University of Virginia Library


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


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scholarship. Whether or not one has discovered a variation in a gathering that identifies a separate impression, one must recognize that a record of gatherings may enable someone else to discover such variation and in any case provides a historical description of how in fact a given book was constructed. Naturally there are times when the scope of a work—as in the case of some short-title catalogues—prevents the inclusion of signature collations; but in those cases other elements of a description are eliminated as well. The scale on which a bibliography is constructed obviously determines how much can be incorporated into the entries; but the period dealt with does not in itself determine the scale. There can be no question that a report or collation of gatherings is essential to bibliographical description on all levels except the most severely abbreviated.

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]


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the format (the number of leaves per sheet), which was the denominator of Bradshaw's fraction, is noted separately (either as a word, sometimes abbreviated, or as a number with a suffix or superscript "o," as in "quarto," "4to," and "4°").[39] It was this system that Pollard, McKerrow, and Greg gave prominence to over the ensuing decades,[40] adding a few useful conventions in the process, notably two Greek letters: thus McKerrow suggested π (for "preliminary") to designate an unsigned preliminary gathering preceding a gathering signed or inferred as "A"; and Greg added χ (for "extra") to designate an unsigned gathering in the body of a book for which no letter (or number) of the regular sequence is available to be inferred. The simplicity of the system and the ease of remembering it carried the day.

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


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is to try to anticipate the various questions that might arise in practice as one uses it and to provide a standard point of reference where every detail is elaborated; but his own convenient appendix, "A Digest of the Formulary" (pp. 457-462), shows how uncomplicated the basic conventions are.[41] The value of a formulaic statement of signature collation is undeniable, for it makes an intricate or irregular book structure more readily apparent and easier to follow than an account in words would.[42] The fundamental rules of the system codified by Bowers—represented by a formula like "4°: π2 A-C8 χ8 D8(D7 + χ1) 2χ4 E8 [F]2"—emerged from the main line of development in descriptive bibliography. Some of those rules (such as indicating the number of leaves in a gathering with a superscript figure) have now been in use in the English-speaking world for a century or so, and all (including the assignment of π and χ to unsigned and uninferred gatherings) have had a life of more than half a century. With these essential conventions so well established and with Bowers's thorough exposition of them available, it would be unwise at this point to tamper with them. They are simple, clear, and widely recognized; we should accept them as the basic grammar of the language of descriptive bibliography and proceed from there.[43]

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


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of botanical literature, Allan Stevenson in his introduction ("A Bibliographical Method for the Description of Botanical Books") to the second volume (1961) of the 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


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poses few problems. A minus sign preceding a reference to one or more leaves denotes cancellation, with periods used to join references to conjugate leaves and commas joining references to disjunct leaves:[46]
A-B4 C4(—C3) D4(—D2.3) E4 (—E3,4)
When a canceled leaf or leaves are replaced by leaves of identical conjugacy that are either unsigned or signed conventionally, a plus-minus sign can be used:
A-B4 C4(±C3) D4(±D2.3) E4(±E3,4)
If the conjugacy of the substitution is different, the deletion and substitution must of course be treated separately:
D4(—D1.4 + D1,4) E4(—E3,4 + E3.4)
This much is straightforward.[47] The trouble largely enters in connection with insertions that are not replacements for canceled leaves. But it is adumbrated even in these simple instances of cancellation and substitution if the substitution is anomalously signed. In the standard formulary (see Bowers, p. 248), the actual signature of the substitution is used in such cases, and it is placed in single quotation marks if it might otherwise prove confusing:
B4(—B2 + b2) C4(—C3 + '3') D4(—D3 + '* D2') E4(—E2 + 2E2)
In this example the replacements in B and E need no quotation marks because they clearly represent actual signing, whereas those in C and D are quoted to call attention to the fact that the cited signatures are not


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misprints.[48] The potential for ambiguity is present here in the fact that the references following the plus signs in this formula are actual signatures, whether they are enclosed in quotation marks or not, whereas those after the plus (and plus-minus) signs in the earlier examples above (as well as those after the minus signs in all examples) are only positional indicators, not necessarily actual signatures.[49] Before pursuing this point, we should see the full dimensions of the problem by examining the notation for insertions.

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

C4(C3 + 1) C4(C3 + χ1)
Of course the regular leaf preceding the insertion must always be named first in order to show the position of the inserted leaf.[51] In these two ways of indicating that gathering C contains five leaves, the use of "1" implies that (with the location of the insertion established) only the barest reference to the existence of one added leaf need be made, whereas the "χ1" treats the leaf as it would be treated if it fell between gatherings and no signature of the regular series were available to be assigned to it.[52] More complicated situations provide further alternatives, as illustrated by these two equivalent formulas derived from examples of Bowers (on pp. 239-240, 242-243):
A-B4 C4(C3 + 'C4',χ1) D4(D2 + χ1,2) E4(E3 + e3.1) F4(F1 + * F1.2)
A-B4 C4(C3 + 'C4' + 1) D4(D2 + 2) E4(E3 + e3.4) F4(F1 + * F2)


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In C, a second plus sign is needed if the second inserted disjunct leaf is to be referred to as "1" rather than "χ1"; in D, the two unsigned disjunct leaves can be noted simply as "2";[53] in E, it is permissible to infer as "e4" the unsigned second leaf of the inserted fold, since the lower-case signature, established by the signed first leaf ("e3"), eliminates any confusion with E4; in F, the conjugacy of the inserted leaves can be indicated by a superscript "2", rather than by a period between the leaf references, since the first leaf of the fold is signed as a first leaf in a gathering.[54]

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


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"2" in D in the last formula above). Of course, one can explain that the "1" in "e3.1" simply means one unsigned leaf, rather than that the second leaf was signed "e1"—as a reader might otherwise think, since "1" is not the number the bibliographer would be expected to infer if no signature were present. And one can further explain the reason for this seemingly anomalous use of "1": if the first leaf of the inserted fold had been signed "E3" rather than "e3", one could not infer "E4" for the unsigned second leaf without producing confusion with the regular E4, and some other reference is needed. Whether "1" solves the problem most efficiently is a real question, since it involves a switch in usage that must be explained. As Bowers says, clarity and simplicity should be aimed for at all times; and one cannot help but wonder whether the standard treatment of insertions has not added an unwarranted complexity and a potential ambiguity into an admirably simple basic system.

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):

D4(D4 + D5) E4(E4 + * E5.6) G4(G4 + 'G5',G6) K4(K3 + 'K4') Q4(Q1 + * Q2) R4(R3 + 'R3'.'R4') S4(S1 + s2)
The inserts in D, K, and R are all signed, even though the one in D is not in quotation marks. In K and R, the quotation marks are necessary to distinguish these anomalously signed leaves from the regular K4, R3, and R4. In D, no quotation marks are needed to indicate signing, because if the leaf were not signed, it would presumably be noted as "χ1" or "1". But there might still be a doubt in a reader's mind, since no quotation marks are present and since "D5", not conflicting with any other leaf in the gathering, would be inferrable.[56] The principle of inferring when no


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conflict results is shown in E and G, where the sixth leaf in each case is unsigned; the treatment of G leaves no ambiguity, but that of E might again raise doubts about whether the final leaf is signed.[57] In commenting on Q and S, Bowers explains that after Q1 comes "a fold with the first leaf signed * Q1" and after S1 "a fold with the first leaf signed s1 and the second s2". The fact that one cannot tell from the formula whether or not the second leaves of the folds are signed shows that these folds are being treated like the regular gatherings: in the main sequence of signatures with their superscript figures, the signing of individual leaves is not made apparent in the formula itself (but only in the statement of signing that follows). Yet for other kinds of insertions, and even for some folds (as in R), the attempt is made to specify the signing of every leaf.[58]

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

A—B8 [C]4 D—E8 or A—B8 C 4 D—E8


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one is saying no more than that the third gathering has no printed signature on any of its leaves[60] and that each of the other gatherings has the designated signature on at least one of its leaves (not necessarily the first). When it is necessary to refer to one of the regular leaves of a gathering, the reference is positional only and carries no implication about signing: "B8(—B5)" says only that the fifth leaf has been canceled (if no copies are known, its signature, if any, is obviously unknown), and "B8(B5 + 1)" says only that the insertion follows the fifth leaf (which might in fact be unsigned or even missigned).[61] For inserted leaves, on the other hand, the actual signature (or lack of signing) of each of them is normally indicated by the notation.[62] The result is that references following plus signs usually represent a different system from those preceding plus signs.

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]


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If a gathering signed "B" contains an inserted leaf signed "b" or an inserted fold signed "†", those are in fact additional signatures, which a register of signatures would have to include. On the other hand, such insertions are subordinate to the gatherings of which they have become a part, and their signatures thus have a different standing from the signatures of the primary gatherings: they do not have a place in the main sequence of signatures except as they are attached to one of those main signatures. In order to show the structure of a book, of course, one must record insertions whether or not they are signed; choosing "χ" for an unsigned inserted leaf or fold, however, seems in some ways inappropriate, because it is treating an insertion in a gathering as if it were an independent gathering. Some such symbol as "χ" is obviously needed for an unsigned and uninferrable gathering, but for an unsigned insertion within a gathering no signature is required, since the leaf or leaves involved take their identity from the gathering itself; therefore assigning to such insertions a symbol that normally serves as a substitute for an actual signature implies a status for the insertions that they do not have.[64] Furthermore, when an insertion has an appropriate letter signature but is numbered anomalously—as when an inserted leaf between E2 and E3 is signed "E3"—quoting the anomalous signature in the formula is treating the inserted leaf differently from other leaves: the signature is not new (and thus does not call for mention even if one regards the formula as a register), and anomalous signing of regular leaves is not reported in the formula. Since the insertions have to be referred to in some fashion, however, one may ask why they should not be referred to by the signatures they actually bear, when they do bear them. Perhaps they should; but, if so, some other adjustments to the formulary ought to be made, so that a uniform approach would underlie all parenthetical elements in a formula. Not to distinguish in the formula (as now sometimes happens) between an inferred and a quoted signature reference betrays an indecision as to the function of the formula.

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]


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A 4(A3 + '3 *') B4('B2' + 'b2'.b3) C4(C3 + 'C3',1)
A 4([A3] + 3 *) B4(B2 + b2.[b3]) C4([C3] + C3,[1])
Both these forms[66] are unambiguous, but they are also rather awkward (the first less so than the second).[67] The gain in clarity is important, but the price paid for it makes neither of these solutions a happy one. Furthermore, this approach, even though it achieves consistency within the parentheses by specifying the signing of regular as well as of inserted leaves, fails to eliminate the split between parenthetical notation (which entails specifying the signing of individual leaves) and notation outside parentheses (which does not attempt to indicate how leaves are signed).[68]


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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(A3 + 1) B4(B2 + 1.2) C4(C3 + 1,2) χ4(—χ3) D4(±D4)
This is indeed a simple system, and it could be made still simpler by eliminating the signature letters within parentheses:
A 4(3 + 1) B4(2 + 1.2) C4(3 + 1,2) χ4(—3) D4(±4)
Whichever of these forms one uses (the second may seem too stripped-down to some people, though the repetition of the letter is unnecessary),[70] this approach still follows the pattern of the standard system for showing


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structure;[71] the established formulary has not resulted in any ambiguity in the reporting of structure but only of the signing of leaves, and here the latter function is simply taken away from the formula. One would have to turn to the separate statement of signing to learn, for example, that in the book represented by this formula the insertion in 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


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with the printer's convention of identifying a leaf by attaching a leaf number to the signature of the gathering: the second leaf of gathering B, for example, becomes "B2". A superscript "r" or "v" can then be appended if reference is being made to the recto or verso page rather than the whole leaf.[73] This notation is taken to be positional only and does not indicate whether the leaf is actually signed (or missigned): "A4" means the fourth regular leaf of A even if that fourth leaf is unsigned or signed "A3". In assigning leaf numbers one must remember that only the leaves of the regular folded quires of a gathering (or substitutions for them) are counted: the last regular leaf in A4 is A4, even if two further leaves have been inserted in A, giving it a total of six leaves. Obviously one cannot simply number the leaves of a gathering in a single consecutive sequence, ignoring deletions and insertions, for the reference notation would not then accurately reflect the place of the leaf in the structure of the book nor would it be consistent with the usage of the formula. There can be little quarrel with these basic rules.

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)":

C(* C2) C(C2 + * C2) C2 + * C2 C2 + 1(* C2)
The first of these does not make explicit the location of the leaf in the gathering and would necessitate reference to the formula for that information; the other three are therefore more appropriate for general use, especially if the formula is not at hand. Of course, since they are based on a formula that mixes positional notation with actual signatures, that mixture is present in these references. Leaving that matter aside, we are still likely to find their form rather cumbersome. Perhaps they could be simplified by observing two points: (1) since reference is being made to a leaf, not a whole gathering, and since a regular leaf of the gathering


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must be specified to locate the insertion, it is superfluous to state the signature of the gathering separately from the notation of the locating leaf, as in "C(C2 + * C2)" above, where the first C is merely repetitious; (2) the use of a plus sign that does not fall within parentheses (as in the last two examples above) awkwardly makes the notation look like a reference to two entities (an awkwardness that is compounded when a superscript "r" or "v" is appended to the second part of the reference). Applying these observations to this example gives us "C2(+* C2)" or, more simply, "C2(* C2)". Regardless of what system one decides to follow in the formula, these two principles should be considered in constructing references based on it.[74]

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(A3 + 1) B4(B2 + 1.2) C4(C3 + 1,2) D4(±D4)
A3(1) B2(1) B2(2) C3(1) C3(2) D4(±) A3(1)r A3(1)v etc.
In the references, the figures in parentheses denote the first and second leaves following the leaves named just before the parentheses, and the plus-minus sign indicates that the leaf in question is a replacement for the one originally occupying that position. The identity of reference to the insertions in B and C shows that matters of conjugacy are not covered in references, their purpose being only to specify location in relation to the basic structure of gatherings.[75] This use of "2" to mean a second leaf in fact follows the standard system of reference; as Bowers points out (p. 260), the location of such a leaf should be stated as the second leaf


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after the preceding regular leaf (the position of which is obvious) rather than as the first leaf after the preceding inserted leaf (the position of which might not be evident without recourse to the formula).[76] References of the form suggested here are quite simple, requiring only single numbers in parentheses, and fully consistent with the formula, focusing on positions of leaves and not their signatures.

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).


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Thus "$3" signifies the third leaf of every (or any) gathering. In the standard statement of signing, however, at least for pre-nineteenth-century books, "$3 signed" is used to mean that the first three leaves of every gathering are signed, requiring the inference that the leaves in each gathering preceding the designated one are also signed. It seems to me that an explicit statement would be preferable, particularly since so little extra space is required: "$1-3 signed" is scarcely more cumbersome, and it involves no special convention, other than knowing that the dollar sign is a generic signature.[79] Although the standard statement uses plus and minus signs to show exceptions to the basic pattern of leaves signed with the correct signature and leaf number—as in "$3(—C2; +H4) signed"—it generally employs words for other irregularities, such as "K2 misprinted as 'K3'". Interpretive words like "misprinted," however, seem supererogatory: it is enough to state how each leaf is in fact signed, and I think an equals mark could be used for the purpose ("K2=K3").[80]

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'


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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
In the second system, the single semicolon separates the account of the conventional signing of regular leaves (or substitutions for them) from the account of the irregular signing of such leaves and the signing of inserted leaves. Any leaves not mentioned in the statement of signing are unsigned.[81] Whether the statement should appear with the formula or as a separate paragraph later in the description (an option discussed by Bowers, p. 271) is not particularly important, although the statement would seem to fulfill its role most conveniently when it is adjacent to the formula.[82] What is important is that the functions of the formula and the statement be clearly differentiated, so that one can know without any hesitation what is located in each place. The proposed system may at times be less economical of space,[83] but it eliminates any ambiguity.

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


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book. Indeed, no one who understands the established system would have any difficulty, even without receiving an explanation, in reading a formula and a statement of signing that employs the proposed plan. But whether this plan is accepted is less significant than understanding the reasoning that brought it about and the necessity for continuing to think critically about what we do.

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.