Collation Formulae - Bibliographica

Bibliographica

SECTION III: COLLATION FORMULAE

Let us suppose that a single line of type could be handed to a stranger on the other side of the world, without supplying photographs, measurements, or the book itself, and from that line alone the entire physical skeleton of a copy could be rebuilt: how many sheets, folded how many times, gathered into how many bundles, in what order, with which leaves inserted or cut away. That line indeed exists. It is the collation formula. A photograph shows one copy's surface; the formula encodes the structure that every sound copy of an edition must share. It is austere, it is compact, and it is the language in which bibliographers actually talk to one another about the anatomy of a book.

The reason it can be so short is that a book is deeply repetitive. This was proved already: fold a sheet and the second half is forced by the first; sign a little over half a gathering and the rest is implied. A structure that repetitive does not need description leaf by leaf. It needs a rule and a count, and that is all the formula is, a rule and a count, written in a notation refined over a century, chiefly through Greg, McKerrow, Bowers, and Gaskell, into something a beginner can learn in an afternoon and a master can argue with for a lifetime.

What it fuses together

The formula welds together the three things already in hand. From Section I it takes the format, the fold, which sits at the very front. From the nesting discussion it takes the gathering, the sewn bundle. From Section II it takes the signature, the letter that names each bundle. One prefix, then a series of terms, each term naming a run of gatherings and how many leaves they contain. Nothing more, until the exceptions arrive, and the exceptions are where the interest lives.

The prefix: format

A formula opens by stating the format, the fold legible from the chain lines and watermark: 2° for folio, 4° for quarto, 8° for octavo, 12° for duodecimo, and so on down to the tiny formats. A colon follows, and then the body begins. So every formula starts life as '8°: ...', meaning 'this is an octavo, and here is how its octavo sheets were gathered'. The prefix reports not the bundle, but the fold. The two are given separate numbers precisely because they answer separate questions, and conflating them is the single commonest error.

The basic term: a letter and a superscript

The heart of the notation is one gathering written as a signature letter carrying a raised number: A⁸. It reads aloud as 'gathering A, of eight leaves'. The letter is the signature the printer set at the foot of the page, marching through the old twenty-three-letter alphabet with no J, no U, no W as we touched upon earlier. The superscript is a count of leaves, not pages, not sheets. This is the rule to write down and not forget: the raised number is always leaves. An A⁸ is eight leaves, therefore sixteen pages, and in a plain octavo it is also one sheet folded three times. A quarto gathering of one sheet is A⁴, four leaves, eight pages. Where a binder nested two quarto sheets, that same quarto is written A⁸, eight leaves from two four-leaf sheets, and the little 8 gives the size of the bundle while the 4° prefix still gives the fold. Same superscript, entirely different meaning from the octavo's 8, and only the prefix disambiguates them.

Ranges, and the alphabet that limps

Books have plenty of gatherings, and writing A⁸, B⁸, C⁸ down to the end would defeat the purpose. Henceforth a run of same-sized gatherings collapses into a range with an en dash: A–M⁸ means every gathering from A through M is eight leaves. Counting how many gatherings that is must be done in the printer's alphabet, not the modern one. A to M looks like thirteen letters but is twelve, because J does not exist in the sequence. This is the sort of quiet trap that separates the careful from the confident, and since the count is not a modern spreadsheet where the letters behave, one counts through A B C D E F G H I K L M and arrives, correctly, at twelve.

When a book outruns the twenty-three letters, the alphabet doubles. After Z the printer begins again with doubled sorts, Aa Bb Cc, which we will regularise as 2A, 2B, 2C so that a long book reads as A–Z⁸ 2A–2K⁸ rather than as a forest of lowercase pairs. A third pass becomes 3A, and so on. Both the doubled-letter and the numeral-prefixed styles appear in the wild, and they mean the same thing.

The mixed formula, and the short tail

Now an example, 8°: A–M⁸ N⁴. The prefix says octavo. The first term says gatherings A through M, twelve of them, are each eight leaves. The second term says gathering N, the thirteenth, is only four leaves. That short final gathering is one of the most ordinary things in bibliography, because a text almost never ends exactly on a gathering boundary. The printer sets the last of the full octavo sheets, finds a few pages left over, and finishes with a half-sheet of four leaves rather than waste a whole sheet. The formula records this honestly: a long clean run, then a stubby tail. An irregular final term is usually nothing more sinister than the arithmetic of a text that would not divide evenly, and that is a reassuring fact rather than a mysterious one.

Reading the book out of the line

Because the superscripts are leaves, the formula also assumes the role of a calculator. Taking 8°: A–M⁸ N⁴ for instance, twelve gatherings of eight leaves is ninety-six leaves; one gathering of four is four more; total one hundred leaves, therefore two hundred pages, therefore the text runs to page numbers somewhere near two hundred if it is paginated straight through. The extent of the book has just been derived from its skeleton, and a copy that then stops at page 140 has a defect: leaves might be missing, or the pagination is eccentric, or the description offered for sale is a lie. This is the everyday power of the thing. The formula is a prediction, and a real copy either confirms it or gives itself away against it.

Format genuinely reshapes the line, and this is easiest to feel by watching it move. The panel takes a text of fixed length and refolds it. Two things repay attention at once: the gatherings on the sewn spine, and the formula underneath rewriting itself as the fold changes. The sewn bundles stay the same total length however the sheet is folded, because the paper is the same paper; the fold only decides whether that length is cut into a few fat gatherings or many thin ones. And the alphabet underneath fills up faster for the thinner gatherings, which is why a quarto of any heft is pushed into the doubled sorts, the 2A, long before an octavo of the same text.

The unsigned, and the Greek letters

Everything so far assumed each gathering carries a signature. Much of a book does not. The front matter, the title leaf and dedication and preface and table of contents, was usually set and printed last, once the printer finally knew the book's length and could cast off the preliminaries to fit. Printed last and meant to sit first, this matter is often signed with whatever the printer had spare, or not signed at all. A notation built only on A, B, C would have no way to name a gathering that carries no letter, and a thing that cannot be named cannot be described. Thus the notation borrows from Greek. The letter π (pi, for 'preliminary') stands for unsigned leaves at the front of the book. A block of four unsigned preliminary leaves is π⁴, and a lone unsigned title leaf is π1. The letter χ (chi) does the same job for unsigned leaves that turn up somewhere in the middle rather than at the front, an inserted plate or an extra leaf with no signature of its own; χ marks it as an unsigned interpolation so that its position is recorded even though the printer left it mute. When a whole unsigned gathering repeats, or an unsigned leaf attaches to a signed one, the same superscript and small-number conventions carry over, so 2π and χ² read exactly as one would now guess. The Greek letters are, in short, the names given to the leaves the printer forgot to name, and their whole purpose is precision about silence.

The literal marks, transcribed as found

There is a second, blunter habit not to be confused with the Greek. Printers frequently did sign the preliminaries, but with typographic ornaments rather than letters: the asterisk, the dagger †, the double dagger ‡, the section mark §, the paragraph mark or pilcrow ¶. Where a printer signs the prelims with daggers, we ought to transcribe the daggers, literally, as they stand, because the formula's deepest loyalty is to what is actually printed on the leaf. So a book might open §⁴ †² and then run into A–Z⁸, and each symbol there is not a bibliographer's abstraction but a faithful copy of the mark the compositor set. The governing rule of the whole enterprise: use π and χ for leaves that carry no signature, and reproduce the actual symbol for leaves that carry an ornamental one. Nothing is invented that the page did not print.

The dollar and a few refinements

The dollar sign $ is a variable meaning 'the typical gathering'. Writing that a book signs $1 through $3 says 'in the ordinary gathering, the first three leaves are signed', without pretending this holds identically, letter for letter, through every last quire. It exists precisely because printers were regular enough to generalise about yet never regular enough to trust blindly, so an algebraic 'any gathering one likes' was needed to describe the pattern while leaving room for the lapses.

The refinements from here are mostly plus and minus. A leaf added to a gathering is a plus, a leaf removed is a minus, and a cancel, that surgical replacement leaf that will be touched upon later on, is written as a minus-then-plus on the same spot, A⁸(±A3), read as 'gathering A of eight leaves, with A3 cancelled and reset'. None of this needs commanding for now. It is enough to see that the formula has a grammar: a prefix for the fold, terms for the gatherings, superscripts that always count leaves, Greek for the unsigned, literal symbols for the ornamentally signed, and plus-and-minus for the surgery. Once that grammar is held, an intimidating line like

8°: π⁴ A–Z⁸ 2A–2C⁸ χ²

simply reads itself out, and the book can be rebuilt in the mind's hand from the paper up.