Printers key
Encyclopedia
The printer’s key, also known as the number line, is a line of text printed on the copyright page (the verso of the title page
Title page
The title page of a book, thesis or other written work is the page at or near the front which displays its title and author, usually together with information relating to the publication of the book...

) of books, used to indicate the print run. Publishers started to use this convention around the middle of the 20th century.

An example follows:
1 2 3 4 5 6 7 8 9 10


This is how the printer's key will appear in the first edition of a book. Numbers are removed with subsequent printings, so if "1" is seen then the book is the first printing of that edition. If it is the second printing then the "1" is removed, meaning that the lowest number seen will be "2".

Examples

Usually it is a series of numbers or letters as in the following examples:
10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10

a b c d e f g h i j k


Sometimes rather than follow in series the numbers alternate from left to right for example:
2 4 6 8 10 9 7 5 3 1


The purpose of this arrangement is to keep the line of numbers roughly centered even as the numbers are removed with subsequent printings. This format is seen in the copyright page image on this page.

Sometimes number lines will also include a date line for example:
2 3 4 5 6    73 72 71 70


This indicates a second printing (aka second impression) that took place in 1970. More specifically, it is this particular imprint
Imprint
In the publishing industry, an imprint can mean several different things:* As a piece of bibliographic information about a book, it refers to the name and address of the book's publisher and its date of publication as given at the foot or on the verso of its title page.* It can mean a trade name...

's second impression of the edition.

Sometimes, when the publisher outsources the printing to a contractor, there will also be a code for which printing company was contracted in this case:
3 4 5 6 7 8 9 10   APC   00 99 98 97 96


The hypothetical printer’s key above decodes as third print run, printed in 1996, contracted to Acme Printing Corp.

First edition vs. first printing

Bibliographers usually define a first edition as all printings from substantially the same type setting, no matter how many printings are done. Book collectors tend to define first edition as the first printing of the first edition. For further information please see Edition (book)
Edition (book)
The bibliographical definition of an edition includes all copies of a book printed “from substantially the same setting of type,” including all minor typographical variants.- First edition :...

.

Why numbers are removed rather than added

With each successive reprint, the publisher needs to instruct the printer to change the impression number, and the theory is that the printer is less likely to make a mistake if they are only removing the lowest number rather than introducing a new number each time. With this arrangement, all the printer has to do is "rub off" the last number in sequence. By changing only the outer number it means that the fewest possible changes are made to the page of characters, which means the smallest possible charge to the publisher. In the days of hot-metal printing, where each character was a metal block, all the printer had to do was to physically pick out the relevant blocks from the "sheet" and then the stack of blocks which would have been laboriously laid out when the page was first set up could be inked up for the reprint. In the case of a Linotype
Linotype machine
The Linotype typesetting machine is a "line casting" machine used in printing. The name of the machine comes from the fact that it produces an entire line of metal type at once, hence a line-o'-type, a significant improvement over manual typesetting....

slug, the lowest number could be filed off and the slug reused. In either case, the change was minimal.
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