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### II

If one of the purposes of bibliographical description is to provide an account of the physical makeup of books, a basic element in it must be an indication of the way in which the printed sheets were folded and in which the series of sheets (and partial sheets) constituting a book were gathered together. It is hard to see how any element in a description is more central than this report of the succession of gatherings, for it is the basic statement of the structure of a book. The nineteenth-century incunabulists came to recognize this point; but those persons who began in the 1880s to produce checklists of modern authors thought of their work simply as providing guides for the identification of first printings, and they saw no need to record details not known to vary and therefore presumably not necessary for identification.[34] Some bibliographers of modern books quickly outgrew this superficial approach. Thomas J. Wise, for example, was noting signatures in eighteenth- and nineteenth-century books by 1901;[35] and in the 1920s Strickland Gibson recommended signature collations as a standard part of descriptions of post-1800 books, except for the most curtailed entries.[36] But traces of the old view have lingered on and are still with us. There are some bibliographers, sophisticated in other respects, who believe that certain details, notably signature collations, can be dispensed with for most modern books. In taking such a position, they are surely not claiming that modern books are simpler and more regular than early books, for their experience must have shown them otherwise; the explanation must be that, in some respects at least, they are harking back to the outmoded notion of a bibliography as a list of points for identification. They cannot have given adequate thought to the nature of descriptive bibliography as historical

Once the importance of accounting for the structure of the gathered
sheets is understood, the next step is deciding how best to write that
account. A statement in words is one possibility: Michael Sadleir, for
example, in his Trollope bibliography (1928) used the form "A-N in
sixteens." But when the situation to be described is more complex and
irregular, the statement in words is likely to become correspondingly more
cumbersome. The urge to devise a concise and formulaic way to report the
matter is therefore an old one. Henry Bradshaw, for instance, in a letter of
1
March 1864 to J. W. Holtrop, says that he has "long had the habit of using
a
fraction to represent the number of leaves and form of a quire"—thus
representing a quarto book of five gatherings in eights as "abcde8/4" (the
fraction showing that each gathering is made up of two sheets).[37] By the end of the century a
somewhat different
basic formula —the one we still use—had become
standard. (One finds it in the early volumes of the Bibliographical Society's
*Transactions*, as in W. A. Copinger's "Incunabula Virgiliana"
in the
second volume, for 1893-94, pp. 123-226.) In this system a series of
regular
gatherings is noted inclusively, without specifying each one individually,
and
the number of leaves in each of those gatherings appears as a superscript
figure (e.g., "A-E8");[38]

That the system is indeed simple should be emphasized, for
unfortunately
it is all too often regarded by those unfamiliar with it as complex and
esoteric. The presence of two Greek letters, superscript figures, and plus
and
minus signs (for insertions and deletions) has led some people to think it is
mathematical; and the fact that Bowers devotes more than fifty pages of the
*Principles* (esp. pp. 196-254) to it has reinforced the view
that it is a
mystery requiring laborious study to comprehend. Bowers gives
considerable
space to the collation formula because his aim

To accept these basic elements, however, is not to suggest that various extensions of the system should not be open to debate and further refinement. There is always the temptation to continue expanding a system of shorthand notation so that it covers ever more situations, and one cannot complain so long as the additional notation is compatible with the old, is kept as simple as possible, and fulfills a clear need. But one must always weigh the benefits of the new notation against the disadvantages of increasing the store of symbols and operations that must be learned. At some point what is gained may not counterbalance the loss in accessibility that results. The process of adding to the formulary after Bowers's codification of it has not been very fruitful, though some notable bibliographers have tried their hand at it—especially two bibliographers

*Catalogue of Botanical Books in the Collection of Rachel McMasters Miller Hunt*, and Willem D. Margadant in his introduction to

*Early Bryological Literature*(1968). And Greg and Bowers themselves made some suggestions, particularly in regard to additions and deletions, that need to be reconsidered. Whatever symbols and devices one is finally persuaded to use in one's own practice, the process of evaluating proposed conventions can, as I hope to show, serve to clarify the basic rationale of the collational formula.

Insertions and deletions. Perhaps the principal element in the standard
formulary that requires some rethinking is the method for indicating
inserted
and deleted leaves. This element is of course a significant one, for such
irregularities in the structure of books occur with great frequency. The
move
from word to symbol for treating this matter lagged behind that for noting
the regular conjugate leaves. Bradshaw used the form "g (3 wanting)" to
show that the third leaf of the gathering signed "g" had been canceled; and
McKerrow some sixty years later was still employing the same system,
even
though the basic formula and the method of referring to a single leaf had
shifted—in the *Introduction* he cites
"A-G6 (G5 and G6
wanting)" as "the usual description" (p. 157).[44] It remained for Greg to substitute
plus and
minus signs for words in this system,[45] as
well as to make a start on the problem of how to refer
to insertions (since some are unsigned and others have anomalous signatures
of their own). Bowers built his discussion on Greg's suggestions but
provided much more detailed guidance for handling the great variety of
situations that could occur. His analysis (pp. 235-251) is the most fully
developed statement we have on insertions and deletions, and any further
thinking on the matter must begin with it.

The basic system is simple, and in its provision for cancellation it

Even the simplest unsigned insertions can be handled two ways in the standard system:[50]

A-B4 C4(C3 + 'C4' + 1) D4(D2 + 2) E4(E3 + e3.4) F4(F1 + * F2)

That this standard formulary is analogous in some respects to a language, providing alternative ways of making the same statement, is not necessarily a defect. One can only agree with Bowers when he says, "Although a rigid system for marking inserted leaves can be devised, the most sensible practice is to permit a certain latitude according to the circumstances and the special problem involved, always with the emphasis on securing clarity and simplicity. However, certain basic principles should hold" (p. 237). One would certainly not wish to have a system so rigid that it could not be stretched to fit unusual situations; such rigidity is obviously self-defeating. On the other hand, a symbolic or formulaic statement must be unambiguous if it is to accomplish its purpose, and definite conventions must be followed. The difficulty is in drawing the line between productive and unproductive kinds of variation. For example, the fact that both "(C3 + 'C4',χ1)" and "(C3 + 'C4' + 1)" mean the same thing does not in itself produce any ambiguity, so long as one knows the rules and is consistent in one's own practice.[55] But since the two denote precisely the same situation, one may wonder whether the existence of these alternative forms offers any positive advantage to offset the slightly increased complexity of the system that undeniably results. In the case of the equivalence of "(E3 + e3.1)" and "(E3 + e3.4)", there is further doubt because of the greater complexity of the rules necessary to eliminate the potential ambiguity. The difficulty here springs from the fact that numbers attached to signatures (such as "E3" or "e3.4") generally make some reference to the position of the leaves so designated, whereas the "1" in "e3.1", though attached to the "e" in the notation, draws its meaning from a separate usage, that of unattached numbers to indicate the total of inserted disjunct leaves (such as the "1" in C and the

This doubt is reinforced by a consideration of the use of single
quotation
marks in the formula. Their function seems easily enough stated: they are
used, in Bowers's words, "to enclose the signature of an insert
(*a*) to
indicate that the signature is anomalous in the gathering; (*b*)
to
distinguish a signed insert from a following unsigned insert with inferred
signature" (p. 459). Nevertheless, I think it is fair to say that determining
in
practice when to use them is the most problematical aspect of writing a
collational formula for many bibliographers and that interpreting the
absence
of quotation marks is often the most puzzling part of reading a formula.
Some of the potential difficulties can be observed in these examples drawn
from two formulas in Bowers's digest of the formulary (pp. 459-460):

The system is nonetheless workable as it stands, and I do not mean to suggest otherwise; I raise these points only in the hope that it can be made still simpler and clearer. What underlies these various complexities is the attempt to register within the collation formula the signatures of insertions and substitutions. That attempt introduces into the formula an approach that conflicts with one used elsewhere in the formula. The basic purpose of the formula, as ordinarily written, is to show the structure of a book and only incidentally to provide information about signing.[59] If the gatherings are signed, the clearest course is to use those signatures in the formula; but there is a limit to the amount of detail about signing that can be incorporated into the formula without making it unwieldy. Most bibliographers, following the standard system, do no more in treating the regular gatherings in the formula than to show which gatherings actually have signatures, reserving for an appended statement on signing a record of precisely which leaves are signed. Thus when one writes

*C*4 D—E8

This situation may invite misunderstanding; at the least it is awkward, reducing the elegance that one expects a formulaic statement to have. The issue is not whether certain information should be reported or concealed, but just how and where it should be reported. If the details of the signing of regular leaves are held for an appended record, should those of inserted leaves be similarly held? That bibliographers have not generally given this question an affirmative answer is a reflection of the extent to which they still think of the formula as a register of signatures.[63]

These considerations suggest two directions for revision of the notation to be employed within parentheses. One is to use actual signatures whenever possible and always to differentiate references to actual from those to inferred signatures. Such an approach could take one of two forms: either placing all actual signature references in quotation marks (all signature references not quoted would be inferred) or placing all inferred signature references in brackets (all signature references not bracketed would be actual):[65]

*A*4(

*A*3 + '3 *') B4('B2' + 'b2'.b3) C4(C3 + 'C3',1)

*A*4([

*A*3] + 3 *) B4(B2 + b2.[b3]) C4([C3] + C3,[1])

The other direction one could go, and I think a more promising one, is not to attempt at all to report actual signatures of leaves within parentheses.[69] The information provided would then be purely structural, the details of signing to be reported separately:

*A*4(

*A*3 + 1) B4(B2 + 1.2) C4(C3 + 1,2) χ4(—χ3) D4(±D4)

*A*4(3 + 1) B4(2 + 1.2) C4(3 + 1,2) χ4(—3) D4(±4)

*A*is unsigned, the fold in B has the first leaf signed "b", the second of the inserted leaves in C is signed "c5", and the substitution in D is signed "* D4". The length of the statement of signing would be increased, but the formula would be shortened and simplified. And each would be clearer and more efficient by focusing consistently on a single function. No one would be likely to have any indecision about how to write or how to read the formula or the accompanying statement of signing. This ease of use—by both bibliographer and reader—would reflect the logic of the underlying conception.

Reference notation. Any examination of the collational formula must give some attention to signature reference notation, for such notation is tied to, and takes its form from, the formula;[72] a revision in the system adopted in the formula may produce a change in the style of the reference notation. The function of signature reference notation is of course to provide a way of referring to a particular leaf or page in terms of the structure of the book; since references of this kind are widely employed in bibliographical discussion, the conventions governing their use are a matter of some importance. Most of the considerations involved in thinking about the formulaic notation of inserted leaves, as outlined above, are relevant here; the parenthetical parts of a formula, after all, make use of reference notation, since they refer to specific leaves. The standard system, set forth thoroughly by Bowers (pp. 255-268), begins

The treatment of inserted leaves, however, poses the same problems we have already noted in connection with the formulary. There is an additional consideration as well, for reference notation may be used at some distance from the formula (even in a separate discussion) and must provide for conveniently locating the cited leaf without constant recourse to the formula. In summarizing the standard approach, Bowers (p. 260) sets forth four ways of referring to an inserted leaf, illustrated by an insertion that would appear in a formula as "C4(C2 + * C2)":

If one does decide to adopt the formulary system proposed above (with notation that consistently focuses on position, not signing), references to leaves and pages are correspondingly simple. References to the inserted leaves (and their pages) in the following formula would take the form illustrated below it:

*A*4(

*A*3 + 1) B4(B2 + 1.2) C4(C3 + 1,2) D4(±D4)

*A*3(1) B2(1) B2(2) C3(1) C3(2) D4(±)

*A*3(1)r

*A*3(1)v etc.

Statement of signing. Some statement, outside the formula itself, is
required in the standard system for specifying the signing of the regular
leaves (or at least peculiarities in such signing),[77] since only the signing of the
inserted leaves is
indicated in the formula in that system. In the revised system proposed as
a
possibility above, a statement of signing takes on the role of dealing with
the
signing of all leaves, regular ones and inserted ones alike.[78] In either case the statement can be
made
concisely using signature reference notation (for the standard treatment, see
Bowers, pp. 269-271). One established convention of reference notation that
is particularly useful in the statement of signing is the dollar sign, which (as
a
form of "s," for "signature," not likely to occur as an actual signature) is
used to stand for every—or, in some contexts, any—signature
(as
McKerrow suggested in the
*Introduction*, pp. 157-158).

Combining these two modifications of the standard statement of signing with the approach to reference notation suggested above results in the kind of statement illustrated below. Because a statement of signing needs to be seen in the context of the formula to which it refers, I take this opportunity to summarize my argument by setting down a formula and statement of signing constructed according to the standard system alongside those constructed according to the system I have outlined here:

*Standard system*

π2(π1 + †1) A-B4 C4(C3 + 'C4', χ1) D4(—D2 + 2) E4(E3 + e3.4)

F4(F1 + * F2; —F3) χ4(—χ2 + '3') G4(—G3,4 + G3.4) H4(±H4)

*I*2

*Signatures*. $3(—B2,D1,F2,G2,3; + B4,H4) signed; C2 misprinted 'C3'; D3 misprinted 'D'

*Proposed system*

π2(π1 + 1) A-B4C4(C3 + 1,2) D4(±D2 + 1) E4(E3 + 1.2)

F4(F1 + 1.2; —F3) χ4(±χ2) G4(—G3,4 + G3.4) H4(±H4)

*I*2

*Signatures*. $1-3(—B2,D1,2,F2,G2,3; + B4,H4); π1(1)=†, C2=C3, C3(1)=C4, D3=D, E3(1)=e3, F1(1)=* F, Fχ2(±)=3

Anyone who suggests alterations in a widely accepted convention should be mindful of the dangers of introducing confusion rather than clarification, and changes should not be proposed lightly. I have attempted here to remain within the standard system as much as possible and not to mention potential changes when I thought the benefits of the change would not compensate for the efforts involved in altering a functioning system. The changes I do suggest are, I believe, conducive to ease of use because they emerge from a simple and consistent distinction of function between a formula that delineates how a book is constructed and a statement that records the location of printer's signatures in a

It takes many words to write about these matters, but the length of the discussions should not obscure the real simplicity of the collational formula, as it has developed over the past century. The aim of the formula, after all, is to facilitate communication between bibliographer and reader, not to place greater distance between them. There is nothing difficult or esoteric about collational formulas or their accompanying statements of signing; anyone who approaches them with an open mind and a basic knowledge of how books are constructed will understand them immediately. Nevertheless, one should not hesitate to attach explanations in words whenever one believes them necessary for clarity. The same point applies to the rules for quasi-facsimile transcription: guidelines serve their function only if they are employed thoughtfully, not mechanically. I hope that my comments in these two areas can serve in some degree to help clarify the essential purposes of quasi-facsimile quotations and collational formulas in bibliographical accounts. Intelligent use of conventions can follow only from a true understanding of the reasons for their existence.

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