When dealing with a laser printer, or, for that matter, an IBM Selectric Composer, a point is exactly what it tends to be thought of as being nominally: 1/72nd of an inch, or 0.01388888...89 inches.
However, with printer's type, a point is slightly different: 0.013837 inches (or 0.03514598 centimeters). And Linotype machines work to a point which is 0.014 inches (or 0.03556 centimeters) in size. (This point is descended from the 0.0137 inch point of Fournier and the 0.0138 inch point of Nelson C. Hawks.)
In Continental Europe, a different type of point, the Didot point or Didone is used. Fourteen Didot points are very close to 15 points in height; a more precise figure is about 14.975 points. The next higher very good approximation to the ratio is that 72 Didot points are almost equal to 77 points in size.
Another value for the ratio between the old French measure and English measure is 1142 to 1071, referenced to a history by Poggendorff by this web site.
Originally, the Didone was 1/72nd of the pre-Revolutionary inch, which in turn was 1/12 of the pied du Roi. As the French foot was originally about 12.7892 inches (various figures, from 12.7889 inches to 12.7893 inches, are given) in length, this works out to about 0.0148023 inches or 0.0375979 centimeters.
In 1879, Firmin Berthold revised the Didot point system to connect it with the metric system: a Didot point became 1/2660th of a metre, which is about 0.014800781 inches or 0.037593985 centimeters.
A metric Didot point of exactly 0.0375 centimeters has been proposed, and may in fact be in use, and the French Imprimerie Nationale is said to use a point of 0.04 centimeters. Also, it has been proposed to measure printing type directly in millimeters.
The first laser printers tended to print at a resolution of 300 dpi. This already was high enough for the dots of which text was composed to be invisible. And 300 is a multiple of 60; since typewriters in the English-speaking world tended to type either at 10 characters per inch, or 12 characters per inch, Pica or Elite, dividing the inch into 60 parts was to achieve the largest unit that could produce both character widths. Proportionally-spaced fonts for electronic daisywheel typewriters, therefore, were based on 1/60th of an inch as the unit.
Some laser printers adopted the resolution of 360 dpi, so that in addition to being able to reproduce 1/60th of an inch with an exact number of dots, one could do the same for 1/72nd of an inch. In this way, lines with different point sizes could fit together in the expected way without having, occasionally, to make a line of type one pixel taller or shorter at times.
Today, of course, laser printers may print at 600 dpi or higher resolutions. It seems to me that it might be beneficial if fonts could be reproduced on a laser printer with an exact unit system, so that the way characters fit together would not change as characters are scaled up for different font sizes.
At 360 dpi, this would mean that fonts could be designed around a system of 5 units to the em, and be reproducible at any integer point size. Such a unit system, however, is too crude for quality typography, although it was used to good effect on some early proportionally-spacing typewriters.
The Monotype type-casting machine used a system of 18 units to the em. This could be achieved with a laser printer resolution of 72 * 18 or 1296 dpi. This would not seem too unreasonable. But it isn't a multiple of 60! Would we have to multiply the resolution by another factor of five?
The fact that a printer's point is 0.013837 inches, not exactly 1/72 of an inch, comes to our rescue. If we raise the resolution to 1320 dpi, which is 22 times 60, then we could reproduce typography by using a point of 0.13636... inches.
But that is a bit small. Also, what about our European friends, who use the Didot point?
Perhaps, instead of using the Monotype standard of an 18-unit system, we could compromise, and use a 14-unit system. Then, for a point of 1/72 inch, we would need a laser printer resolution of 1008 dpi. To achieve a multiple of 60, we could adjust this to 1020 dpi, giving a point size of about 0.0137255 inches. This is still a bigger difference from 1/72 inches than a real printer's point provides, though.
Why a 14-unit system? Then, we could also devise a separate version of each font, designed around a 15-unit system! And *that* version of each font would be the one used when setting things to Didot points; one Didot point would be divided into 15 dots at that resolution, two Didot points into 30, and so on, just as one English/American point would be 14 dots, two points 28 dots, and so on.
But while the two kinds of points would be nearly in the correct ratio, they would both be too small. Thus, to satisfy all the conditions more closely, perhaps the way to go would be to use a resolution of 360 * 3 dpi, or 1080 dpi, and a 15-unit system for fonts based on the 1/72 inch point. The Didot point would just be more crudely approximated by using a 16-unit system. 16 dots at 1080 dpi would be 0.37629629... millimeters, though; this is too large instead of too small, and is actually closer to the traditional Didot point of 0.37593985 millimeters than the metric Didot point of 0.375 millimeters is. Thus, it seems as if this should yield an acceptable result.
Incidentally, if we do not worry about having a multiple of 60 dpi, but instead design a laser printer only for typesetting and not for reproduction of typewritten text, other possibilities become available. Thus, Autologic sold laser printers with a 723 dpi resolution, and with a 1016 dpi resolution. The 723 dpi resolution corresponds to a 720 dpi resolution, reduced in scale by about 0.414%, so that 10 dots would equal a point, not of 1/72", but of 0.01383126...", a close approximation to the standard printer's point of 0.013837". The 1016 dpi resolution corresponds to a 1008 dpi resolution, so that 14 dots equal a point, and 15 dots equal a Didot point, with a scale reduction of 0.787%; in this case, 14 dots equal a point of 0.0137795...". A 1012 dpi resolution, for example, would have given a better approximation of 0.013834..." to the point.
Just as the Didot point could be rounded to 0.375 millimeters, the English point could also be approximated in the metric system by 0.35 millimeters. In that case, a laser printer with a nominal resolution of 360 dpi would instead have five dots to the point by having a dot pitch of 0.07 millimeters. This would allow Pica and Elite typewriter faces to have pitches of 10 and 12 characters to a metric "inch" of 2.52 centimeters, instead of the actual inch of 2.54 centimeters.
Given this discussion, it seems opportune to mention here the old names for type sizes:
Points Bruce Johnson Fergusson Caslon
Canon 48 48 80 48 1 3/4 48 48
Trafalgar 44 42.76 72 43.2 2 42 41.64
Two-line Double Pica 40 38.1 64 38.4 2 1/4 37 1/3 38.83
Two-line Great Primer 36 33.94 56 33.6 2 1/2 33 3/5 33.88
Two-line Columbian 32 30.24 52 31.2 2 3/4 30 6/11 31.14
Two-line English 28 26.94 44 26.4 3 28 28.33
Double Pica 24 24 40 24 3 1/2 24 24
Two-line Pica 22 21.38 36 21.6 4 21 20.82
Paragon 20 19.05 32 19.2 4 1/2 18 2/3 19.42
Great Primer 18 16.97 28 16.8 5 16 4/5 16.94
Columbian 16 15.12 26 15.6 5 1/2 15 3/11 15.57
English 14 13.47 22 13.2 6 14 14.16
Pica (Cicero) 12 12 20 12 7 12 12
Small Pica 11 10.69 18 10.8 8 10 1/2 10.41
Long Primer 10 9.52 16 9.6 9 9 1/3 9.71
Bourgeois 9 8.49 14 8.4 10 8 2/5 8.47
Brevier (Petit) 8 7.56 13 7.8 11 7 7/11 7.78
Minion (Colonel) 7 6.73 12 7.2 12 7 7.08
Emerald (Mignonette) 6 1/2
Nonpareil 6 6 10 6 14 6 6
Agate (Ruby) 5 1/2 5.35 9 5.4 16 5 1/4 5.20
Pearl 5 4.76 8 4.8 18 4 2/3 4.85
Diamond 4 1/2 4.24 7 4.2 20 4 1/5 4.24
Brilliant (Gem) 4 3.78 6 3.6 22 3 9/11
Ruby 3 1/2 3.37 24 3 1/2
Excelsior 3 3 5 3 28 3
The first two columns give the old typeface names as used in English-speaking countries followed by the size, in points, of type usually thought of as corresponding to those sizes today.
However, before the point system was adopted, the different sizes of type were not actually all multiples of a single small unit. Thus, as noted on this site, before the point system came into general adoption, one George Bruce proposed a system in which successive sizes of type would be in the ratio of the sixth root of two. (One web site gives 1882 as the year in which this was done, but that would have been decades after his death. It could have been a typographical error for 1822, which would have been plausible.) What this would lead to is shown in the third column.
A point system devised by J. R. Johnson, called the "Monometrical" system, based on the pica being 20 points instead of 12 is next shown, the fourth column showing the point sizes in that system, and the fifth column showing the equivalent size in conventional points for purposes of comparison.
I had wondered if the previous tendency had been to divide the column inch into a fixed number of parts. This does not appear to have been the case, as the sizes of the various bodies varied from one typefounder to another; however, it is recorded that one James Fergusson did propose such a system in 1824 in Scotland. In his system, twelve lines of Nonpareil type corresponded to exactly one inch, and the other sizes of type were defined in terms of the number of lines of those type sizes which would take up the same space as 14 lines of Nonpareil. What this results in is shown in the sixth column in terms of the number of lines in 14 lines of Nonpareil, and in the seventh column in terms of the size in points of exactly 1/72 of an inch.
Finally, in the eighth column, one example of actual sizes, based on what the Caslon typefounders used in 1841, is given.
This image:
illustrates another issue connected with type sizes.
In the illustration, we see the word "palaces" in a typeface from 1930, intended for use in a newspaper, and the word "regole" in a typeface from 1691, used for printing fine books.
Both words include one lowercase letter that ascends above the line (in some typefaces, they are noticeably taller than capital letters), and one lowercase letter that descends below the line. The height of lowercase letters that have neither ascenders nor descenders is called the x-height; it determines the visual size of printed letters, but it isn't tied to the point size of the type, which is determined by the size of the type body (shown in the diagram by the blue boxes around the letters).
Because the descenders in the newspaper face are short and stubby, while those from the old book face are long, in order to make the baselines of the two words line up, leads have to be used, below the newspaper face and above the old book face.
This will work if the height of the leads required happens to be a size which the printer happens to have on hand. Thus, the height needs to be an exact multiple of 1/2 point, and, ideally, it should be a multiple of 1 point for the greatest convenience.
In order to allow this, type foundries, during the 19th Century, adopted systems by which the distance of the baseline of letters above the bottom of the type slug was standardized. Thus, the letters printed by type bodies of a certain point size were slightly smaller than they would otherwise have been in order to fit into the standard.
For type of any one point size, the baseline usually could be in one of three positions; a very low position, for titling fonts (in which only capital letters were present, and so there were no descenders to worry about); a standard position which was still fairly low, as, at the time, economical use of paper was a great concern, and so most typefaces had short and stubby descenders like those still used for newspaper typefaces; and a high position for script faces and authentic versions of older typefaces. Thus, the Inland Type Foundry referred to these three positions as the Standard Title Line, the Standard Line, and the Standard Script Line; Barnhart Brothers and Spindler referred to them as the Cap Line, the Uniform Line, and the Text Line; American Type Founders at one point referred to them as the American Title Line, the American Common Line, and the American Script Line; and then later used the term Art Line in place of Script Line.
Combining contradictory information from multiple sources, it appears that the American Common Line allowed the following amount of space at the bottom of the letter for the descender:
Type Size: 5 6 7 8 9 10 11 12 14 16 18 20 24 30 36 42 48 54 60 72 Common Line: 1 1 2 2 2 2 3 3 3 3 4 4 5 7 8 9 10 11 12 14
The space allowed for the descender was usually a minimum 1/5 of the height of the type body, rounded upwards to the next nearest point; while two exceptions were made, 1/6 in the case of 6 point type, and 3/16 in the case of 16 point type, 48-point and 60-point type did not copy those sizes.
All these distances differed from one another by even multiples of a point, and also from the distances applying to all other point sizes, making it practical to mix types of different sizes and styles on the same line of text as required, and yet keep a perfectly aligned baseline.
As for old books, it may also be of interest to note the terms for page sizes:
Traditional American Demy Metric
Sheet size: 18" x 24" 17" x 22" A0: 841mm x 1189mm
Quarto 4to 9" x 12" 8 1/2" x 11" A2: 420.5mm x 594.5mm
Sextodecimo 16mo 4 1/2" x 6" 4 1/4" x 5 1/2" A4: 210.25mm x 297.25mm
Folio 12" x 18" 11" x 17" A1: 594.5mm x 841mm
Octavo 8vo 6" x 9" 5 1/2" x 8 1/2" A3: 297.25mm x 420.5mm
Tricesimo-secundo 32do 3" x 4 1/2" 2 3/4" x 4 1/4" A5: 158.625mm x 210.25mm
Duodecimo 12mo 6" x 6"
Vicesimo-quarto 24to 4" x 4 1/2"
Many different paper sizes exist, a different series of sizes being used in the United States and in Britain. Some of the most common British paper sizes are:
Imperial 29 1/2" x 21 1/2" Royal 23 1/2" x 19 Demy 19 1/2" x 15 1/4" Foolscap 16 1/2" x 13 1/4"
American Foolscap was 14" x 17", thus giving rise to the traditional legal size page of 8 1/2" x 14", just as American Demy gave the standard 8 1/2" x 11" sheet of typewriter paper, which is approximated by the metric A4 size.