The book as a folded sheet

Beside Page One

Open a hand-press book to page one. On the very same side of the very same sheet, printed upside down and a few page-widths away, is the last page of the gathering. Nobody chose to put it there. The fold did, and the fold decided everything else too.

A printed book before about 1820 is not made of pages. It is made of sheets, each folded down into a little booklet called a gathering, and the gatherings sewn in sequence. The reader meets the pages in order, 1, 2, 3. The printer never did. To print page 1 and page 16 on the same pass of the press, the compositor had to lock them into the metal frame side by side, one of them inverted, with fourteen pages of nothing between them in reading order but nothing at all between them on the sheet.

The arrangement looks arbitrary. It is the opposite of arbitrary. There is exactly one way to lay the pages out so that folding the printed sheet brings them into reading order, and it falls out of the geometry of folding the way a shadow falls out of a shape. This page carries a small model that knows how paper folds and knows nothing about printing. Everything below is read off it, live.

Nothing in the model above knows a single imposition scheme. It folds a blank unit square with three operations, fold left-half onto right, fold top onto bottom, quarter-turn, and then reads which numbered leaf lands where. The page numbers, the inversions, the chain-line direction and the watermark's corner are all consequences. The same 210-line model is what the verifier checks, and it is served to your browser as fold.mjs beside this page.

Forward: the printer's problem

Fold a sheet in half once and you have a folio: two leaves, four pages. There is no real choice to make. Page 1 and page 4 go on one side, pages 2 and 3 on the other, and because a single fold turns nothing over, no page is upside down. The interesting thing begins at the second fold.

Fold again, into a quarto, and now half of every forme is inverted. This is forced, not stylistic: the second fold turns the upper half of the sheet over onto the lower, so whatever was printed up there has to have been printed head-downward for it to read the right way up in the bound book. Fold a third time into an octavo and the count doubles again: eight of the sixteen pages on the sheet are upside down relative to the other eight. Set the instrument to each format and watch the ticks flip.

The pages that share a side of the sheet are not random either. They obey one arithmetic rule that every printer's manual states and the model reproduces without being told it: the outer forme, the side that carries page 1, carries exactly the pages whose numbers are one-more or zero-more than a multiple of four. In octavo that is 1, 4, 5, 8, 9, 12, 13, 16. The inner forme takes the rest. That is why, if you tear a leaf from an old octavo, the page numbers on its two sides differ by a fixed amount that tells you how deep in the gathering it sat.

One more consequence, visible on any shelf of old books. Because hand-press sheets were not cut in the ratio 1 to root 2, halving does not preserve the shape, so the leaf proportion alternates. The model computes 1.60 for a folio, 1.25 for a quarto, 1.60 again for an octavo, 1.25 for a sixteenmo. Folio and octavo are the upright ones; quarto is the squarer one, which is exactly how Carter's ABC for Book Collectors describes it, "essentially squarish in shape".¹³ A quarto looks squat next to an octavo not by anyone's design but because two folds and three folds land on opposite sides of the same alternation.

Four printers' manuals from four different centuries print these grids, and the model matches them cell for cell, page numbers and inversions alike, for all four of folio, quarto, octavo and 16mo. The manuals are Moxon (1683), Smith (1755), Cowie (1830) and De Vinne (1904); the transcriptions and the search across the model's foldings are in research/beside-page-one/attested.mjs and match.mjs. Reading forme diagrams from three centuries and seeing your own model come out of them, exactly, is the closest thing to a handshake this project offers.

A note on the exact picture. The set of pages on a forme is fixed by the geometry, but their spatial arrangement and which specific ones are inverted depend on the folder's habit, which half is lifted at each fold. Every one of the 2^k lifting choices produces a legal gathering; they differ only by mirror and rotation, and hand-press shops genuinely used more than one. The instrument shows one consistent choice. What never varies is the set, the count of inversions, and the forensic signature below.

Backward: the bibliographer's problem

Here is the quiet turn. Reverse the arrow and the very same fold model answers a different profession's question. A bibliographer is handed a leaf and must say what format it came from, and the trap is that size will not tell you. A book's format is not how big it is; it is how many times its sheet was folded, and a large sheet folded three times can end up the same height as a small sheet folded twice. Cataloguers get this wrong constantly, calling any tall book a folio.¹ The evidence that does not lie is physical, and it is the same fold, read in reverse.

The chain lines. European paper was made on a wire mould whose thick chain wires, spaced roughly an inch apart, left translucent stripes in the finished sheet. On the full sheet those stripes run in one fixed direction. Each fold turns the sheet ninety degrees before the next, so the chain lines in the final leaf run one way after an odd number of folds and the other way after an even number. Vertical in a folio, horizontal in a quarto, vertical again in an octavo, horizontal in a sixteenmo.² The model computes this from the fold sequence alone; the instrument's leaf shows it. Hold a real octavo to a lamp and the chain lines stand vertical, just as it says.

The watermark. The papermaker sewed a wire device into the middle of one half of the mould, so the watermark sits at the centre of one half of the full sheet. Follow that fixed point through the folds and it migrates to a different, predictable home in each format. This is the check that most surprised us, because it is exact. McKerrow, in 1928, says the watermark goes to "the middle of a leaf" in a folio, to "the centre of the inner margins of the leaves" in a quarto, and "upright at the top of the inner margin" in an octavo. Ask the model where a point at the centre of half the sheet ends up, and it answers, in leaf coordinates where 0 is the spine edge and 1 the head: (0.5, 0.5), then (0, 0.5), then (0, 1). Dead centre; the middle of the spine edge; the top of the spine edge. Three sentences of prose from a bibliography manual and three exact coordinates out of a fold, and they are the same three places.³

Where the model breaks: twelve is not a power of two

Every format so far came from halving: fold once for two leaves, twice for four, three times for eight. The leaf count is always a power of two, because that is what repeated halving gives you. So how did printers make a duodecimo, a twelve-leaf gathering, when twelve is not a power of two and no sequence of folds in half will ever reach it?

They cheated the geometry, on purpose, with a knife. The sheet is divided into thirds. One outer third is cut away and folded separately into a little four-leaf quire, and that quire is slid into the middle of the eight leaves the other two thirds make. Twelve leaves, twenty-four pages, one sheet, one cut.

The trade had two words for the same piece of paper, one for each end of the shop. William Savage's Dictionary of the Art of Printing (1841) gives both:⁴

OFFCUT. That part of a sheet which, when printed, cuts off, and when folded is inserted in the middle of the other part, which together form a regular and orderly succession of all the pages in the signature.

INSET. The same as offcut: with printers it is called an offcut; when the work comes into the hands of the bookbinder, and the sheets are folded, it then becomes an inset, being inserted in the middle of the sheet, to complete the regular succession of pages.

The same object, named twice: an offcut to the man who removes it, an inset to the man who puts it back. John Southward's Practical Printing (1884) explains why it cannot be avoided: fold the sheet without cutting and "the pages cannot be got to follow in their proper numerical order" unless that third "are cut off and folded in 'quire wise'".⁵

Does the model reach it?

The fold model had two operations. Adding one more, a cut (an edge across which nothing is ever joined again), plus an inset that slides one quire into the middle of another, is enough. Nothing else was told to it. What comes out, and every line of this is recomputed by the verifier, is a gathering of twelve leaves whose conjugate pairs are 1.12, 2.11, 3.10, 4.9, 5.8, 6.7; whose offcut third carries pages 9 to 16, that is leaves 5 to 8, exactly the middle four; whose side carrying page 1 carries 1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, 24; and whose leaf comes out tall and narrow, at a proportion of 1.67 against the octavo's 1.60.

Those numbers can be checked against a real published diagram. Gaskell's figure 55, "Sheet of common duodecimo, or twelves", gives the same forme set and puts the offcut on the same four leaves.⁶ Two honest qualifications. The arrangement within each third differs from Gaskell's by a cyclic shift, because the direction of each fold is the folder's habit and not forced, the same freedom the instrument's note above describes. And duodecimo had genuinely many schemes: Savage numbers 133 impositions and lists several for twelves alone, including one "to fold without cutting" that he traces through Luckombe, Stower, Johnson and Hansard but which appears in neither Moxon (1683) nor Smith (1755).⁴ The model reproduces the common one.

The reward is that the forensic reading survives the cut. Because the quarter turn that stands a duodecimo leaf upright leaves its pages lying across the sheet rather than up it, the chain lines come out horizontal in a twelvemo, which is what the Rare Book School's own teaching sheet says to look for.⁷ The model was not told that. It folded, cut, and tucked, and the horizontal lines fell out.

The fold reached into the words

Everything so far has been geometry. Here is where the geometry stops being only geometry.

To set an octavo forme, the compositor needs pages 1, 4, 5, 8, 9, 12, 13 and 16 standing in type at once. Page 9 has to be set before page 2 exists. But you cannot know where page 9 begins until you know exactly how much text filled pages 1 through 8. So before a single letter was set, somebody had to read the manuscript and mark it up: this much copy becomes page one, this much page two, all the way through. The trade called it casting off copy, and John Smith's Printer's Grammar (1755) devotes a section to it that opens without enthusiasm: "To cast off Manuscript, is unpleasant and troublesome work, which requires great attention; and therefore ought not to be hurried".⁸

It was a genuine estimate, done by counting. Smith describes setting one line in the composing stick, seeing how much manuscript it swallowed, and then counting the copy off in that ratio: "if 2 lines of Copy make 3 lines in print; then 4 make 6; 6 make 9; 8 make 12". Estimates drift. And here is the sentence that matters, because it is a printer in 1755 describing the escape hatch:⁸

the Compositor takes notice how his Matter runs; and if he finds that it keeps not even with the Copy, he drives either out, or gets in, where he conveniently can

Driving out is making the text take more room. Getting in is making it take less. The compositor had no authority over the words, so he reached for everything short of them: wider spacing, an extra blank line, a longer or shorter spelling of the same word, an abbreviated speech prefix, a dropped full stop. The fold set a target, and the target was hit with orthography.

You can see it happening. The Digital Renaissance Editions text of Chapman's An Humorous Day's Mirth (Q1599) goes through the quarto forme by forme looking for exactly this, and finds both directions on adjacent pages: on one, "Laberuele" shortened to "La.", an ampersand, the shorter spelling "therfore", "women" squeezed to "womẽ" with a tilde, and lines left without final punctuation. On another, extra spaces inserted between words and three blank lines added. The editors read the pattern as "adjustments being made to fit text into the pages unset between already composed formes".⁹

And when the estimate failed at the scale of a whole play, it left a monument. In the Shakespeare First Folio, Timon of Athens occupies a space that had been cast off for a longer play, Troilus and Cressida. Two pages were left with no play on them. One of them was filled with a list of characters. Only seven of the Folio's thirty-six plays carry such a list, and they are the plays where a casting-off mismatch or some other accident left the room.¹⁰ The descriptions in those lists, "Caliban, a saluage and deformed slaue", have been read for centuries as authorial characterisation. They exist because a sheet of paper had a size.