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The printers key, also known as a number line, is a convention that publishers started to use after World War II to indicate the print run of a book. It is found on the copyright page (the verso of the title page).

Usually it's 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

This format is also seen in the copyright page image above.

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. Which means that the lowest number seen will be "2".

Sometimes number lines will also include a date line for example:

2 3 4 70 71 72

This indicates a second printing that took place in 1970.

Bibliographers usually define a first edition as printings from substantially the same type setting, no matter how many printings are done. Book collectors tend to define a first edition as the first print of the first edition. For further information please see first edition.

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 outer number that's lowest in the 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 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.^[1]