip against its card slip and reject it as unusable rather than estimate the field that is missing;
• read twenty-one steps and a masked patch from each of sixteen strips in a recorded, randomised order, with the calibration step re-checked often enough that a drift costs three strips and not an afternoon;
• extract four quantities from one strip by named constructions — base plus fog, the density at the greatest exposure the batch delivered, the relative speed point, and the contrast index — and a fifth, the shape ratio, which is this page’s own and is defined before the data exists;
• separate the Type A terms you measured — your own repeatability figures — from the Type B terms you took off a certificate, combine them by the course’s stated rule, and quote both that figure and the root-sum-of-squares figure with a label saying which is which;
• write the resolution sentence — the smallest difference in contrast index and in speed point this apparatus may report — before plotting anything;
• read four curve families and say, for each, what the data supports, what it does not, and which of the arm’s confounds could produce the same picture;
• set your own numbers beside published ones without merging them, and say plainly which is more likely to be wrong.

Prerequisites

Designing an experiment that yields a number owns the method: the hypothesis with a size in it, the uncertainty budget written first, and the resolution decision that follows from it. This page is that lesson executed on data that already exists.

Calibrating the densitometer is the hard prerequisite. You need its instrument certificate in front of you — warm-up rule, calibration step and its value, working range, stray-light ceiling, placement tolerance, repeatability figures and the uncertainty band table. Without it there is no Type B column and the budget cannot be built.

The activity series and the solvent series made the strips and hold the design decisions this page inherits, including the ones that limit it. The characteristic curve is the shape being measured; the contrast-index convention and the speed criterion are the two constructions this page applies and does not restate.

Safety classification

Level B, and only for the top-up run.

The measuring session is Level A in substance and arguably below it: dry, fixed, washed film, a low-voltage instrument, a bench lamp and a notebook. Nothing is opened, weighed, poured or heated. The classification on this page is set by the worst case it authorises, which is the bounded top-up run, and that run can reach Level B because replacing a sulfite or an alkali cell means weighing metol and sodium sulfite as fine powders and, for the carbonate cell, handling an alkali in concentrate. Under the course’s rubric that is Level A’s controls plus chemical splash goggles and an apron whenever concentrate is open, weighing over a tray with a particulate mask where the safety data sheet requires one, and an eyewash and spill kit within reach.

If no top-up is needed, the Level B controls stay in the cupboard, and the same is true if the only missing cell is a dilution cell, which is measured out of a bottle mixed in Part VIII and weighs nothing.

What is not a hazard here, and why. The strips themselves present no chemical hazard. The silver in them is metallic, locked in a hardened gelatin layer, and the soluble silver–thiosulfate complexes that were in the emulsion at the end of fixing were washed out months ago; a strip that had not been washed would be a different object, and the residual-hypo test in the residual hypo and silver SOP is how you would know. The densitometer’s light-emitting diode is a low-power visible source at the film plane, not an ultraviolet one — Part XV chose a narrow green band for photometric reasons, not for brightness — so there is no eye hazard of the kind the UV exposure unit carries, and no exposure limit applies. Neither of those two absences is a general statement about silver or about diodes; both are statements about this object in this state, which is what a hazard assessment is.

Hazards

For the measuring session:

Hazard	Where it arises	Control
Eye strain and reading error	Four hours of small numbers, and tiredness is a systematic error rather than a random one	Break the reading into blocks; capture the terminal to a file rather than transcribing; re-check the calibration step every third strip
Physical damage to an irreplaceable archive	Sixteen strips handled repeatedly on a stage, some of them the only record of a cell	Handle at the edges only; a soft camel-hair brush and nothing else on the emulsion; one sleeve open at a time
Trip and spill risk from cables	A bench instrument, a laptop and a lamp	Route and secure the leads before the first strip comes out

For the top-up run, the hazards are Part IX’s own and are set out in full on the activity series and the solvent series pages. In summary, and at the scale of one or two cells of about 100 mL each: metol and hydroquinone are skin sensitisers and are hazardous as inhalable powders; sodium sulfite and sodium carbonate are weighed as fine powders and carbonate is classified for serious eye damage; borax carries a reproductive-toxicity classification that the alternative route below addresses; potassium bromide is handled here only as a made-up solution. Spent developer is alkaline and must never meet the acidic, silver-bearing fixer.

Required PPE

For the measuring session, the protection that matters is for the film rather than for you: clean dry hands or lint-free cotton gloves, so that fingerprints — which the X-Rite manual names as a cause of error on a reference — do not become part of the data. Nitrile gloves are not worn, because nothing wet is handled and a glove that makes handling clumsier raises the risk to the archive.

For the top-up run, Part IX’s full set: single-use nitrile gloves, splash goggles, an apron while concentrate is open, and a particulate mask while any powder is on the balance. Donning and removal follow the PPE SOP.

Ventilation

For the measuring session, ventilation is not among the controls, because nothing here produces a vapour, an aerosol or a dust: the session handles dry, fully processed film and a sealed instrument. Ordinary room ventilation for comfort over four hours is all that applies.

For the top-up run, Part IX’s control applies unchanged: weigh powders over a tray in a draught-free place, then work with the room ventilated while solutions are open, exactly as the mixing SOP sets out.

Materials

Item	Quantity	Note
Archived Part IX strips	16	Seven from the activity series, seven from the solvent series, and the two shared reference strips
Their card slips	16	The eight-field slip specified by the test-negative lab. A strip without one is not data
The Part IX notebook pages	—	Both sessions, open at the cell tables and the deviations
Transmission step wedge	1	The same T2115 the strips were exposed through, for the axis convention and for the placement check
Densitometer reference wedge	1	Whatever your certificate names as the calibration reference, handled at the edges
Soft camel-hair brush	1	The only thing that touches an emulsion surface
Lint-free cotton gloves	1 pair	Optional but recommended for a long session
Spare exposed strips from the Part IX batch tin	0 to 4	Only if a top-up is needed. See the Preparation
Squared paper or a spreadsheet	—	Four curve families and one residual plot

Chemicals

The measuring session handles no chemical at all. The only substances present are the silver and gelatin in the strips, both immobilised and fully processed, and neither is opened, weighed or poured. Inventing a quantity so that this table has a row would be exactly what Rule 1 forbids.

The table below is therefore the top-up run’s worst case: the largest set the run could need, if one cell from each of the four arms had to be replaced. Most sessions need none of it.

Chemical	Quantity	Form
Metol	0.75 g per 100 mL cell of base	Fine crystalline powder, weighed
Sodium sulfite, anhydrous	1 to 10 g per 100 mL cell, according to which sulfite cell is missing	Powder, weighed
Borax	2.00 g per 100 mL cell	Decahydrate, weighed
Boric acid	As the solvent series’ buffer table gives, only if a sulfite cell is replaced	Powder, weighed
Sodium carbonate, anhydrous	1.00 g per 100 mL cell	Powder, weighed
Potassium bromide	0.5 to 2.0 mL of the Part IX 10 % w/v stock	Solution, kept from Part IX
Hydroquinone	—	Present only as part of the D-76 stock mixed in Part VIII; nothing is weighed here
Ammonium thiosulfate	40 mL of concentrate, to make 200 mL at 1+4	Liquid concentrate, diluted

Equipment

The densitometer from Part XV, with its certificate and its terminal logging to a file. A lightbox or an even lamp for the provenance audit, at the geometry Part IX read the strips on. A stopclock. The curve-plotting worksheet, sixteen copies. The lab notebook sheets. A spreadsheet or a short script that can solve one equation by trial, because the contrast-index construction is a one-unknown root find and doing it sixteen times by hand invites arithmetic slips into the results.

For the top-up run only: the balance and thermometer checked to their SOP, a 0.01 g balance, graduated cylinders, a water bath, a changing bag, a developing vessel that takes a 135 mm strip in 80 mL, and the film clips and line.

Estimated cost

££, and in most sessions almost none of it is spent. The measuring half consumes nothing but electricity and paper; the band is carried entirely by the possibility of a top-up run, whose cost is a strip or two of film from the Part IX batch, a little of the Part VIII stocks and a working strength of fixer. The capital — the densitometer, the wedge, the balance — was bought in earlier parts and is not consumed here. The planner carries the numbers.

Estimated consumables cost

Two cases, and the difference between them is most of the band.

With no top-up, the session consumes stationery and nothing else. There is no priced row, because the price file carries no stationery line, and the honest subtotal is nothing that this file can price.

With a top-up of two cells, one strip each, plus one bridge strip at the reference condition:

Consumed	This session	Sourced price	Cost this session
Test strips from the Part IX exposure batch	3	Costed in preparing standard test negatives	—
Metol	0.75 g, only if a sulfite or alkali cell is replaced	£16.20 per 50 g	£0.24
Sodium sulfite, anhydrous	up to 10 g	£13.68–£19.98 per 1 kg, anhydrous	£0.14–£0.20
Borax	2.00 g	£9.98 per 200 g, decahydrate	£0.10
Sodium carbonate, anhydrous	1.00 g	£7.20 per 500 g, anhydrous	£0.01
Potassium bromide	about 0.2 g, from the stock kept in Part IX	£23.00 per 250 g	£0.02
D-76 and D-23 stock, from Part VIII	up to 300 mL	Costed in Part VIII’s mixing lab	—
Rapid fixer concentrate	40 mL, to make 200 mL at 1+4	£21.05–£25.98 per 1 L of concentrate, diluted 1+4 for film	£0.84–£1.04
Wetting agent	1 mL, for 200 mL at 1+200	£28.70 per 1 L of concentrate, diluted 1+200	£0.03
Negative sleeves and card label slips	3 pockets, 3 slips	None. A named price gap: sleeving that passes the Photographic Activity Test	—
Squared paper for the residual plots	3 to 5 sheets	None. The planner carries no stationery line	—

The priced rows come to £1.38 to £1.64 for a two-cell top-up, at the retail ranges read on 5 September 2026 and recorded in the laboratory planner. That is a floor, not a total: 4 of the 11 rows carry no dated price, so they are counted as nothing here and are certainly not free. A priced entry is a dated range to plan against, never a quotation. The balance, the wedge, the densitometer and the water bath are equipment and are deliberately absent from the table — a page that quietly counts them has stopped measuring what the consumables calculator needs.

Waste streams

With no top-up there is no waste stream at all, which is worth stating rather than leaving to inference: nothing is consumed and nothing is discarded, and the strips go back into their sleeves.

With a top-up, Part IX’s three streams apply at a fifth of the scale:

1. Alkaline developer, up to about 300 mL, carrying the metol, hydroquinone, sulfite, borax, carbonate and bromide of the replaced cells. One labelled container, routed per the general waste SOP.
2. Spent fixer and the first rinse after it, silver-bearing, to the silver stream.
3. Rinse and wash water. The rinse that follows the developer goes with stream 1; the first change after fixing goes with stream 2 and the rest with the general stream.

Streams 1 and 2 are never combined: stream 1 is a sulfite solution at high pH and stream 2 is acidic.

Alternative route

The measuring session needs no darkroom, no safelight and no darkness of any kind. Sixteen dry, fixed strips are read in room light at a bench. That is why the manifest records this page as needing no facility, and it is the reason this experiment is the one to run first if your access to a darkroom is intermittent: the chemistry happened months ago, and what is left is arithmetic.

The top-up run is the only part that needs anything, and there are three routes through it in decreasing order of what they preserve.

Route one, and the one to prefer: a spare strip from the Part IX batch tin. Part IX exposed every strip for the whole part in one sitting and stored the surplus, still latent, in a light-tight tin. A strip taken from that tin needs only a changing bag to reach the developing vessel, and the whole top-up then runs in room light with the strip in a closed vessel, exactly as Part IX’s sessions did. It has one cost, and it is not small: the latent image has aged. ILFORD’s own instruction for FP4 Plus is to process exposed film as soon as practical, and the course has no figure at all for what months of keeping do to a latent image on this film. The bridge strip specified in the Procedure is how that cost is measured rather than assumed.

Route two: re-expose. If the tin is empty, a new strip has to be exposed on the Part IX contact rig, which needs a room that can be darkened. The film is the same emulsion batch or the top-up is worthless; the lamp, its distance, the wedge and the exposure time are set back to the batch block in the notebook; and the result is a new exposure batch that must be tied to the old one by exposing two strips and developing one at the reference condition alongside a leftover from the original batch. If you have no room that can be darkened, this route is closed and there is no substitute for it — the exposure has to happen in the dark, and no arrangement of a changing bag will let a lamp shine through a wedge onto film that a bag exists to keep dark.

Route three, when neither is available: report the arm as incomplete. Plot the cells you have, leave the missing level out with a gap on the axis rather than an interpolated point, and write in the result what was missing and why. An arm with a stated hole in it is evidence. An arm with a guessed point in it is not.

A route for a reader avoiding borax. The reproductive-toxicity classification on borax makes the A2 and sulfite cells the ones a reader may wish not to remake. Both are replaceable only with borax, so if a top-up of those cells is refused on that ground, route three is the answer for them and the other arms run unchanged — which is the same trade the activity series already named, arrived at from the other end.

Preparation

About 90 minutes, in a separate sitting the evening before. The 240 minutes on this page is the Procedure, and every decision below has to be made before a number exists, because a decision made after the numbers are in is not a decision, it is a preference.

The sixteen strips, and where each one comes from

The sixteen strips this session reads, and the six it deliberately does not

1. 1pH arm, three strips — A1 base, A2 borax 20 g/L, A3 carbonate 10 g/L; equal time, 10 min at 20 °C
2. 2Bromide arm, four strips — B0 to B3, 0 to 1.96 g/L in D-76 stock; equal time, 10 min at 20 °C
3. 3Sulfite arm, three strips — S10, S50, S100 at one pinned pH; equal time, 10 min at 20 °C
4. 4Dilution arm, four strips — stock, 1+1, 1+3 at 16 min, plus stock at 8 min as the compensated partner
5. 5The two reference strips — D-76 1+1, 11 min, one per session. This page reads them against each other
6. 6Read elsewhere, or not at all — the agitation cells belong to the agitation experiment; the edge targets carry no wedge

Sixteen strips read, six set aside, and one cross-session pairing that is a result about keeping rather than about sulfite. The map is drawn before the session because a strip picked up without knowing what it is for is a strip read twice.

The provenance audit, and the fields that make a strip usable

Lay the sixteen sleeves out with their card slips and check each one against the eight fields the test-negative lab specified. A strip is usable on this page only if its slip gives, without ambiguity: the batch (film, emulsion batch, lamp, distance, exposure time, wedge part, date of exposure); the arm and cell in words; the developer with its version code, dilution, addition in g/L and, for the pH arm, the measured pH with its temperature; the development — time, temperature at start, middle and end, agitation script, vessel and volume; and the date.

Where a field is missing, the strip is unusable and is not estimated. This is the rule the whole page rests on, and it will feel harsh at the moment it costs you a cell. A strip whose temperature record says “20 °C” with no start-and-end pair could have run at 20.0 or drifted to 21.5, and Kodak’s process-control practice treats a third of a degree as significant; a strip whose version code is missing cannot be tied to a bottle; a strip whose agitation is recorded as “normal” was developed by a person who has since changed what normal means. Write the missing field in the audit table, mark the strip UNUSABLE, and decide whether the top-up run will replace it.

📓The audit table, and the two columns people forget

One row per strip: sleeve number, arm, cell, every field present, every field missing, the verdict, and two more.

The archival interval in days, from the development date on the slip to today. It is a term in the budget and it is different for the two sessions.

Storage conditions since, in one line. The Image Permanence Institute’s quick reference names silver image decay as the temperature-and-humidity-related decay of a black-and-white film, and names harmful enclosures and poor air quality among the other concerns. The recommendation it reports depends on the base, and 35 mm film is usually the stricter case. For polyester-base black-and-white film it gives an ISO recommendation of 21 °C and 50 per cent relative humidity as maxima; for acetate-base black-and-white film the maximum temperature falls to 2 °C at 50 per cent relative humidity, 5 °C at 40 per cent and 7 °C at 30 per cent, because acetate decay is in play as well as the silver. ILFORD’s own sheet states that FP4 Plus in 35 mm is coated on acetate and only the sheet film is on polyester, so a Part IX archive on 35 mm is the acetate row. If your strips have spent the interval in a cool, dry, dark drawer in the sleeves Part IX specified, write that. If they spent a summer in a loft, write that instead, and read the closing paragraph of the Analysis before you trust the two reference strips to agree.

The axis convention, fixed before any reading

Every strip in the archive was exposed through the same Stouffer T2115 in the same rig, so the exposure axis is the wedge’s own and is the same axis for all sixteen. This page uses:

log H_rel(k) = 3.05 − D_wedge(k)

This page's relative log exposure axis

where D_wedge(k) is the wedge’s density at step k. On a nominal T2115 that is 0.05 at step 1 rising by 0.15 a step to 3.05 at step 21, so log H_rel runs from 3.00 at step 1 down to 0.00 at step 21. Step 1 passes the most light and therefore carries the most exposure and the highest density.

Two things must be said about this axis and then never forgotten.

It is relative, and the course says so on every plot it appears on. There is no lux-second on it. Part IX’s rig had no illuminance meter, so H itself was never measured; what the axis records is how much less exposure each step received than step 1. Differences along it are meaningful and absolute positions are not, which is exactly enough for a contrast index and for a speed shift, and not enough for a film speed.

If your wedge is uncalibrated, 0.15 is a manufacturing intention rather than a measurement. Stouffer are explicit about what the two grades differ in: the same quality is to be expected from an uncalibrated part as from a calibrated one, they come from the same production batches, and what calibration adds is a densitometer reading of each step recorded for reference, giving the optical density value that can be used for densitometry. So a calibrated part’s twenty-one certified numbers go straight into the axis; an uncalibrated part’s nominal ladder carries an unquantified systematic error which the budget below has to carry as unquantified and cannot pretend to bound.

The five quantities, defined before the data exists

Four of these are the course’s, defined elsewhere and cited rather than restated. The fifth is this page’s own and is defined here because it does not exist anywhere else.

Quantity	Construction	Where it is defined
Base plus fog, D₀	The mean of three readings on the masked patch of that strip, taken at three places along it	Part XIII; the mask is Part IX’s
D(step 1)	The density at the greatest exposure the batch delivered	This page; see the warning below
Relative speed point	log H_rel where the curve reaches D₀ + 0.10, by linear interpolation between the two bracketing steps	The course’s speed criterion, point m only
Contrast index, CI	ΔD ÷ √(4 − ΔD²), with ΔD the density difference solving the course’s condition	The course’s contrast-index convention
Shape ratio, R	G_upper ÷ G_lower over the two halves of the contrast-index chord	This page. Definition below

The shape ratio, defined. Let D₁ and D₂ be the two contrast-index chord points and D_mid their mean density. Take G_lower as the gradient between D₁ and D_mid and G_upper as the gradient between D_mid and D₂, each over its own half of the run. Then:

R = G_upper ÷ G_lower

The shape ratio, this page's own definition

R is 1.00 for a curve that is straight between the chord points, below 1.00 for one whose upper scale has flattened relative to its lower scale, and above 1.00 for one that is still steepening. It exists because the dilution arm asks a question that a contrast index cannot answer, and it is written down here, with its arithmetic, before any strip is read, so that it cannot be adjusted afterwards to make an arm look better.

✕Why D(step 1) is not called maximum density until you have earned it

Maximum density means the density at which the curve has stopped climbing — the shoulder. What step 1 gives you is the density at the largest exposure this batch delivered, which is the same thing only if the exposure was generous enough to shoulder the film.

The test is on the plot and takes two seconds: if the last three steps are separated by roughly the gradient of the straight line, the curve has not shouldered and D(step 1) is a point on the straight line that happens to be the last one. Quote it as D(step 1) in that case, everywhere, and never as D-max. Part IX’s cells make this a live risk in both directions: the restrained cells and the dilute cells may not have reached a shoulder at all, and the carbonate cell may have run several steps together at the top, in which case D(step 1) is a maximum density and the steps beneath it are unusable for a gradient.

The run order, and why it is drawn from a hat

Number the sixteen strips, shuffle the numbers, and write the order down before the session. Read in that order. There are three reasons and only the first is obvious.

The instrument drifts, and a drift that runs along the session will otherwise be read as a trend along whichever variable you happened to read in order. Reading A1, A2, A3 in that sequence and finding density rising is not evidence about pH if the zero was also rising.

The reader drifts. Placement, brushing, how long a strip is left to settle: all of these get slightly different at hour three, and randomising spreads that across the arms instead of concentrating it in the last one read.

And you know what you expect. A person who has just read A1 and A2 and seen the difference the hypothesis predicted will place A3 on the stage in a particular frame of mind. Randomising does not remove that, but it stops it from lining up with the variable.

Do not blind the identities. Part IX blinded its by-eye readings, and was right to: a judgement by eye is exactly the kind that expectation moves. A densitometer reading is not a judgement, and the audit trail matters more here than the blinding — every reading has to be traceable to a sleeve. Randomise the order, log everything, and leave the labels on.

The data table, drawn before the data

Two tables and one plot decided in advance, per the design lesson.

The reading table: one row per step per strip — sleeve, strip, step, log H_rel, density, the file line number the reading came from, and a flag for any step read outside the instrument’s working range.

The strip table: one row per strip — the five quantities, each with its own uncertainty, plus the provenance fields copied from the slip and the archival interval.

The plots: four curve families on four pairs of axes, all with the same axis limits so that they can be laid side by side; plus one plot of each quantity against its arm’s variable. Decide the axis limits now.

If a top-up run is needed

Only for cells the audit marked unusable, and only at the Part IX conditions the missing cell was run at. Read the Alternative route above for the three routes and their costs, then:

1. Mix only the missing cells, at 100 mL each, from the Part VIII stocks and the Part IX bromide solution, recording a new version code for every one per the versioning SOP on the formula version record. A remake is a new version, not the old one: same recipe, different bottle, different day, different water.
2. Add one bridge strip, developed in freshly mixed D-76 at 1+1 for 11 minutes at 20 °C — the reference condition. Kodak’s sheet is explicit that a 1:1 dilution is made just before use and discarded after one batch, so it is mixed on the day.
3. Develop at the Part IX script: the equal time for that arm, 20 °C held within 0.3 °C, the same agitation wording, a plain water rinse rather than an acid stop if a carbonate cell is among them, fixing for twice the clearing time, the published wash, a wetting-agent rinse at 1+200, and no squeegee.
4. Sleeve and slip them exactly as Part IX did, with one extra line: TOP-UP, the date, and the route used. That line has to survive onto the plot.

Procedure

The session in four hours

The 240 minutes, and where the slack is

Warm-up and preflight

warm-up rule, dark, zero, cal step, blank — 25 min

Provenance and order

audit check, run order, sleeves laid out — 20

Reading, 16 strips

21 steps + masked patch ×3 each; cal step every third strip — 110

The repeat block

3 steps × 3 strips × 10 replaced readings — 30

Closing check

dark, zero, cal step again — 10

Arithmetic and plots

five quantities per strip, budget, four families — 45

0 min60120180240

The reading block is the one to check against your own instrument. Sixteen strips at twenty-one steps plus three masked-patch readings each, with six calibration re-checks, is 390 readings in 110 minutes — about 17 seconds a reading including handling. Part XV's characterisation assignment budgets fifteen strips at twenty-one steps, 315 readings plus repeats, into an unhurried hour, which is about 11 seconds each. The slack is deliberate: this session handles archived film out of sleeves, which the other did not.

!If the reading block will not fit, and what it costs to split it

Time your own instrument on three strips before the session and multiply. If your reading rate makes 390 readings longer than about 130 minutes, split the session into two sittings rather than hurrying it — tiredness at reading 300 is a systematic error and hurrying is how a strip gets scratched.

The split has a price and the budget has to carry it. The four families are read in one sitting so that the instrument’s state is a constant rather than a variable, and two sittings break that. The repair is to bracket each sitting with the full preflight, take the difference between the two sittings’ calibration-step readings as an additional Type B term, and apply it to every comparison that crosses the boundary. Split the arms rather than splitting an arm: three strips of the pH arm read on different days is a worse experiment than four hours in one chair.

Stage 1 — Preflight, about 25 minutes

1. Switch the instrument on and obey your own warm-up rule from the certificate. Log the minutes since switch-on beside the first reading; a warm-up rule you did not follow is a Type B term you have to add later.
2. Run the densitometer daily check in full: dark, zero, the calibration step, the opaque blank. The calibration step must read within 0.02 D of its certified value — the tolerance a commercial instrument specifies for exactly this check — and the blank must give the stray-light fraction your certificate quotes.
3. If the calibration step is out, recalibrate before a single strip goes on the stage. A reading taken before the instrument is checked is not a reading; it is a number.
4. Record the certificate’s date and the reference wedge’s serial in the session header. Every density this session produces will be quoted against them.

Stage 2 — The provenance check on the day, about 20 minutes

5. Lay out the sleeves in the run order, still closed.
6. Re-read the audit table and confirm that no strip marked UNUSABLE has crept back in, and that every top-up strip carries its TOP-UP line.
7. Write the archival interval for each session at the head of the strip table, in days.

Stage 3 — Reading, about 110 minutes

For each strip in the run order:

8. Open one sleeve, take the strip by the edges, brush it with the camel-hair brush if it needs it and with nothing else, and let it sit flat on the stage for a few seconds before the first reading.
9. Read all twenty-one steps in one pass, clear end first, capturing to the log file. Never transcribe a number: the commonest way an afternoon like this is lost is a digit typed wrongly at reading 200.
10. Read the masked patch at three places along its length. That is this strip’s base plus fog, and it is the strip’s own — the carbonate cell and the bromide cells have genuinely different floors, which is half of what the two arms exist to show, so a shared value would erase the result.
11. Note any step read above your instrument’s working range, from the certificate. Flag it in the table. It is not a density; it is a reading of your own stray light.
12. Return the strip to its sleeve before opening the next one. One sleeve open at a time.
13. Every third strip, re-read the calibration step and log it. A drift found at strip 6 costs three strips; a drift found at strip 16 costs the afternoon.

Stage 4 — The repeat block, about 30 minutes

This is the Type A term, and it is measured on the same film, on the same day, by the same hands, which is why it is worth more here than the figure on the certificate.

14. Choose three strips spanning the session — an early one, a middle one and a late one — and on each choose three steps: one near the toe, one on the straight line, one near the top.
15. Read each of those nine positions ten times, lifting the strip off the stage and replacing it between readings. Replaced-sample repeatability, not undisturbed repeatability, is the figure this page needs: every strip in the session was placed on the stage by hand.
16. Compute the standard deviation at each of the nine positions and record all nine. Do not average them into one number yet. Look first at whether the spread depends on density, because if it does, the budget needs a figure per band rather than one figure.

Stage 5 — The closing check, about 10 minutes

17. Repeat the preflight: dark, zero, calibration step. Record all three.
18. The difference between the opening and closing calibration-step readings is the session’s drift term. Write it into the budget as a Type B term. If it exceeds your certificate’s zero-stability figure, say so in the result and consider the session’s later strips suspect relative to its earlier ones — which is precisely what the randomised run order was for.

Stage 6 — The arithmetic and the four families, about 45 minutes

19. For each strip, compute the five quantities. The contrast index is a one-unknown root find: try three values of ΔD, interpolate, and let the spreadsheet do it sixteen times identically.
20. Plot the four families, all on the same axes, with the reference strips on a fifth pair.
21. Plot each quantity against its arm’s variable, with error bars from the budget below.
22. Do not interpret anything yet. The budget comes first, and the resolution sentence comes out of it. This is the discipline the whole part exists to teach: the analysis method was fixed before the numbers were seen, and the numbers do not get a vote on it.

Expected observations

Everything in this section is either a statement about the instrument, which the session either confirms or does not, or a prediction carried over from Part VIII’s mechanism and Part IX’s hypotheses. Predictions are marked as such, they have falsifiers attached, and none of them is a course finding. The course has published no measurement of what any of these four variables does to any film.

From the instrument, and these are checks rather than predictions. The opening and closing calibration-step readings should agree to within your certificate’s zero-stability figure. The nine repeat positions should give standard deviations of the same order as your certificate’s replaced-sample repeatability; if the session’s figure is much worse, the difference is the archived film, the sleeves or your handling, and it belongs in the result. The masked patches should be the lowest densities on each strip. Two reference strips developed months apart should agree — and if they do not, that disagreement is the most important number produced today.

From the pH arm — predicted, with a falsifier. Part IX predicted that raising the pH of a metol-sulfite base raises the rate of development, so that at a fixed ten minutes the curve moves up and left, the contrast index rises and base plus fog rises with it. The prediction that can fail is Part IX’s own second thought: metol’s amine is already neutral above about pH 8, so a metol-only bath may barely respond to a ladder that runs from about 8.4 to about 10.4. If A1, A2 and A3 give contrast indices that agree inside the budget, that is a result, not a failure, and it is a sharp one — it says the alkali’s effect on a metol bath at this sulfite concentration is smaller than a home sensitometric apparatus can see, which is a statement a great deal of darkroom writing does not survive.

From the bromide arm — predicted, with a falsifier. Part IX predicted that base plus fog falls with added bromide and reaches its floor early, while the image is still developing strongly. The falsifier is a fall in base plus fog no larger than the budget across the whole ladder — which is entirely possible, because Part IX’s ladder tops out at 1.96 g/L, and that is only just reaching the lowest addition in the published family plotted below, whose own ladder runs sixty-four times further.

From the sulfite arm — predicted, with a falsifier. Part VIII’s mechanism predicts that more sulfite means more halide dissolved during development, so finer grain and a lower speed point: the toe should move to the right as the sulfite rises. The falsifier is a speed point that does not move by more than the budget, or one that moves the other way — which would be a real finding, because it would mean something other than solvent action dominates across this ladder.

From the dilution arm — predicted, and this is the one to be most careful with. Diluting D-76 at a fixed sixteen minutes leaves less developing agent per unit area, so the upper scale should flatten while the toe holds, and the contrast index should fall. That prediction is nearly untestable as stated, because a curve whose whole gradient has fallen looks the same in a contrast index whether it compensated or was simply under-developed. The shape ratio R is what separates them, and the compensated cell — stock at eight minutes — is what it is compared against.

Across all four arms. Expect the differences to be smaller than you hope, and expect at least one arm to land inside the budget. Part IX said the same thing about its by-eye readings and it is not less true with an instrument: an instrument reports more decimal places, not more signal.

What is happening chemically

Nothing is happening chemically today. Everything on this page happened in Part IX and the film has been sitting in a drawer since. What this section does is name the chemistry each arm actually varied, because a curve family is only as good as the account of what its axis means — and in three of the four arms the axis means more than one thing.

The reaction the whole archive records

Every density on every one of these strips is metallic silver, reduced from silver bromide by the developing agent, at a rate set locally by how many latent-image centres the crystal carries.

AgBr(s) + e⁻ → Ag(s) + Br⁻

Chemical development, per formula unit: the silver stays where it was and the bromide goes into the bath

That single equation is why three of the four arms are what they are. The electron comes from the developing agent, whose willingness to give it up depends on pH, which is the pH arm. The bromide ion released opposes the reaction that released it, which is the bromide arm. And the agent is consumed as it works, so the rate at which fresh agent arrives sets what happens where density is high, which is the dilution arm. The fourth arm, sulfite, is the one that acts on the crystal rather than on the electron.

The pH arm changed the alkali, and two other things with it

Part IX raised the pH of a metol-sulfite base with borax and then with carbonate, and computed a ladder of about 8.4, 9.0 and 10.4 from published dissociation constants. Three things moved along that ladder, and only the first is what “pH” usually means.

The proton activity, which sets how readily the agent’s oxidisable form exists at all, and which is the intended variable.

The buffer capacity. A1 is buffered by the sulfite–bisulfite couple alone; A2 adds borate; A3 adds carbonate at a pKa more than three units above the sulfite couple. As development proceeds it makes acid, and a bath with more reserve holds its pH better through ten minutes than one with less. So the three cells did not merely start at different pH values, they held them differently.

The ionic strength. Twenty grams of borax and ten of carbonate per litre are not nothing beside 0.8 mol/L of sulfite, but they are not negligible either, and ionic strength changes how far gelatin swells and therefore how fast anything diffuses through it.

What did not move within the arm is worth naming too, because it is the arm’s strength. All three cells were poured from the same 600 mL of D-23 base, so the agent concentration, the sulfite concentration and the age of the base are identical between them. That last one is common to all three and therefore cancels inside the arm — but it does not cancel when A2 is set beside S100, which was mixed fresh from solids, and that is exactly why the S100-against-A2 pair is a keeping comparison and not a duplicate.

What the pH arm therefore tested, stated plainly: the effect of adding a named alkali at a named quantity to a named base, developed for a fixed time — not the effect of pH holding everything else still, which no bench experiment can deliver.

The bromide arm is the cleanest of the four

Adding potassium bromide to D-76 changes the bromide-ion concentration and, at these quantities, very little else. Part IX topped every cell to the same added volume precisely so that the four cells could not differ in dilution as well, and 2 mL in 102 is a two per cent change that would otherwise have sat underneath every result invisibly. The mechanism is Part VIII’s: bromide in solution opposes the release of bromide from the crystal, and the opposition bites hardest where the crystal has least reason to develop — an unexposed grain — so chemical fog falls before the image does.

The honest limit is the range. Part IX’s ladder is 0 to 1.96 g/L, and its own account of the choice is that it spans the bromide quantities Kodak’s published film developers actually carry. That is a ladder inside the range manufacturers use, and it is a narrow one for an effect the published literature below demonstrates over two orders of magnitude.

The sulfite arm cannot separate three things and the course says so

Sulfite is a preservative, a buffer and a silver solvent at once, and Part IX’s arm moved all three together by a factor of ten.

C₆H₄O₂ + SO₃²⁻ + H₂O → C₆H₆O₂ + SO₄²⁻

Regeneration: the oxidised developing agent restored at the sulfite's expense, which is the preservative role

The solvent role has no equation here, and that is deliberate. Part VIII states that this course holds no formation constant for a silver–sulfite complex and no measured solubility of silver bromide in sulfite solution, so it will not write a complex-formation equation it cannot source, and neither will this page. What is established is the consequence: halide dissolved during development breaks the contacts between crystals and removes the marginal specks that carry the toe, which is why solvent developers are associated with finer grain and less speed. The concentration at which that becomes significant is exactly the question, and the course could not source a threshold figure from a photographic-chemistry reference it has read. Your arm is a three-point measurement of it, and three points bracket a threshold rather than locating one.

The confounds, named. The 10 g/L cell is also the least-protected cell, so part of any weakness in it may be agent lost to air. The tenfold change in sulfite is also a tenfold change in ionic strength. Part IX pinned the pH with a borate buffer so that at least the alkalinity was held, which is why the arm is worth reading at all.

The dilution arm changed four things, and the fourth is time-in-bath

Diluting D-76 at a fixed sixteen minutes changes the agent concentration, the sulfite concentration, the buffer reserve and the total quantity of agent available per unit area of film. The first three fall together in proportion; the fourth is the one that produces compensation, because where density is high the local reservoir runs down and development slows there and only there.

⚗Compensation and under-development are the same curve seen from two angles

Both lower the top of the curve. They differ in what they do to the bottom.

Under-development — less agent, less time, less activity — lowers the gradient of the whole curve. Highlights come down, and so do the mid-tones, and so does the shadow separation that was never the problem.

Compensation acts where consumption is fastest and leaves the toe alone. It manufactures a shoulder out of local chemistry.

At a fixed sixteen minutes both are present in the dilute cells at once, and a contrast index cannot tell them apart because it is a single slope. The shape ratio can, which is why it was defined before the session. And the compensated cell is the comparison that makes the answer interpretable: if D-76 at 1+3 for 16 minutes and D-76 at stock for 8 minutes reach a similar contrast index, then any difference in R between them is a difference in shape at matched contrast, which is what compensation means when it is measured rather than claimed.

Whether the literature has a mechanism beyond local exhaustion, this course cannot say. Part VIII’s account is local exhaustion and diffusion, and its evidence for the trade is a manufacturer’s datasheet describing a dilution that reduces contrast and gives back the speed gain. The course has not read a photographic-chemistry text that distinguishes compensation from under-development experimentally, and it will not describe one it has not read. What it can give you is a definition — R at matched CI — that makes the distinction testable on your own strips.

Data to record

Session header. Date; densitometer serial and certificate date; reference wedge serial and whether it is a calibrated part; minutes since switch-on at the first reading; room temperature at the start and end; the log file’s name; your name; the notebook page.

The audit table, from the Preparation, in full — including the rows for the strips you rejected. A rejected strip is data about the archive.

Per strip, copied from the card slip, and never from memory: batch block; arm and cell; developer version code; dilution; addition in g/L; measured pH with its temperature where the arm records one; development time; temperature at start, middle and end; agitation script; vessel and volume; date of development; archival interval in days; storage conditions; and, where it applies, the TOP-UP line with its route.

Per strip, measured today: twenty-one step densities with their log H_rel values and their file line numbers; three masked-patch readings; any step flagged as outside the working range; and the five computed quantities with their uncertainties.

The repeat block: all ninety readings, the nine standard deviations, and the density each was taken at.

The instrument log: opening dark, zero, calibration step and blank; every calibration re-check with the strip number it followed; closing dark, zero and calibration step.

The completed uncertainty budget, on the form below, and the resolution sentence written out in words.

The deviations. Every one. A strip dropped, a sleeve that turned out to hold two strips, a reading taken before the brush, a lamp knocked, an interruption of twenty minutes in the middle of the reading block.

Analysis

The uncertainty budget, which is the actual subject of this page

The course keeps two kinds of term apart, and now has a source for the distinction it did not have when Part XV wrote its own definitions.

!Type A and Type B, from NIST, and how they meet Part XV's definitions

NIST’s reference on uncertainty — the plain-language presentation of the Guide to the Expression of Uncertainty in Measurement that stands behind NIST Technical Note 1297 — defines a Type A evaluation as the “method of evaluation of uncertainty by the statistical analysis of series of observations”, and a Type B evaluation as the “method of evaluation of uncertainty by means other than the statistical analysis of series of observations”. It lists what a Type B evaluation may be based on: previous measurement data; experience with, or general knowledge of, the behaviour and property of relevant materials and instruments; manufacturer’s specifications; data provided in calibration and other reports; and uncertainties assigned to reference data taken from handbooks.

Those are the definitions Part XV arrived at independently and labelled as the course’s own because it could not obtain a source that met the sourcing standard. They agree. The course’s definitions stand, and from this page on they are cited rather than asserted.

On combining them, NIST gives the combined standard uncertainty as the positive square root of a variance obtained from the law of propagation of uncertainty — a root-sum-of-squares of the components weighted by their sensitivity coefficients. The course’s own convention remains Part II’s: quote the arithmetic sum as a bound, because it is arithmetic anyone can check, and quote the root-sum-of-squares figure beside it with a label saying which is which. Never print the smaller number bare. On these budgets the two differ by roughly a factor of two, and that gap is not a rounding difference — it is a statement about whether the terms are independent, which on a home bench you have not demonstrated.

Build the budget in two halves, because this page measures objects that somebody else’s session made, and the two halves fail in different ways.

Half one: the reading budget, which is what today’s session contributes to a density.

Term	Type	Where the figure comes from	Behaviour
Replaced-sample repeatability	A	The repeat block, per density band	Random; improves with more readings
Session drift	B	Opening minus closing calibration step	Systematic within the session, random between sessions
Chain non-linearity	B	Arm 8 of your calibration, by superposition	Systematic, density-dependent
Stray-light residual	B	Your certificate, at the density being read	Systematic, and grows fast at the top
Reference wedge certificate	B	The certificate, or unquantified if the reference is uncalibrated	Systematic, common to every reading
Placement	B	Arm 7 of your calibration, the millimetre tolerance	Random, and included already if the repeat block replaced the sample

Half two: the provenance budget, which is what Part IX contributes and today cannot improve.

Term	Type	Where the figure comes from	Behaviour
Exposure-axis scale	B	The wedge’s certificate, or unquantified for a nominal ladder	Systematic, common to every strip, cancels in a comparison
Exposure repeatability between strips	B	Part IX’s own control set, in wedge steps	Random between strips within a batch
Development temperature	B	The start, middle and end readings on each slip, against the 0.3 °C the course works to	Random between cells; systematic if the bath drifted along the session
Development timing and agitation	B	The slip. Bound it; a missing figure makes the strip unusable	Random between cells
Archival interval	B	Unquantified. Bounded empirically by the two reference strips	Unknown, and possibly systematic with interval
Latent-image keeping, top-up strips only	B	Unquantified. Bounded by the bridge strip	Applies to top-up strips and to nothing else

📓Two terms with no number, and how to bound them anyway

Archival stability of silver density over months. The course looked for a figure and did not find one it could use. The Image Permanence Institute’s guidance is about decay over decades and names its mechanisms qualitatively — silver image decay as microspots, silver mirroring or overall image discoloration, driven by temperature, humidity, harmful enclosures and poor air quality — and gives storage recommendations by base rather than a rate of change. None of that bounds a change in density to 0.01 over the months an archive of test strips actually sits, and no source this course has read does. Nor is it the kind of question conservation guidance is written to answer: it is written for collections over centuries, and a sensitometric argument needs a bound at the scale of a hundredth of a density unit over one winter.

So the argument for measuring rather than re-developing rests on something weaker than a citation and stronger than a hope: the two reference strips. They were developed months apart, at the same condition, from the same exposure batch, and they have been in the archive for different intervals. If their five quantities agree inside the reading budget, then whatever the archive has done to silver density is smaller than the budget across that interval, on this film, in this storage — which is exactly the claim the page needs and no more. If they disagree, the page has found the very thing it was worried about, and the honest response is to report the four families within each session only, with the between-session comparison refused.

Latent-image keeping. Same shape of problem, different object. ILFORD’s instruction for FP4 Plus is to process once exposed as soon as practical, which establishes that keeping matters and gives no interval. The bridge strip in the top-up run is the same trick: developed today at the reference condition from a months-old latent image, it can be compared with the archived reference strips, and the difference bounds latent-image keeping plus archival drift plus the difference between two bottles of D-76. It cannot separate them. Say so in the result, and if the number is large, use route three and report the arm as incomplete rather than plotting a point you cannot defend.

The resolution sentence, and how to get to it

Two propagations, both of which you can do on your own table in a spreadsheet, and neither of which needs any statistics beyond a standard deviation.

For a density, the smallest reportable difference between two strips is straightforward: each reading carries the combined uncertainty u from half one of the budget, so a difference carries 2u under the course’s bound and u√2 under root-sum-of-squares. Base plus fog and D(step 1) are read directly, so this is their whole answer.

For the contrast index and the speed point, the propagation cannot be done in your head, because both are the outputs of constructions rather than readings. The method is to perturb the table and re-solve: add a random error of your own u to every density in the strip’s table, including the base plus fog, re-run the construction, and repeat a few thousand times. The spread of the answers is the uncertainty of the quantity. A spreadsheet does this with one column of random numbers and a recalculate key.

Worked on Kodak’s published eleven-point sample table — not on any strip, and not a measurement of anything — the propagation gives the following, and the shape of it is the useful part:

How a reading uncertainty becomes an uncertainty in the two derived quantities

• Uncertainty of the contrast index
• Uncertainty of the relative speed point, log H

Show the numbers behind this plot

Two nearly straight traces rising from the origin against the standard uncertainty of a single density reading, running from 0.005 to 0.030 on the horizontal axis. The lower trace is the uncertainty of the contrast index, rising from 0.005 at a reading uncertainty of 0.005, through 0.011 at 0.010 and 0.021 at 0.020, to 0.034 at 0.030 — a slope of about 1.1, so the contrast index is about as uncertain as one density reading. The upper trace is the uncertainty of the relative speed point in log exposure units, rising from 0.019 at 0.005, through 0.037 at 0.010 and 0.071 at 0.020, to 0.111 at 0.030 — a slope of about 3.7, so the speed point is nearly four times worse from exactly the same readings. Two horizontal guides mark 0.02, the contrast-index tolerance a manufacturer's process-control practice works to, and 0.10 in log exposure, which is a third of a stop. The point of the drawing is that one set of readings does not have one resolution: the contrast index and the speed point are computed from the same numbers and are not equally trustworthy, because the speed point is read where the curve is flattest.

Series	Standard uncertainty of one density reading, u(D)	Standard uncertainty of the derived quantity
Uncertainty of the contrast index	0.005	0.01
Uncertainty of the contrast index	0.010	0.01
Uncertainty of the contrast index	0.015	0.02
Uncertainty of the contrast index	0.020	0.02
Uncertainty of the contrast index	0.025	0.03
Uncertainty of the contrast index	0.030	0.03
Uncertainty of the relative speed point, log H	0.005	0.02
Uncertainty of the relative speed point, log H	0.010	0.04
Uncertainty of the relative speed point, log H	0.015	0.05
Uncertainty of the relative speed point, log H	0.020	0.07
Uncertainty of the relative speed point, log H	0.025	0.09
Uncertainty of the relative speed point, log H	0.030	0.11

Computed by adding random error to Kodak's published eleven-point sample table and re-solving both constructions thirty thousand times at each level. It is arithmetic on a published table, not a measurement of any instrument or any film. Run the same perturbation on your own twenty-one-step table: the contrast-index slope will be close to this one, and the speed-point slope will be one divided by the gradient of your own toe, which may be very different. 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.

Two results come out of that, and both belong in your notebook before you look at an arm.

The contrast index is about as uncertain as a single density reading. The construction is defined above the measured base, so a pure offset in the whole scale — a stale zero, a lamp that has crept — cancels exactly, provided base plus fog is read on the same day through the same offset. That is worth knowing: the term everybody worries about is the one this construction is immune to.

The speed point is three to four times worse, from the same readings, because it is read where the curve is flattest. The multiplier is simply one divided by the local gradient at the toe, the same conversion Part XIV and Part XV both insisted on:

u(log H) = u(D) ÷ G

Reading uncertainty converted along the exposure axis

On a strip whose toe gradient is 0.27 that is a multiplier of 3.7. On a badly under-developed dilute cell whose toe gradient is 0.12, it is 8.3, and the speed point on that strip is worth almost nothing. Compute the multiplier per strip, not once for the session.

🧮A worked resolution sentence, on numbers that are not yours

Suppose your repeat block gives a replaced-sample standard deviation of 0.010 D on the straight line, your certificate’s chain non-linearity is 0.004, the stray-light residual at the densities you are working in is 0.006, the session drift came out at 0.003, and your reference wedge is uncalibrated so that term is unquantified and is carried as a note rather than a number.

Part II’s bound, on the quantified terms: 0.010 + 0.004 + 0.006 + 0.003 = 0.023 D. Root-sum-of-squares, labelled as such: √(0.0001 + 0.000016 + 0.000036 + 0.000009) = 0.0128 D.

Take the bound. Then, interpolating the plot above at u(D) = 0.023: u(CI) is about 0.025 and u(speed point) is about 0.082 log H, and a difference between two strips carries twice each of those.

The sentence to write down, before plotting:

On this apparatus, on this day, a difference between two cells of less than 0.05 in contrast index or 0.16 in log exposure at the speed point — a little over half a stop — will not be reported as a difference. Base plus fog and D(step 1) differences below 0.046 will not be reported either. The wedge is uncalibrated, so no absolute contrast index is quoted at all, and the figures above are comparisons within one wedge and one session.

Every number in this callout is invented for the arithmetic. None of them is a measurement of anything, and yours will be different — quite possibly better, if your wedge is a calibrated part and your repeat block comes in nearer 0.005.

✕Three ways a budget gets quietly cheated

Quoting the root-sum-of-squares figure without the label. It is roughly half the bound, it looks much more impressive, and it assumes the terms are independent — which the stray-light residual and the chain non-linearity are not, since both come from the same detector.

Applying one figure across the whole density range. Stray light is negligible at 0.5 and dominant at 2.5. A budget with one row is an average of incompatible things; Part XV’s certificate has a band table for exactly this reason, and it is the band containing the reading that governs.

Leaving the unquantified terms out because they have no number. An uncalibrated wedge and an eight-month archival interval do not become zero by being unmeasured. They go in the table as unquantified, and the result names them. A budget of 0.023 with two unquantified terms is an honest statement; a budget of 0.023 that has silently dropped them is a false one.

Reading the pH arm

Plot the three curves on one pair of axes, then plot contrast index, base plus fog and relative speed point against the measured pH — never against the predicted pH, and never against “borax” and “carbonate” as categories, because the arm’s own record contains the numbers.

Ask four questions in this order.

Did anything move by more than the budget? If not, stop and write the null. It is informative and it is publishable in your own notebook as a result: on this film, in this base, at this sulfite concentration, a pH ladder of about two units did not produce a contrast difference this apparatus can see.

Did base plus fog move faster than contrast at the top of the ladder? Kodak’s 1928 primer says that too much alkali gives chemical fog, and that is the shape to look for: a carbonate cell whose contrast index has stopped improving while its base plus fog is still climbing. If you find it, you have located the point at which the alkali is buying nothing and costing something — which is a genuinely useful number for anybody designing a developer.

Is the ladder’s shape consistent with the ladder’s spacing? The predicted rungs are about 0.57 of a pH unit and then about 1.41. If the measured effect per rung is roughly proportional to the pH interval, the arm is behaving like a rate that depends on pH. If the second rung produced far less than three times the first, something saturated.

Is the induction period visible? No, and here is why the question is worth asking anyway. Development has an induction period before anything appears — Part VIII gives ILFORD’s figure of 35 seconds for a correctly exposed fibre-base print — and it is commonly said that a more active bath shortens it. The course has no source that gives the induction period as a function of pH, and this page will not supply one. Even if it had, a shorter induction period on a fixed-time strip is indistinguishable from a higher rate: both deliver more density in ten minutes, and one arm at one time cannot separate them. So write the observation if you have it — say, that the carbonate cell’s threshold step moved further than a rate argument alone would suggest — and mark it as unexplained rather than attributing it. The experiment that could separate the two is a time series at two pH values, which is two sessions and not this one.

Reading the bromide arm, and the published family beside it

This is the arm with a published comparison, and it is worth setting the two side by side precisely because they are not the same experiment.

Hurter and Driffield's bromide family, 1890s — a published comparison, not this course's data

• No bromide
• 2 parts per 1,000 — about 2 g/L
• 8 parts per 1,000
• 32 parts per 1,000
• 128 parts per 1,000

Show the numbers behind this plot

Five traces of density against log exposure from about 0.1 to 1.6, from Hurter and Driffield's Experiment 15: one plate, one pyro-soda developer, three minutes of development, and five levels of potassium bromide expressed in parts per thousand of developing solution. The trace at zero bromide rises steeply from 0.565 at the lowest exposure to 2.500 at the highest. The trace at two parts per thousand runs well below it, from 0.120 to 2.020, and is the one to compare with this course's ladder because two parts per thousand is about two grams per litre, just above the top rung Part Nine used. The trace at eight parts is far lower again, from 0.065 to 1.190, and has an extremely long flat foot. The traces at thirty-two and one hundred and twenty-eight parts are almost flat along the bottom of the plot, reaching only 0.290 and 0.100 at the highest exposure, which is Hurter and Driffield's statement that one hundred and twenty-eight parts almost entirely prevented development in three minutes. The unexposed densities that go with the five traces, which are not plotted because they have no log exposure, are 0.160, 0.090, 0.065, 0.060 and 0.060, so the fog floor is essentially reached by eight parts per thousand while that same cell still develops to 1.190 at the top of the scale.

Series	Log exposure (candle-metre-seconds)	Density
No bromide	0.10	0.56
No bromide	0.40	1.04
No bromide	0.70	1.53
No bromide	1.00	1.94
No bromide	1.30	2.25
No bromide	1.60	2.50
2 parts per 1,000 — about 2 g/L	0.10	0.12
2 parts per 1,000 — about 2 g/L	0.40	0.38
2 parts per 1,000 — about 2 g/L	0.70	0.79
2 parts per 1,000 — about 2 g/L	1.00	1.25
2 parts per 1,000 — about 2 g/L	1.30	1.70
2 parts per 1,000 — about 2 g/L	1.60	2.02
8 parts per 1,000	0.10	0.07
8 parts per 1,000	0.40	0.09
8 parts per 1,000	0.70	0.14
8 parts per 1,000	1.00	0.33
8 parts per 1,000	1.30	0.70
8 parts per 1,000	1.60	1.19
32 parts per 1,000	0.10	0.06
32 parts per 1,000	0.40	0.06
32 parts per 1,000	0.70	0.06
32 parts per 1,000	1.00	0.09
32 parts per 1,000	1.30	0.17
32 parts per 1,000	1.60	0.29
128 parts per 1,000	0.10	0.06
128 parts per 1,000	0.40	0.06
128 parts per 1,000	0.70	0.06
128 parts per 1,000	1.00	0.06
128 parts per 1,000	1.30	0.07
128 parts per 1,000	1.60	0.10

Hurter and Driffield's own densities, from Experiment 15 of the Memorial Volume: pyro-soda on their plate D2, all cells developed three minutes. Their instrument, their plate, their developer and their 1890s emulsion — set beside your numbers, never merged with them. Their fog row, which has no log exposure and so is not plotted, falls 0.160, 0.090, 0.065, 0.060, 0.060 across the same five cells.

What the published family is good for. It establishes the direction beyond argument, it shows the shape of the whole effect over two orders of magnitude, and — the useful part — it tells you where Part IX’s ladder sits on it. Two parts of bromide per thousand parts of solution is about 2 g/L, so Part IX’s top rung, 1.96 g/L, is essentially Hurter and Driffield’s second cell, and the other three rungs are below anything they measured. Their second cell dropped the unexposed density from 0.160 to 0.090 and the top density from 2.500 to 2.020. If your own ladder shows a fog fall of a similar order and a top-density fall of a similar order, you have reproduced the bottom rung of a 130-year-old family on modern film with an instrument you built.

What it is not good for. Different plate, different developing agent, different developer composition, different photometry, and a fixed three-minute development where yours is ten. Their numbers are not a prediction of yours and a disagreement is not an error. If your bromide arm shows a much smaller effect than 2 parts per thousand did for them, the most likely explanations are the emulsion — a 1990s FP4 Plus is not an 1890s gelatin dry plate — and the agent pair.

Then ask three questions of your own data.

Where did base plus fog reach its floor? Their arm reached it by 8 parts per thousand while the top of the scale still developed to 1.190. Yours may reach it inside the first rung, or not at all. The level at which it stops falling is the useful engineering answer, because bromide beyond that point is costing speed and buying nothing.

What did it cost at the speed point? Report the shift in log H_rel and convert it to stops by dividing by 0.301. Then set it against Hurter and Driffield’s conclusion from Experiment 14, which is that the retarding influence of bromide can be fully compensated by time of development and that the speed of the plate is not really altered by its addition. That is a claim about a fixed degree of development, and your arm is at fixed time — so a speed loss on your strips does not contradict them. It is the same difference that runs through this whole page, and it is the reason the time series is the next experiment in the part.

Did the straight-line gradient move? Restraint that acts only on the toe leaves the gradient alone and moves the curve to the right. Restraint that also slows the exposed grains lowers the gradient. The two look similar at a glance and are entirely different mechanisms, and your contrast index against the speed shift is the plot that separates them.

✕What bromide does at high pH compared with low — and why these strips cannot tell you

It is the obvious next question, and it is a real one: a restrainer opposes development and an alkali drives it, so the two levers might cancel, or one might swamp the other, or the restrainer might bite harder in a faster bath because more bromide is being released for it to add to. Part VIII’s mechanism supports all three stories and settles none.

This archive cannot answer it, and the reason is in Part IX’s design rather than in your reading. The pH arm is a metol-only base and the bromide arm is metol–hydroquinone D-76. Two different agent systems, two different sulfite concentrations, two different buffers. The seven cells are not a grid, they are two ladders that happen to have been run on the same afternoon, and setting A3 beside B3 to argue about an interaction would be comparing four differences at once and attributing the result to one of them. Part IX says this plainly in its own limits and this page repeats it because the temptation arrives exactly here, with the two families side by side on the bench.

What would answer it is a two-factor grid: one base, one agent system, three bromide levels crossed with two or three alkali levels, at one time — nine cells rather than seven, one exposure batch, one session. That is a session of its own and a reasonable one to design once you have this page’s resolution sentence in hand, because the resolution sentence tells you in advance whether nine cells would be enough to see an interaction or whether you would need replicates as well. Interaction effects are typically smaller than the main effects that produce them, which is precisely why an apparatus that can just resolve the main effect cannot usually resolve the interaction.

🔬A warning from the same experiment that applies to your instrument

Hurter and Driffield also recorded that as bromide is increased the image changes from black towards a fawn colour, and that once it has, “photometric measurements are no longer a reliable indication of the amount of silver present in the image”. They found a deposit at 128 parts per thousand that carried nearly two and a half times as much silver per unit of density as a black deposit.

At 1.96 g/L you are far below that, and the course does not predict a visible colour change on your strips. But the principle bites at any level: your densitometer reads a narrow green band, modelled on nothing, with ISO 5-3 cited only by number as what a spectral condition is. A difference in image tone between two cells will read as a difference in density on that instrument and would read differently on another. If two strips in any arm differ visibly in colour on the lightbox, write it in the observations, because it means the density difference you measured is partly a colour difference, and no arithmetic in this budget will find that for you.

Reading the sulfite arm

Plot the three curves, then the four quantities against sulfite concentration on a log axis, because the ladder is 10, 50 and 100 g/L and a linear axis puts two of the three points next to each other.

The claim under test is the classic one: that solvent developers cost speed. The measurement is the relative speed point against sulfite concentration, and the answer has to be quoted with the budget attached, because this is the quantity the plot above showed to be three to four times worse than contrast from the same readings. A speed shift of 0.05 log H across the arm, against a worked resolution of 0.16 log H, is not a finding, and reporting it as one would be the exact failure this page exists to prevent.

Then ask what else could produce the same picture, and there are two candidates the arm cannot exclude. The 10 g/L cell is the least protected against aerial oxidation, so a weak curve there may be a loss of agent rather than a want of solvent action. And the tenfold change in ionic strength changes gelatin swelling and diffusion. Report the arm as “sulfite, and whatever a tenfold change in salt concentration does to a gelatin layer”, which is what it measured.

The cross-session pair is worth its own line in the result. S100 and A2 are the same composition developed for the same time, differing in that A2’s base had stood in a bottle and S100’s was mixed fresh. Any difference between them is a keeping result. It is one strip against one strip, so it is an observation rather than a measurement — but it is bounded by the same budget as everything else, and if the difference exceeds the resolution sentence it is worth a session of its own.

Reading the dilution arm, and the fifth measurement

Plot the three sixteen-minute cells and the eight-minute compensated cell on one pair of axes. Then do the thing the arm was built for.

Two curves with the same contrast index and different shapes

• Straight between the chord points: R = 1.00
• Compensated shape: R = 0.64, same CI of 0.62

Show the numbers behind this plot

Two traces of density against relative log exposure, sharing an identical toe that rises from a base-plus-fog level of 0.120 and passes through 0.225 at log exposure 0.90, and meeting again at 1.275 at log exposure 2.602. Between those two points the traces differ. The first is a straight line whose gradient is the same over both halves of the span, so its shape ratio is 1.00. The second rises steeply at first, reaching 0.866 by the midpoint of the span where the straight one has reached only 0.750, and then flattens, arriving at the same 1.275 at the far end; the gradient over its lower half is 0.753 and over its upper half is 0.480, so its shape ratio is 0.64. Beyond the meeting point the straight trace continues climbing at its own gradient while the compensated one climbs at less than half that rate. Because the contrast-index construction depends only on the two chord points and the run between them, both traces return exactly the same contrast index of 0.62, which is the entire point of the drawing: a single slope cannot tell a compensated curve from a straight one, and the shape ratio can.

Series	Relative log exposure	Density
Straight between the chord points: R = 1.00	0.15	0.12
Straight between the chord points: R = 1.00	0.45	0.13
Straight between the chord points: R = 1.00	0.75	0.18
Straight between the chord points: R = 1.00	0.90	0.23
Straight between the chord points: R = 1.00	1.24	0.43
Straight between the chord points: R = 1.00	1.58	0.65
Straight between the chord points: R = 1.00	1.75	0.75
Straight between the chord points: R = 1.00	1.92	0.85
Straight between the chord points: R = 1.00	2.26	1.06
Straight between the chord points: R = 1.00	2.60	1.27
Straight between the chord points: R = 1.00	2.80	1.40
Straight between the chord points: R = 1.00	3.00	1.51
Compensated shape: R = 0.64, same CI of 0.62	0.15	0.12
Compensated shape: R = 0.64, same CI of 0.62	0.45	0.13
Compensated shape: R = 0.64, same CI of 0.62	0.75	0.18
Compensated shape: R = 0.64, same CI of 0.62	0.90	0.23
Compensated shape: R = 0.64, same CI of 0.62	1.24	0.52
Compensated shape: R = 0.64, same CI of 0.62	1.58	0.76
Compensated shape: R = 0.64, same CI of 0.62	1.75	0.87
Compensated shape: R = 0.64, same CI of 0.62	1.92	0.96
Compensated shape: R = 0.64, same CI of 0.62	2.26	1.13
Compensated shape: R = 0.64, same CI of 0.62	2.60	1.27
Compensated shape: R = 0.64, same CI of 0.62	2.80	1.32
Compensated shape: R = 0.64, same CI of 0.62	3.00	1.36

Both curves are constructed arithmetic, not measurements: the same base plus fog, the same two chord points and the same 2.00 chord, so the contrast-index construction returns 0.62 for both. Only the path between the points differs. Perturbing the three densities that define the shape ratio by a standard uncertainty of 0.01 gives a spread of about 0.05 in R for the straight curve and about 0.03 for the compensated one, so the gap of 0.36 between these two is several times the noise. 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.

The procedure. Compute R for the stock, 1+1 and 1+3 cells at sixteen minutes, and for the eight-minute compensated cell. Then answer:

Do the dilute cells have a lower R than the stock cell at the same time? If they do, their upper scale has flattened relative to their own lower scale, which is the signature compensation is supposed to leave. If R is the same across the arm and only CI has fallen, the dilute cells are simply developed less, and the word “compensating” should not appear in the result at all.

Is R lower at matched contrast? This is the sharp version, and it needs the compensated cell. D-76 at 1+3 for 16 minutes and D-76 at stock for 8 minutes are the two times ILFORD publish for the same film at the same meter setting, so they are intended to reach a similar contrast. If your measurement confirms that their contrast indices agree inside the budget, then their difference in R is a difference in shape at matched contrast, and it is the cleanest evidence a home apparatus can produce that dilution changes the shape of a curve and not merely its slope. If their contrast indices do not agree, the comparison is not at matched contrast and R cannot be read this way; say so, and use the stock-at-sixteen cell as the reference instead, with the caveat that it is over-developed by design.

How big is R’s own uncertainty? R is a ratio of two differences, each of which carries the reading budget, so it is noisier than a contrast index. Perturb the three densities that define it, exactly as you did for CI, and get a figure. On the constructed curves above, a reading uncertainty of 0.01 gives about 0.05 in R — which is why a difference of 0.36 is a finding and a difference of 0.06 is not.

=Which way the confounds push, in the arm most likely to be over-read

The stock cell at sixteen minutes is over-developed by design — twice ILFORD’s published time — and may have run its top steps together. If it has, its own upper gradient is depressed by the shoulder rather than by exhaustion, and R falls for a reason that has nothing to do with dilution. Check the top three steps of every strip in this arm before computing R, and if the stock cell has shouldered, restrict the chord to the region where it has not, applying the same restriction to all four cells.

The 1+3 cell is the one where the manufacturer’s minimum quantity of developing agent per unit area is closest to being crossed, and the arithmetic is worth doing rather than assuming. Kodak’s D-76 sheet gives one 135-36 roll — which it states as 80 square inches, about 516 cm² — in 473 mL of the 1:1 dilution. A 135 mm strip of 35 mm film is about 47 cm², so the same ratio asks for roughly 43 mL, and Part IX developed each strip in at least 80 mL. That is nearly double, so a shortage of agent is unlikely to be the explanation on these strips — but it is the first thing to check on any dilute cell that comes out weaker than the arm’s trend, and the slip records the volume for exactly this purpose. Note also that Kodak’s figure is for a 1:1 dilution and Part IX’s most dilute cell is 1+3, where the same volume carries half as much agent again.

Setting the result beside the mechanism, and saying which is more likely wrong

Part VIII’s account of all four variables was written from published chemistry and manufacturer data. Your four families are sixteen strips read once. When they disagree, the honest default is that your strips are more likely to be wrong than the mechanism — not because the mechanism is sacred, but because the mechanism rests on more evidence than one session does, and a single unreplicated comparison on one film in one darkroom is exactly the kind of evidence that turns out to have had a thermometer error in it.

That default is rebuttable, and here is what rebuts it. A disagreement is worth taking seriously when it is larger than twice the budget, when it survives a re-read of the same strips on another day, and when the mechanism’s own prediction was quantitative in the first place. Part VIII is quantitative about very little of this: it gives direction and mechanism, and says plainly where it has no numbers — no pH for D-76, no formation constant for a silver–sulfite complex, no sourced threshold for solvent action. A result that contradicts a direction is interesting. A result that contradicts a number the course never gave is not contradicting anything.

The one place the comparison is genuinely two-sided is the pH arm, because Part VIII made a specific argument — that metol is already neutral above about pH 8, so its ionisation barely changes across this ladder — that a measured null would support and a large measured effect would undermine. That is the arm where your sixteen strips can actually push back, and it is worth writing up either way.

What cannot be concluded from this session

Written out, because a result section without one invites the reader to conclude it anyway.

Nothing about another film. One emulsion batch of one film. Toe shape, which sets the speed point’s uncertainty, is a property of the emulsion.

Nothing about another developing agent pair, and nothing about how the arms interact. The pH and sulfite arms are metol-only; the bromide and dilution arms are metol–hydroquinone. The two cannot be crossed, so no statement of the form “bromide does more at high pH” is available from these sixteen strips, however suggestive the two families look laid side by side.

Nothing about another temperature or time. Every arm is at one fixed time, and the fixed-time design is why a speed loss here is not the same claim as a speed loss at matched contrast. That distinction is what the development time and temperature series exists to settle.

Nothing about grain. This experiment does not measure granularity and cannot. A granularity figure needs a defined aperture, a magnification and a stated density, and this instrument’s aperture is a millimetre-scale hole chosen for step reading. Part IX ranked grain by eye; that ranking is not upgraded by anything done today.

Nothing about sharpness or adjacency. The edge targets were not read here and a step wedge cannot show an edge effect.

Nothing absolute. No film speed, because the exposure axis has no lux-second on it. No absolute contrast index if your wedge is uncalibrated. No claim of conformance to ISO 5-2, ISO 5-3 or ISO 6, all of which this course cites by number and quotes nowhere.

And nothing at all about a difference smaller than the budget. That is what the resolution sentence was for, and the only way it fails is if you write it and then argue with it.

Troubleshooting

What you see	Likely cause	What to do
The opening calibration step is out by more than 0.02 D	Zero taken through something, a stale dark reading, the reference handled on its measurement area, or a genuine drift since the last session	Recalibrate per the SOP before any strip. If it happens every session, the certificate’s warm-up rule is too short
The closing calibration step differs from the opening one by more than your certificate’s zero stability	Lamp or detector drift over four hours, or room temperature moved	Add the difference as a Type B term and say so. Consider re-reading the last three strips
The repeat block’s spread is much larger than the certificate’s replaced-sample figure	The archived film is not lying flat, or the sleeve has left a curl, or the stage is being knocked	Let each strip sit flat before reading. If the curl is the cause, weight the strip at the edges — never across the wedge image — and record that you did
A strip reads high on every step, including the masked patch	An offset: the zero, or a strip read through its sleeve	Re-read one step with the sleeve definitely open. Note that a pure offset does not change the contrast index, so the arm may still be usable if you can show it is an offset
The top steps of a strip are all within a few thousandths of each other	Either the film has shouldered, or you are above the working range and reading stray light	Compare against the certificate’s working range. If the steps are above it, they are not densities and must be flagged, not fitted
The contrast-index solver does not converge on a strip	The curve does not span the density range the construction needs — usually a badly restrained or badly diluted cell	Report no contrast index for that strip. Do not extend the curve by extrapolation; a construction that cannot be satisfied is a fact about the strip
The two reference strips disagree by more than the budget	Archival drift, a process difference between the two Part IX sessions, or two different bottles of D-76	Refuse the between-session comparison, report each session’s arms on their own, and say which of the three you could not exclude
A strip’s card slip and the notebook disagree	One of them was written later	The slip loses, because the notebook was written at the bench. If the notebook is silent too, the strip is unusable

Clean-up

The instrument goes through its closing check and off. The reference wedge goes back into its dark, cool, dry storage, handled at the edges, because the manual is explicit that fingerprints and foreign substances on the measurement area cause errors and that nothing but a soft camel-hair brush should touch it. The log file is copied somewhere else before the laptop is closed: a session’s readings that exist in one place have not been recorded, they have been risked.

With a top-up run, Part IX’s clean-up applies: cylinders and vessels rinsed and dedicated, the balance and its surround wiped down, the waste containers labelled and closed.

Storage

The strips go back into their own sleeves, with their own slips, and each slip gains one line: the date they were read, the instrument serial, the certificate date, and the notebook page the readings are on. That line is what makes a re-read possible in two years, and a re-read is the only way anybody will ever bound the archival term properly.

Store them as the conservation guidance says, which is cool and dry rather than merely indoors: the Image Permanence Institute’s simplified recommendation for black-and-white film is cool storage at no more than 50 per cent relative humidity to minimise the possibility of silver image decay, and it names harmful enclosures and poor air quality among the other threats. Its ISO row for polyester-base black-and-white film is 21 °C and 50 per cent as maxima; for the acetate base that 35 mm FP4 Plus is coated on, the ISO row is colder still. A domestic refrigerator is not the answer without addressing condensation, and this course has no procedure for that; a cool interior cupboard away from radiators, damp and traffic fumes is the achievable version. The sleeving is part of it, and sleeving that passes the Photographic Activity Test is the specification — the course’s price file has no UK price for it, which is a gap rather than a licence to use anything to hand.

Keep the log file and the completed budget with the notebook. The four families are re-derivable from them; they are not re-derivable from a plot.

With a top-up, keep nothing wet. The replaced cells are one-shot working solutions and two of them are experiments in what an alkali does to a metol bath, which includes what it does to its keeping. Discard them and keep the version records instead.

Disposal considerations

With no top-up, this session generates no chemical waste at all.

With a top-up, the chemistry is Part IX’s at a fifth of the scale, and so is the reasoning. The developer waste is alkaline and carries almost all of the metol and hydroquinone that went into it, because three small strips reduce very little silver; both agents carry aquatic-hazard classifications, so the bath goes into a labelled container rather than to drain. The fixer and its first rinse are acidic and silver-bearing and go to the silver stream, which is where the dissolved silver–thiosulfate complexes belong. The two are never combined, because a sulfite solution at high pH meeting an acidic bath is a way to make sulfur dioxide.

Local regulation governs, and it differs between jurisdictions in what it permits a domestic user to do with each stream. The disposal page explains why the course states the chemistry and the general practice and does not give a jurisdiction-specific instruction as though it were universal. Check what applies where you are before the first container is filled.

Questions

1. Your repeat block gives a replaced-sample standard deviation of 0.008 D on the straight line and 0.011 D near the top of the range. Your certificate’s stray-light residual is 0.002 at 1.0 and 0.014 at 2.5. Why is a single budget row wrong here, and which of your sixteen strips is most affected by the difference?
2. A colleague reports that their contrast index moved by 0.04 when they recalibrated the instrument between two strips, and concludes that the instrument is unreliable. Given how the contrast-index construction is defined, what is the more likely explanation, and what single reading would settle it?
3. The two reference strips agree to 0.01 in contrast index but differ by 0.06 in base plus fog. What can and cannot be concluded, and which arm’s results are most threatened by the difference?
4. Your dilution arm gives contrast indices of 0.71, 0.58 and 0.44 at stock, 1+1 and 1+3 at sixteen minutes, and shape ratios of 0.95, 0.93 and 0.91. What does that pattern say about compensation, and what would the shape ratios have to look like for the word to be justified?
5. A strip’s slip records the development temperature as “20 °C” with no start-and-end pair. Argue both sides of whether to use it, then say what the page’s rule is and why the rule is worth more than the strip.
6. Hurter and Driffield’s second bromide cell is at about the same concentration as Part IX’s top rung. Name three reasons their density figures are not a prediction of yours, and one thing their family does tell you about yours.

Further experiments

Re-read the same sixteen strips in six months. Nothing else changes: same instrument, same certificate, same constructions. The differences are a direct measurement of the archival term this page had to carry as unquantified, and they are the only way this course will ever get a number for it. Two readings a year apart on twenty-one steps of sixteen strips is a genuinely useful dataset and nobody else is collecting it.

Read three strips on somebody else’s densitometer. Your certificate establishes repeatability; agreement with a different instrument of a different geometry and a different spectral condition is the only thing that speaks to trueness. Expect a disagreement, and expect it to be larger on the dense steps than the thin ones. The difference between the two instruments at the criterion density, plotted against density, is the most informative half-hour available to anybody who owns one home-built instrument and can borrow another.

Solve the contrast index three ways on one table — the marked straightedge on a hand-plotted curve, the course’s arithmetic construction, and a least-squares straight line over the same span — and record the spread. The course expects agreement to about 0.02 between the first two, and this is how you find out whether that holds on a curve with a difficult toe.

Run the perturbation properly. The spreadsheet method above is a Monte Carlo with a rectangular distribution, which is what a spreadsheet can do. If you have the tools, run it with the distribution your repeat block actually suggests, and compare the resolution sentence you get with the one Part II’s bound gave. Where they disagree, say which you would quote to somebody buying a print from you.

Take the two reference strips seriously as a control chart. Every session in Part XXVII produces one. Plot their contrast index and base plus fog against date on a chart with your own action lines, the way ILFORD’s process-control introduction describes for speed, contrast and minimum density. By the end of the part you will have six points, which is not many — but it is the difference between knowing your process drifted and believing it did not.

Check your understanding

Question 1. Why does a stale zero on the densitometer — an offset that adds the same amount to every reading on a strip — leave the contrast index almost unchanged?

• Because the construction places both chord points at fixed fractions of the density rise above the measured base plus fog, so an offset that moves the base moves both points with it
• Because the contrast index is a ratio and all ratios are immune to offsets
• Because the offset is small compared with the densities being read
• Because the wedge steps are equally spaced, which cancels the offset

Show the answer and why

Answer: Because the construction places both chord points at fixed fractions of the density rise above the measured base plus fog, so an offset that moves the base moves both points with it

The two chord points are D0 + 0.1 dD and D0 + 1.1 dD, both defined above the measured base plus fog. If the whole scale shifts by a constant and the masked patch is read through the same shift, D0 moves by the same amount and the two points sit at the same places on the curve, so the solved density difference and the run are unchanged. Perturbing the published Kodak sample table by an offset of 0.03 with the base tracked moves the contrast index not at all; the same offset with the base NOT tracked — that is, base plus fog misread by 0.03 — moves it from 0.616 to 0.594. The immunity is not to offsets in general, it is to offsets that base plus fog shares, which is exactly why the masked patch on each strip is read on the same day, on the same instrument, as the strip beside it.

Question 2. From one set of readings on one strip, the speed point turns out to be three to four times more uncertain than the contrast index. What sets that multiplier?

• The gradient of the curve where the speed point is read: the uncertainty along the exposure axis is the density uncertainty divided by the local gradient
• The number of wedge steps, since the speed point is interpolated between two of them
• The stray-light residual, which is worst at the toe
• The wedge certificate, which is the largest Type B term

Show the answer and why

Answer: The gradient of the curve where the speed point is read: the uncertainty along the exposure axis is the density uncertainty divided by the local gradient

The conversion is u(log H) = u(D) divided by G, the local gradient. The speed point sits on the toe, where G may be 0.27 or less, so a density uncertainty of 0.01 becomes 0.037 in log exposure — nearly four times worse. On a badly under-developed dilute cell with a toe gradient of 0.12 the multiplier is 8.3 and the speed point on that strip is worth almost nothing. The consequence is practical: compute the multiplier per strip rather than once for the session, because it is a property of the curve on that strip and not of the instrument.

Question 3. Which of these belong in the uncertainty budget as UNQUANTIFIED terms rather than being left out?

• The step values of an uncalibrated wedge
• The change in silver density over the months the strips spent in the archive
• The replaced-sample repeatability from the repeat block
• Latent-image keeping on a top-up strip taken from the Part IX batch tin

Show the answer and why

Answer: The step values of an uncalibrated wedge, The change in silver density over the months the strips spent in the archive, Latent-image keeping on a top-up strip taken from the Part IX batch tin

The repeatability figure is the one term here you measured, so it is a Type A term with a number. The other three have no number this course can source: Stouffer publish a nominal 0.15 increment as a manufacturing intention and only the calibrated parts carry recorded readings; the conservation guidance on silver image decay is qualitative and about decades; and ILFORD say to process exposed film as soon as practical without giving an interval. Leaving them out because they have no number would make the budget smaller and the result false. They go in the table marked unquantified, they are named in the result, and two of them are bounded empirically instead — by the two reference strips and by the bridge strip.

Question 4. Two cells in the dilution arm give contrast indices of 0.58 and 0.57, and shape ratios of 0.95 and 0.71. The resolution sentence for the session allows 0.05 in contrast index and about 0.10 in the shape ratio. What may be reported?

• That the two cells reach the same contrast index within the budget, and that the more dilute one has a measurably flatter upper scale at matched contrast — which is compensation, measured rather than claimed
• That the dilute cell is under-developed, since its contrast index is lower
• Nothing: neither difference exceeds the budget
• That the dilute cell has more shadow separation, since its lower gradient is steeper

Show the answer and why

Answer: That the two cells reach the same contrast index within the budget, and that the more dilute one has a measurably flatter upper scale at matched contrast — which is compensation, measured rather than claimed

The contrast indices differ by 0.01 against a resolution of 0.05, so they agree — which is the condition that makes the comparison a matched-contrast one. The shape ratios differ by 0.24 against a resolution of about 0.10, so that difference may be reported. A lower shape ratio at matched contrast means the upper half of the chord is shallower relative to the lower half, which is a shoulder made by local exhaustion rather than a slope lowered everywhere. The third option is the trap: applying the contrast-index resolution to the shape ratio and concluding nothing throws away the one measurement the arm was designed around.

Question 5. Hurter and Driffield found in 1890s work that the retarding influence of bromide can be fully compensated by time of development, and that the speed of the plate is not really altered by its addition. Your bromide arm, developed for a fixed ten minutes, shows the speed point moving by a third of a stop. Which statement is correct?

• There is no contradiction: their claim is about matched degree of development and yours is a measurement at fixed time, so the two are answers to different questions
• Their conclusion is refuted by your measurement, since yours is on modern film with an instrument
• Your measurement must be in error, since theirs rests on far more data
• Both are correct only if your ladder reaches 128 parts per thousand

Show the answer and why

Answer: There is no contradiction: their claim is about matched degree of development and yours is a measurement at fixed time, so the two are answers to different questions

This is the distinction the whole part turns on. At fixed time, a restrained cell is developed less far, so its curve sits lower and its speed point moves right; at matched degree of development — reached by giving the restrained cell more time — Hurter and Driffield found the speed came back. Their own Experiment 14 demonstrates it directly, with density 2.50 in three minutes without bromide against 2.425 in fifteen minutes with 90 parts per thousand. So a fixed-time speed loss is real and is not a refutation, and the way to test their claim on your own film is a time series, not a bromide series. Reporting a fixed-time speed loss as "bromide costs speed" without the qualification is the commonest way this measurement is misread.

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