Assignment: Night, the Very Long Exposure and Solargraphy

The intention

Make one night negative whose exposure you computed, corrected and then had to defend; and start one solargraph that will not be finished until the season has changed. Both are exercises in the same thing: an exposure long enough that the correction is bigger than the calculation it corrects, and an honest statement of how far you can trust it.

This is the assignment where the arithmetic stops giving comfortable answers. Two of the numbers you are about to compute are measured in days, and one of them is measured in decades. Getting those numbers before you go out is the difference between a night session and a wasted night.

Learning objectives

By the end of this session you should be able to:

• Compute a night exposure from a measured illuminance and say at what light level the answer becomes impractical for each material you own — with the crossing point as a number, not an impression.
• Apply an extrapolated reciprocity exponent and state the uncertainty band it carries, because at these durations the band is a factor of two.
• Show, with order-of-magnitude photometry, why a star cannot record on paper at f/200 in any exposure you could actually give, and why the moon’s disc can record in about a minute.
• Explain what forms a solargraph’s image chemically, why it is scanned rather than fixed, and predict roughly how many clear days it takes for the sun’s arc to appear.
• Plan and run a night session in which nothing goes wrong that could have been foreseen.

Prerequisites

Landscape, Sky, Foreground and Filters precedes this page. Part IV’s latent-image behaviour lesson owns why the latent image decays and what keeping an exposed sheet costs; Part VI’s exposure and reciprocity lesson owns the correction and the makers’ published forms of it; and Part I’s unfixed silver photogram owns the whole chemistry of the printing-out image, which is what a solargraph is. Read that Part I page again before you build the solargraph camera; this page adds the geometry and the arithmetic and repeats none of the chemistry.

Safety classification

Level A. No new chemistry: the night negative is processed in the same three baths as every previous assignment, and the solargraph is never processed at all. The classification is Level A because of what is in the trays, and everything genuinely risky about this assignment is locational and temporal — where you are, and when.

• Substances. Paper developer, stop and rapid fixer at working dilution, indoors, afterwards.
• Energies. None emitted by anything you are using. Traffic, in the dark, is the energy that matters.
• Procedures. Standing still outdoors after dark for tens of minutes, often alone; loading paper by a dim safelight or in a changing bag away from home; fixing an object outdoors for months.
• Waste. Used fixer is silver-bearing and is collected. The solargraph produces no waste at all, which is unusual enough in this course to be worth noticing.

What is not a hazard here, and why. An unfixed sheet of photographic paper left in a can for six months is not a chemical hazard: it is silver halide in hardened gelatin on a resin-coated base, sealed inside a container, at ambient temperature, reacting with nothing but light. It does not off-gas, it does not become unstable, and if a passer-by opens the can they are exposed to nothing worse than a disappointing piece of paper. The reasons the solargraph camera needs care are that it must not fall on anybody, must not be mistaken for something alarming, and must not be attached to property that is not yours.

Hazards

Being out after dark, stated as the course’s own conditions. Choose a location you have visited in daylight and photographed in daylight, so that you know the ground, the exits and where the light falls. Tell somebody where you are going and when you will be back, and tell them again when you return. Take a charged phone and a torch you are not depending on for the exposure. Prefer to go with somebody; if you go alone, choose somewhere overlooked rather than somewhere remote. Set a time at which you leave regardless of how the pictures are going.

Being seen. The Highway Code’s rule 3 is explicit that in the dark you should “use reflective materials (eg armbands, sashes, waistcoats, jackets, footwear)”, which can be seen by drivers using headlights up to three times as far away as non-reflective materials. A photographer standing beside a tripod at the kerb for four minutes is exactly the stationary pedestrian that rule is about. Rules 1 and 2 still apply: pavements where provided, and where there is none, keep to the right-hand side so you can see oncoming traffic.

Obstruction, and an unattended camera. Section 137(1) of the Highways Act 1980 makes it an offence in England and Wales to wilfully obstruct the free passage along a highway. A forty-minute exposure is forty minutes of tripod: leave a clear passing width, and stay with the camera. An unattended camera in the dark is a problem for other people as well as a risk to itself.

Torch discipline. Loading paper in the field means a changing bag, in the dark, with the torch off. If you use a dim red torch to find the holder, it points at the ground and never at the paper. Kodak’s K-4 makes the general point that the word safe in safelight is relative — most papers retain some sensitivity to the colours a recommended filter transmits — and that safelight exposure should therefore always be minimised. A torch in a field is not a specified safelight at all, so the only defensible rule is that the paper never sees it.

Mounting a solargraph camera. Fix it where it cannot fall on anyone and where it obstructs nothing. Get permission from whoever owns the thing you attach it to, in advance, and label the camera with your name, a contact and the date you will collect it. This course states that as a requirement of the assignment rather than as a legal claim: the law of fixing objects to street furniture, trees and buildings varies, and the requirement here is simply that you asked.

Required PPE

• Reflective or light-coloured outer clothing, which is the protective equipment for this assignment in the way gloves are protective equipment in the darkroom.
• Warm layers, because standing still for forty minutes after dark is colder than walking for forty minutes after dark, and cold degrades judgement before it degrades comfort.
• A torch, and a spare light source, kept off during exposures.
• Back indoors: nitrile gloves, eye protection and one pair of tongs per tray.

Ventilation

Not among the outdoor controls. Indoors, an openable window or an extractor rather than a sealed cupboard, which is ILFORD’s general instruction; none of the three baths at these dilutions generates a vapour that calls for extraction.

Materials

Item	Quantity	Notes
Variable-contrast RC paper	10 sheets	Six for the twilight sequence, two for the solargraphs, two spare.
Panchromatic sheet film	4 sheets	For the full-dark exposures, where paper cannot reach.
A drinks can or an opaque plastic tube	2	The solargraph bodies. Two, because one will be lost or opened.
Aluminium drink-can shim or brass shim	small piece	The pinhole, made by the Part VI method.
Matt black paint or tape	as needed	The inside of the can.
Waterproof tape and a cable tie or strap	as needed	Sealing and mounting.
A label, weatherproof	2	Name, contact, date of collection.
A lux meter or calibrated phone app	1	Readings at every step of the falling light.
Prediction sheet, folded	2	Predictions on the left, observations on the right.

Chemicals

Chemical	Quantity	Form
Paper developer concentrate	100 mL	Diluted 1+9 to make 1 L; 60 seconds at 20 °C for RC paper.
Stop bath concentrate	50 mL	Diluted 1+19 to make 1 L. A citric acid stop.
Rapid fixer concentrate	200 mL	Diluted 1+4; 30 seconds for RC paper. An ammonium thiosulfate fixer.
Film developer	per its own sheet	Only if you take the film route; dilution and time from the maker’s table.
Water	about 15 L	Dilution and washing.

The solargraph uses no chemicals whatever, and that is the point of it. The sheet inside it is never developed, never stopped and never fixed. Its image is made by light alone, and section 6 explains why adding any of the three would destroy it.

Equipment

The modular camera with its flat back; the plate register, including your largest hole, because at night the aperture is the only thing you can change that does not cost time; a tripod that is actually stable, since a four-minute exposure records every knock; a timer that will run for an hour; a torch; a changing bag if you load in the field; and the processing kit.

Estimated cost

Cost band £. Ten sheets, four of film, and two drinks cans. Dated prices live in the laboratory planner.

Waste streams

Used fixer is silver-bearing, and so is the first change of wash water; both are collected in the labelled container rather than poured away. Developer and stop carry no silver. Local regulations govern where the container goes next, and they differ between authorities.

Preparation

1. The night exposure table, computed before you believe it

The relation is Part VI’s, unchanged: t = N²C/(E**S), with C ≈ 310. What changes at night is that E falls by four or five orders of magnitude, and t rises with it.

Measured illuminance at the subject	Paper, ISO 3, f/200	HP5 PLUS, ISO 400, f/200, metered	HP5 PLUS, corrected at P = 1.31
12,150 lux — heavy overcast daylight	340 s	2.6 s	3 s
1,000 lux — late dusk, or under a bright shop front	1.15 h	31 s	90 s
100 lux — deep twilight	11.5 h	310 s	31 min
10 lux — a well-lit street	4.8 days	3,100 s	10.4 h
1 lux — a poorly lit street	48 days	8.6 h	8.9 days
0.25 lux — full moonlight	191 days	1.4 days	—

Computed from t = N²C/(E**S) with C = 310, and corrected with the exponent ILFORD publish for HP5 PLUS. Nothing in the table is measured, the illuminance descriptions are labels rather than data, and the corrections in the right-hand column are extrapolations far beyond the range ILFORD illustrate — which is the subject of section 2.

Read the table for its verdict rather than its numbers, because the verdict is what changes your plans. Paper runs out at dusk. By the time the light has fallen to 100 lux, paper at f/200 wants eleven and a half hours, and the practical conclusion is unavoidable: the paper route to a night picture is a twilight route. You start while there is still light in the sky and you finish in the dark, and the sheet records the brighter part of that. Film reaches into the dark, and pays for it in correction rather than in aperture. And the full moon does not light a landscape you can photograph, whatever the phrase “moonlit picture” suggests.

🧮DO THE MATHS: the illuminance you need for an exposure you can wait out

Turn the relation round and ask what light level gives a half-hour exposure.

E = N²C/(t**S) = 200² × 310 / (1,800 × 3) = 12,400,000 / 5,400 = 2,296 lux on paper.

That is not a night light level. It is roughly the illuminance under a shop canopy or a floodlit forecourt — brighter than a well-lit street by more than two orders of magnitude. So a thirty-minute paper exposure at f/200 is a picture of a light source, not a picture lit by one.

On film at ISO 400 the same half-hour metered gives E = 40,000 × 310 / (1,800 × 400) = 17 lux, and applying the correction backwards, a corrected half hour corresponds to a metered 305 s, so about 101 lux. That is deep twilight. Film buys you a little over one order of magnitude of darkness, and no more — the ISO ratio is worth two orders, and reciprocity failure takes most of one of them straight back.

2. The correction, when the correction is most of the exposure

Every published reciprocity correction stops well short of where this assignment goes. ILFORD’s own sheet says so in plain words: “for very long exposures at very low light levels then some other variables come in to play such as the accuracy of the light measurement. This means that some trial and error may be required.”

Apply their exponent anyway, and watch what fraction of the answer it becomes.

Metered time	Corrected at P = 1.31	The correction, as a multiple	Correction’s share of the exposure
1 s	1 s	×1.0	0 %
31 s	90 s	×2.9	66 %
310 s	1,835 s	×5.9	83 %
3,100 s	37,470 s	×12.1	92 %

By the time the meter says fifty minutes, nine-tenths of the exposure you actually give is correction. You are no longer applying a small adjustment to a measurement; you are relying almost entirely on an extrapolated exponent, and the measurement has become a minor input.

⁇Three makers, three different shapes for the same law

The manufacturers do not agree about what form low-intensity reciprocity failure takes, and the disagreement is visible in how they publish it. This is not a dispute about a date; it is a dispute about a mechanism’s mathematical shape, and it is the reason your extrapolation carries a band rather than a value.

ILFORD publish a single exponent per film — T_c = T_m^P, with P = 1.26 for FP4 PLUS and 1.31 for HP5 PLUS — which asserts that one power law describes the material over the whole range where a correction is needed.

Kodak publish a table and no exponent at all, giving corrections at 1, 10 and 100 metered seconds and, for TRI-X, a development reduction at each. Part VI back-calculates P from their points and finds 1.15 to 1.18 for T-MAX 100 and 1.54 to 1.70 for TRI-X — a range rather than a value for the same film, which is a table declining to claim a single exponent exists.

FOMA publish multipliers that imply two different exponents at their own two points, 1.90 at ten seconds and 1.60 at a hundred. That is a sheet saying, in its own numbers, that the exponent falls as the exposure lengthens.

What the course does. It uses the exponent the maker publishes where there is one, states the range where there is not, and carries the uncertainty explicitly into the answer rather than picking a middle value and looking confident. It does not claim to know which of the three shapes is right; nothing in this part could settle that.

Corrected exposure at night, and the band that the exponent's uncertainty opens

• No correction — what the meter assumes
• P = 1.26 — the mild end of the range
• P = 1.31 — ILFORD’s published figure for HP5 PLUS
• P = 1.36 — the severe end of the range

Show the numbers behind this plot

Four rising curves of corrected exposure against metered exposure, over a metered range of one hundred to three thousand one hundred seconds, which is the region a night exposure on film actually lands in and which lies far beyond the range any manufacturer illustrates. The lowest curve is the reference line where no correction is applied: one hundred metered seconds stays one hundred, one thousand stays one thousand, three thousand one hundred stays three thousand one hundred. The three curves above it are the same power law computed with three exponents. At an exponent of one point two six, the mild end of the plausible range, one hundred metered seconds becomes three hundred and thirty-one, one thousand becomes five thousand seven hundred and fifty-four, and three thousand one hundred becomes twenty-five thousand and sixty, which is seven hours. At the exponent of one point three one that ILFORD publish for HP5 Plus, the same three metered times become four hundred and eight, eight thousand one hundred and twenty-eight, and thirty-seven thousand four hundred and seventy seconds, which is ten point four hours. At an exponent of one point three six, the severe end of the same range, they become five hundred and twenty-five, eleven thousand four hundred and eighty-two, and fifty-six thousand and eighty seconds, which is fifteen point six hours. The vertical spread between the mild and severe curves at three thousand one hundred metered seconds is from seven hours to fifteen point six hours, a factor of two point two on the same scene with the same meter reading, and that spread is the honest uncertainty of the method rather than a defect in it. A shaded band between the outer two curves marks it.

Series	Metered exposure, seconds	Corrected exposure, seconds
No correction — what the meter assumes	100.00	100.00
No correction — what the meter assumes	500.00	500.00
No correction — what the meter assumes	1000.00	1000.00
No correction — what the meter assumes	2000.00	2000.00
No correction — what the meter assumes	3100.00	3100.00
P = 1.26 — the mild end of the range	100.00	331.00
P = 1.26 — the mild end of the range	500.00	2223.00
P = 1.26 — the mild end of the range	1000.00	5754.00
P = 1.26 — the mild end of the range	2000.00	13760.00
P = 1.26 — the mild end of the range	3100.00	25060.00
P = 1.31 — ILFORD’s published figure for HP5 PLUS	100.00	408.00
P = 1.31 — ILFORD’s published figure for HP5 PLUS	500.00	2996.00
P = 1.31 — ILFORD’s published figure for HP5 PLUS	1000.00	8128.00
P = 1.31 — ILFORD’s published figure for HP5 PLUS	2000.00	20140.00
P = 1.31 — ILFORD’s published figure for HP5 PLUS	3100.00	37470.00
P = 1.36 — the severe end of the range	100.00	525.00
P = 1.36 — the severe end of the range	500.00	4038.00
P = 1.36 — the severe end of the range	1000.00	11482.00
P = 1.36 — the severe end of the range	2000.00	29450.00
P = 1.36 — the severe end of the range	3100.00	56080.00

Computed from Tc = Tm^P at three exponents spanning ±0.05 around ILFORD's published figure; nothing here is measured, and the whole plotted range lies beyond where any maker illustrates the correction. The gap between the outer curves is what you are actually uncertain about: at a metered fifty minutes it is the difference between a seven-hour exposure and a fifteen-hour one. 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.

What to do about a factor of two. Not despair, and not pretend. Bracket by hole, not by time, because you cannot afford to give three exposures of ten hours but you can give one exposure and change N. Two plates a stop apart cover a factor of two exactly, which is the size of the band. And log the exponent you used and where it came from, so that when the sheet comes out thin you know which of the two suspects to question.

3. What records at night, and what does not

Two order-of-magnitude arguments settle the two questions students most often ask, and both are built from a single published figure — the midday summer sun at English latitudes delivers about 100,000 lux — plus two apparent magnitudes from NASA’s fact sheets.

🧮DO THE MATHS: the moon's disc records in a minute; a moonlit landscape does not record at all

Step 1: how much light the full moon delivers. NASA give the Sun’s visual magnitude as −26.74 and the Moon’s apparent visual magnitude at opposition as −12.74. The difference is exactly 14 magnitudes, and the magnitude scale is defined so that five magnitudes are a factor of a hundred, so the ratio is 10^14/2.5 = 398,000.

E_moon = 100,000 / 398,000 = 0.25 lux

Step 2: the moonlit landscape. Put 0.25 lux into the exposure relation for paper at f/200: t = 40,000 × 310 / (0.25 × 3) = 1.65 × 10⁷ s = 191 days, before any reciprocity correction, which at that light level would be enormous and is entirely unpublished. A moonlit landscape is not photographable on this camera with this material.

Step 3: the moon’s own disc, which is a different question. The disc is not lit by moonlight; it is lit by the sun. Its apparent diameter is 1896 seconds of arc, or 0.527°, so it subtends a solid angle of 6.64 × 10⁻⁵ steradian, and its luminance is 0.25 / 6.64 × 10⁻⁵ = 3,785 cd/m². The image illuminance from an extended source is πL/(4N²) = π × 3,785 / 160,000 = 0.074 lux, and the image-plane exposure paper needs works out at about 4.65 lux·s (section 4 derives it). So the disc needs 63 seconds.

Step 4: but it moves. The sky turns 15° per hour, so the moon crosses its own diameter in 0.527 / 15 hours = 126 seconds. At the 63 seconds it needs, the moon has already travelled half its own width. The full moon records as a short bright streak in about a minute, in a frame that is otherwise empty, and there is no exposure that gives you both the disc and the land.

One correction this ignores. At 0.074 lux the paper is deep in low-intensity reciprocity failure, for which no manufacturer publishes a correction. So 63 seconds is a lower bound, and the real figure is longer — which makes the streak longer too, and the argument stronger rather than weaker. Treat the number as “of the order of a minute or two”, and go and find out.

🧮DO THE MATHS: why no star will ever appear on your paper

The star’s illuminance. Take a bright star of visual magnitude 0. It is 26.74 magnitudes fainter than the Sun, a factor of 10^26.74/2.5 = 5.0 × 10¹⁰, so it delivers 100,000 / 5.0 × 10¹⁰ = 2.0 × 10⁻⁶ lux at the pinhole.

A point source is not an extended source, and the arithmetic is different — and simpler. All the star’s light that gets in passes through the hole, an area π(d/2)², and lands in the blur circle, which for a distant subject has the same diameter d, because the geometric image of a point is just the shadow of the hole. The two areas are equal, so they cancel: the illuminance in the star’s image on the paper is the same 2.0 × 10⁻⁶ lux the star delivers to the front of the camera. That is a pleasing result and it makes the rest easy. It is also optimistic, because diffraction spreads the spot wider than d — at f/200 the diffraction blur is 2.44 λ N = 0.27 mm, comparable with the hole itself — so the real image illuminance is lower by a factor of a few and every number below is a best case.

Time required. At the 4.65 lux·s the paper needs, t = 4.65 / 2.0 × 10⁻⁶ = 2.3 × 10⁶ s = 27 days of continuous exposure on one spot.

And it will not stay on the spot. The sky turns at 15 arcseconds per second, which at f = 50 mm moves the image at 3.6 × 10⁻³ mm/s. Crossing its own 0.25 mm image takes 69 seconds. So each clear night contributes 69 seconds of dwell to any one patch, and you would need 2.3 × 10⁶ / 69 ≈ 33,000 clear nights, which is about 90 years of them.

Then make it worse. All of that ignores reciprocity failure at 2 × 10⁻⁶ lux, which is six orders of magnitude below where anybody publishes a correction and where the practical answer is that no stable development centres form at all. The honest conclusion is not “90 years” but “never”, and the 90 years is how you know.

What this does not say. It does not say stars are unphotographable. It says they are unphotographable at f/200 on ISO 3 paper. A lens at f/2 is 10,000 times faster than f/200, and ISO 3200 film is another ten stops beyond paper; multiply those and the same star arrives inside a few minutes. The pinhole’s f-number is the whole of the difficulty, which is worth saying because it locates the problem in the instrument rather than in the sky.

What arrives, on one logarithmic scale, against what the paper needs

1. 1Sun’s disc at f/200 — about 29,000 lux at the film — what a solargraph records; needs about 160 s of dwell to print out
2. 2Sunlit white wall — about 0.5 lux — the daylight case; correctly exposed in tens of seconds
3. 3Full moon’s disc — 0.074 lux — three stops under the wall, because it is a sunlit surface; 63 s
4. 4Magnitude-0 star — 0.000002 lux — nine decades below the sun’s disc; 27 days of dwell
5. 5The half-hour threshold — 0.0026 lux — left of this line, nothing is photographable in one session

Computed from the two NASA magnitudes, the cited 100,000 lux figure and the image-plane exposure derived in section 4. Bars are placed by calculation, not measured. Each division is one decade, so the distance from the moon to the star is nine of them.

4. Where the 4.65 lux·s comes from

Two of the arguments above lean on a single number — the exposure a paper negative needs at the image plane — so here is where it comes from, in three lines, because a number you cannot derive is a number you should not use.

For an extended subject of reflectance ρ under illuminance E, the luminance is ρE/π and the illuminance in its image is πL/(4N²) = ρE/(4N²). Multiply that by the correct exposure time t = N²C/(E**S) and everything except three constants cancels:

H = E_image · t = ρ C / (4 S)

Image-plane exposure a material needs, from the incident constant

With ρ = 0.18, the conventional mid-grey reflectance, C = 310 and S = 3, that is 4.65 lux·s. The same relation at S = 400 gives 0.035 lux·s for ISO 400 film.

What this is and is not. It is Part VI’s derived constant rearranged, and it inherits everything uncertain about that constant. The 0.18 is a convention about what an incident reading means, not a measurement of anything. So treat 4.65 lux·s as good to a factor of two, which is entirely sufficient for arguments whose answers differ by nine orders of magnitude, and entirely insufficient for anything finer.

5. Planning the twilight sequence

The twilight route is the one that produces a picture in an evening, and it is a race: the light falls faster than you can process, and every exposure sits in a different light from the one you metered.

The order of operations for a falling-light sequence

1. 1Arrive in daylightPlace the camera, level it, frame it and log the framing while you can still see. Everything after this is done in the dark on a camera you have already aimed.
2. 2Meter, and keep meteringA reading before and after every exposure. Two timestamps per sheet. The rate of fall is as useful as the values.
3. 3Compute forward, not backwardThe light at the middle of the exposure is what matters, so predict it from the fall rate rather than using the reading you took at the start.
4. 4Choose the hole, not the timeThe session has a fixed length. Bracket by fitting a different plate, which changes N² and leaves the duration where you can afford it.
5. 5Log the exponent and its sourceWhich material, which sheet, which P, and the band you are carrying. This field is what makes the negative diagnosable three weeks later.
6. 6Leave at the time you setWritten down before you left home, and not renegotiated in the dark.

The third step is the one people skip. During a twenty-minute exposure at dusk the light can fall by more than a stop, so the exposure you compute from the opening reading is systematically too short.

The lamp-colour problem, stated honestly. Blue-sensitive paper responds to what a light source emits in the blue, and street lamps differ enormously in that respect: a low-pressure sodium lamp is close to monochromatic yellow, a metal-halide lamp is broad, and modern white LEDs have a strong blue peak. A photopic lux meter weights all three by the eye’s response, not by the paper’s, so a lux reading under sodium light overstates what paper can use and a reading under white LED probably understates it.

This course has no published effective-speed figure for paper under any named lamp type, and it will not invent one. What it has is the direction of each error and the instruction that follows: under sodium, bracket wider and expect to need more than the computed time; under white LED, expect to need less. Record the lamp type in the log as an observation, and after a season of them you will have the correction nobody publishes.

6. The solargraph: a picture made of days

A solargraph is a pinhole camera loaded with ordinary photographic paper, sealed, pointed at the sky and left for weeks or months. It is never developed. The image is a printing-out image, formed by light alone, and it is read by scanning the paper and inverting the scan.

Part I’s unfixed silver photogram owns the chemistry completely and it is not repeated here. Three of its conclusions are the ones this page uses.

Light does the whole job, badly. With no developer to amplify anything, the silver specks have to grow until they are big enough to see, which takes something like a million times the exposure a developed image needs. That factor is the whole reason a solargraph takes months.

The image has a ceiling. A developing-out paper contains an excess of halide and no free silver, so the liberated halogen has nowhere good to go and re-oxidises the photolytic silver. Photolysis and its back-reaction fight to a standstill, which is why a solargraph is a pale violet or brown trace rather than a rich black one, and why leaving it for two years does not give twice the image of one year.

Fixing it would destroy it. Part I quotes the Getty atlas: printing-out papers require deliberate overprinting because the image intensity falls during processing. A solargraph’s density is partly photolytic silver so finely divided that the fixer attacks it, and partly the darkening of the halide crystals themselves, which the fixer dissolves outright. A fixed solargraph is a blank sheet with a faint stain, and this is not a warning about a risk; it is a statement about what would certainly happen.

🧮DO THE MATHS: how many clear days before the sun's arc appears?

The camera. A 330 mL drinks can, internal diameter about 66 mm, with a 0.3 mm hole in its side and the paper lining the opposite wall. The axial focal distance is the can’s diameter, so N = 66/0.3 = f/220.

The brightest thing there is. NASA give the Sun’s apparent diameter at 1 A.U. as 1919 seconds of arc, or 0.533°, so its solid angle is 6.80 × 10⁻⁵ sr and its luminance is 100,000 / 6.80 × 10⁻⁵ = 1.47 × 10⁹ cd/m². Its image illuminance at f/220 is πL/(4N²) = π × 1.47 × 10⁹ / 193,600 = 23,900 lux.

What print-out needs. A million times the 4.65 lux·s a developed image needs, so about 4.65 × 10⁶ lux·s.

t = 4.65 × 10⁶ / 23,900 = 195 seconds of the sun sitting on that patch of paper.

How much sun a patch gets per day. The sun crosses its own diameter in 0.533/15 hours = 128 seconds. So one cloudless day deposits about 128 seconds on each point of the arc.

The prediction: about one and a half cloudless days for the faintest visible arc, and the months that follow are building density and, more importantly, sweeping the arc across the paper as the declination changes. That is why the exposure has to be long: not because the sun is dim, but because you are waiting for the seasons.

Two things this estimate is not. The factor of a million is an order of magnitude from Part I, not a measurement, so the 195 seconds is good to a factor of a few. And the can’s geometry is not the concentric cylinder Part VI analysed — the paper lies on a circle through the pinhole, so the distance from hole to paper varies across the sheet, and only the axial point is at 66 mm. Expect the arcs to be sharper and brighter near the middle and to spread near the edges, and treat that as a prediction to check rather than a defect.

A drinks-can solargraph in section, and what its finished sheet shows

1. 1Pinhole in shim, taped over the can wall — made and measured by the Part VI method; tape removed to start, replaced to end
2. 2Paper wrapped emulsion inwards — lies on a circle through the hole; axial distance = the can’s internal diameter
3. 3Every joint sealed; label outside — name, contact, collection date — the condition of leaving it anywhere
4. 4One arc per sunny day — highest at the June solstice, lowest in December; 46.9° between them
5. 5Gaps are cloud — the sheet is a weather record as much as a sun-path diagram

Solstice elevations computed for latitude 51.5° N from the NOAA zenith relation with the hour angle at zero, which reduces to elevation = 90° − latitude + declination, and NASA's obliquity of 23.44°. The drawing is schematic; nothing in it is traced from a solargraph.

📓What this course can and cannot tell you about solargraphy's history

The previsualisation lesson has already set out what the course can support about where solargraphy came from, and it is less than the internet believes: the attribution of the practice to a Solaris project around the year 2000 could not be traced to a primary source this course has read, and it is flagged there rather than repeated here as fact.

So this page makes no historical claim at all. What it makes is a chemical claim, which comes from Part I and from Ware’s account of print-out silver, and a photometric prediction, which comes from two NASA fact sheets and one cited illuminance figure. Typical exposure durations quoted in the solargraphy literature — the familiar “six months, solstice to solstice” — are not something the course has verified from a source that meets its standard, which is why this assignment tells you to start two cameras and open one of them early rather than telling you how long to wait.

7. Write the predictions, then fold the sheet

For the night sequence: the metered light with two timestamps per sheet, the computed metered time, the exponent and its source, the corrected time and its uncertainty band, the plate fitted, and one sentence saying what you expect to record and what you expect to be missing.

For the solargraph: the start date, the intended retrieval date, the compass bearing and elevation the can points at, the predicted number of clear days before the first arc, and a sketch of where you expect the solstice arcs to fall on the sheet. Fold it, and keep it with the log for six months.

The making

Stage 1 — Build and site the two solargraphs (60 minutes)

Paint or tape the inside of each can matt black. Pierce and mount a pinhole by the Part VI method and measure it, because the f-number in your prediction depends on it. In the dark, or in a changing bag, wrap a sheet of RC paper emulsion inwards around the inside of the can opposite the hole. Seal every joint with waterproof tape, cover the pinhole with a tab of tape, and fix the label.

Site them pointing at the part of the sky the sun crosses — south, in the northern hemisphere — tilted up enough to include the highest summer arc. Ask permission for the place you attach each one. Remove the tape from the pinhole, and write the time down. Then set a calendar reminder, because nobody remembers in March what they left on a fence in September.

Stage 2 — The twilight sequence (75 minutes)

Arrive an hour before sunset. Frame and level in daylight. Then expose four to six paper sheets as the light falls, metering before and after each, changing the plate rather than the duration when the computed time runs past what the session allows. Keep the exposures continuous rather than leaving gaps: the sequence is the data.

Stage 3 — The full-dark exposure on film (45 minutes)

One or two sheets of film, at the corrected time, with the exponent and its band written down first. This is the exposure you will not be able to repeat, so log everything before you start it and stay with the camera.

Stage 4 — Process the night sheets (40 minutes)

Paper by the usual method. Film by the processing lesson’s route.

Two notes about keeping. Kodak’s instruction for TRI-X is to process exposed film as soon as possible after exposure, and HARMAN say the same of their direct positive paper, using the term latent image regression for the decay. Part IV owns the mechanism. On a night session, the sheet exposed first may wait three hours before it reaches the developer, so log the time between exposure and processing — it is a variable you have introduced whether or not you meant to.

One development decision. ILFORD state that contrast is increased with long exposures and that pulling development may be required. Kodak give the numbers for TRI-X: 10, 20 and 30 per cent less development at 1, 10 and 100 metered seconds. At a metered fifty minutes you are far past the end of that table; extrapolating it is a decision, and the log should say you made it.

Stage 5 — Read, then unfold (20 minutes)

Rank the night negatives, reconcile against the predictions, and put the folded solargraph prediction somewhere you will find it in six months.

Stage 6 — Retrieve and scan a solargraph (later; 20 minutes)

Open the first can after about six weeks, in subdued light and never in sun. Scan the paper immediately, face down on the platen, with the lid closed. Invert the scan. Then put the paper in a light-tight envelope, because the image continues to fade in room light exactly as Part I’s twin sheets did — it is the same experiment, run for longer.

Expected observations

On the twilight sheets. A sequence in which the sky holds up longer than the land, because the sky is the source. Lamps, once lit, as blown white discs with visible flare. The land emptying from the bottom of the frame upwards as the session goes on.

On the full-dark film sheet. Lit windows, lamps and their pools; traffic as continuous trails rather than as vehicles; and large areas of nothing at all. A negative with a very long tonal range and almost nothing in its middle.

On the moon, if it is in frame. A streak rather than a disc, unless the exposure was under about a minute, in which case there will be a disc and nothing else on the sheet.

On the solargraph, after six weeks. A pale violet or brown ground with a handful of bright arcs across it, broken wherever cloud passed. Very little of the landscape. The arcs sharper near the centre of the sheet than near its edges, for the geometric reason section 6 gives.

Evaluation and reconciliation

1. How far out was the corrected exposure? State the discrepancy in stops, and say whether it lies inside the uncertainty band you wrote down before exposing. A result inside your own stated band is a success even if the negative is poor.
2. Back out an exponent. From the time that actually worked and the time you metered, compute P = log(T_actual)/log(T_metered). Compare with the published figure. One sheet gives one very uncertain estimate; the portfolio review collects them.
3. Which light sources recorded, and which did not? List them with the lamp type beside each, and see whether the sodium-versus-LED prediction of section 5 holds up in the direction predicted.
4. How far did the light fall during the session? From your paired readings, in stops per ten minutes. Then say which sheet that explains.
5. Read the solargraph as data. Count the arcs and compare with the number of sunny days in the period; measure the highest and lowest arcs against the predicted solstice elevations; and say what the gaps tell you about the weather.

The critique

One paragraph per submitted picture, naming causes. The intention as written; which optical or photometric fact produced the look; whether the exposure landed and by how much; whether the correction was the dominant term and how confident you are in it; what recorded and what was simply absent; and the one change you would make.

Then the question this page adds, and it is the one the brief’s own framing raises: is your night negative a document of a place, or a fiction assembled from an hour of light? A four-minute exposure shows a street nobody ever saw: the cars are gone, the pedestrians are gone, the lamps are far brighter relative to everything else than they look. Argue your own answer in three sentences rather than reaching for a phrase. The course does not have a position on this, and neither should your critique pretend to have settled it.

Troubleshooting

What you see	Most likely cause	What to check, and what to change
Night negative almost blank	The exposure was inside the region where paper simply cannot reach	Check the illuminance against the section 1 table; the fix is film or twilight, not more time
Negative thin by two or three stops	The exponent is too mild for this material, or the light fell during the exposure	Back out the exponent; compare with the two-timestamp readings
Lamps blown out, everything else empty	Correct exposure for a scene whose range exceeds the paper’s	Not a fault. Compose for it, or move to film
Moon a streak when a disc was wanted	The exposure exceeded about a minute	126 s is the moon’s own diameter in time; there is no other fix
Solargraph blank after months	The pinhole tape was never removed, or the can leaked and fogged uniformly	Check the tape tab; check the seams; a fogged sheet is dark everywhere, an unopened one is clear everywhere
Solargraph arcs present but the sheet is very dark overall	Light leak, or the can was opened in bright light before scanning	Open in subdued light; check every seam and the lid
The solargraph image faded between scanning and showing it	Room light continuing the exposure, exactly as Part I predicts	Scan immediately, store in a light-tight envelope, and show the scan

Clean-up, storage and disposal considerations

Used fixer and the first change of wash water are silver-bearing and are collected. Developer and stop carry no silver. Check your local regulations, which govern where the collected container goes and differ between authorities.

The solargraph’s paper is stored in a light-tight envelope, labelled with its start and end dates and its site. It is not fixed, so it is not stable, and its permanent form is the scan. Retrieve every camera you sited. A can left on a fence for two years is litter with your name on it.

What to submit

• One night negative and working positive, with its full log entry including the exponent, its source and the band you carried.
• The twilight sequence, as evidence, with the paired light readings.
• One solargraph scan, with the start and end dates, the site, the bearing and the measured pinhole diameter.
• The folded prediction sheets, unfolded, with observations beside predictions.
• Your backed-out exponent for the material you used, with its uncertainty.
• A critique paragraph for the night picture, including the document-or-fiction answer.

Further work

The exponent series. Six exposures of the same static night scene, at metered times spanning two decades, each corrected with the published exponent, and each judged. Plotting actual against metered on log-log axes and fitting a slope gives your exponent for your material — the measurement Part VI said the log would eventually supply, and the one the portfolio review will ask for.

The second solargraph, opened at the solstice. You sited two. Leave the second until the sun has reached its extreme and compare the two sheets: the difference between them is a season, recorded by a beer can.

The lamp-type test. One paper sheet exposed under a sodium lamp and one under a white LED lamp, at the same metered lux and the same computed time. The difference in density is the effective-speed shift this page could not give you a number for. Two sheets and one evening buys you a figure that is not in any manufacturer’s literature, and it is a genuine, if small, piece of research.