This section, and the one that follows, I am compelled to admit, cross the line from obvious and useful features to add to the IBM Selectric Composer to the realm of wretched excess.
On the various versions of the Selectric Composer, a knob is available to adjust the amount of space the paper will advance at each carriage return, in increments of a single point.
Changing the smallest unit to half a point would correspond to what is commonly available to printers using metal type.
On a typewriter, typically, the paper is advanced by one-twelfth of an inch, or six points, for each click of the knob; spacing can be single, double, or one and a half.
However, the Mag Card Executive came with an alternate spacing option; it was recommended to use a 48-tooth ratchet on its platen roller, which was 4 1/2 inches in circumference. Two clicks of that ratchet would cause text to be spaced at 5 1/3 lines to the inch, instead of 6 lines to the inch. This was thought to be more appropriate to the proportional typestyles on Mag Card elements, which were designed to be about the same height as, for example, Documentary on the IBM Executive (typebar) typewriter.
And on this hangs a tale.
The Mag Card Executive had available for it a Symbol Proportional element, which fulfilled much the same role as the Symbol element for a conventional Selectric typewriter. Like the Symbol element, it had a set of superscript digits on it.
Whereas one click up on the roller on a regular Selectric typewriter turned the superscript digits into subscript digits, when that typewriter was fitted with the normal 54 tooth ratchet (six teeth for every one of the nine half inches of that roller's circumference, advancing it 1/12 of an inch per click)... the superscript digits were just a tad higher on the Symbol Proportional element for the Mag Card Executive. So that one click up would turn them into subscripts... if you had a 48-tooth ratchet.
This is (perhaps) the reason why IBM never made a 96-character version of the Symbol Proportional element for the use of the owners of their Electronic Typewriter Models 50, 65, 85, and 95, which could use elements having many of the same typestyles as were provided for the Mag Card Executive.
Incidentally, IBM's Executive typewriters, like their other typebar electric typewriters, had a larger platen roller than the Selectric. That roller was 5 1/2 inches in diameter.
So a conventional ratchet gear, that advanced the paper 1/12 of an inch per click, had 66 teeth instead of 54.
For Documentary, and certain other of the larger proportional typestyles with which the Executive could come, IBM recommended a 58 tooth ratchet.
4 1/2 inches divided by 48 teeth is 0.09375 inches. 5 1/2 inches divided by 58 teeth is 0.948275862... inches. So IBM indeed chose a recommended linespacing for its Mag Card Executive typestyles very close to that recommended for its full-size Executive typestyles:
Now, a 4 1/2 inch circumference roller could easily be connected to an alternate ratchet wheel by means of a 9 to 11 gear ratio, so that when using three units of 1/96", or two units of either 1/72" or 1/90", to type with typestyles designed for the typebar Executive, the paper could advance by the exact amount that a 58 tooth ratchet on a 5 1/2" platen would cause, despite the platen on the Selectric being smaller.
There is, of course, one obvious advantage of the 5 1/2" platen circumference of IBM typebar electric typewriters over the 4 1/2" circumference chosen for the Selectric. Five and a half is half of eleven, which is half of twenty-two.
And 3 1/7, a close approximation to pi, can also be expressed as 22/7.
Therefore, a platen with a 5 1/2" circumference has a diameter which is very close to 1 3/4", or about 1.750704374... inches. Thus, given that the paper in a typewriter has a nonzero thickness, it would not at all be surprising if the platen was simply specified as having a diameter of 1 3/4 inches.
In the case of a diameter of 4 1/2", the nominal diameter of the platen would be 1.43239... inches. A diameter of 1 7/16" would be 1.4375", so the closest diameter in conventional measure would be too large instead of too small. However, specifying a platen diameter of, say, 1.432" would not present any insuperable technical difficulties - and, indeed, .0007 of an inch likely would have been too small an allowance to make for the thickness of the paper in any case.
A 9 to 10 gear ratio could, similarly, allow the platen to advance by amounts which were aliquot parts of the 5" circumference of yet another platen size.
And what unusual vertical spacings could be provided by this option?
Let us suppose we were to place 127 teeth on the ratchet wheel for a 5" platen. In that case, advancing the paper by one click would advance it by one millimetre. Four clicks, therefore, would advance the paper four millimetres, which is only slightly less than 1/6".
A Swiss company by the name of Hermes made typewriters that had completely metric spacing. They typed at 4 millimetres the line, and instead of pica and elite characters at 1/10" and 1/12", the two major options were characters that were 2.5 mm wide and 2 mm wide. Small-sized printing with characters 1.5 mm wide, instead of at 15 characters to the inch, was also available.
So one could imagine adding gears that could be brought in by a lever which would change the fundamental typewriter unit of horizontal motion from 1/60" to 0.5 mm. In that case, though, the "pica" equivalent would take five units per character instead of six, and the "elite" equivalent four units instead of five - and small size printing would take three units per character, not four. So that would mean adding one more symbol to the Pitch Selection Lever, an open square, representing three units per character.
So it is feasible to offer the Hermes typestyles, at actual size, for those who would like their correspondence to be metric compliant instead of embodying that archaic unit, the inch!
Gearing to simulate a 5 inch platen would permit approximating another European unit of vertical motion.
Given 72 points to the inch, there are 36 points in a half inch. There are nine half inches in 4 1/2", but ten half inches in 5".
360 can be divided by 15. Thus, if one wanted to replace every 15 teeth on a ratchet that correspond to one point by 14 teeth that correspond to a slightly larger unit, one could now do so.
And, as it happens, 15/14 of an Anglo-American point... is an approximation to the Didot point. (Since 1/72" is slightly larger than a real Anglo-American point, though, 16/15 of that would actually come closer to a real Didot point, but I see no need to get picky.)
Thus, the complement of controls needed to control vertical spacing would be like this:
A lever to choose between using the leading dial, or the line space lever.
The leading dial.
Associated with the leading dial, a lever to choose whether one point is one tooth on a 324-tooth gear with a 4 1/2" circumference directly on the platen, or one tooth on a 336-tooth gear with a 5" circumference geared to move at the same rate as the platen.
The line space lever.
Associated with the line space lever, a lever to choose whether one-half line is: one tooth on a 4 1/2" gear with 54 teeth, one tooth on a 4 1/2" gear with 48 teeth (Mag Card Executive), one tooth on a 5 1/2" gear with 58 teeth (Executive), or two teeth on a 5" gear with 127 teeth (Metric).
Vertical motion on the page on a typewriter normally requires rolling the platen to move the paper. If one rolls the paper up by half a line, to turn superscripts into subscripts, and then back down again, there is always the possibility of a little bit of slippage taking place, and affecting the quality of the typed result.
Thus, a possible desirable feature for an advanced typewriter intended to offer the ultimate in versatility and flexibility might be for there to be some means of moving the printing assembly downwards (in an arc with its center at the center of the platen) so as to allow printing some characters in a lower position without moving the paper.
With the Symbol 10 and Symbol 12 elements, the most important distance to move down would be 1/12" of an inch, or six points.
For setting equations using 4-line mathematics, multiples of half a point would be the obvious choice.
With the Symbol Proportional element, though, one click of a 48-tooth rachet is the amount sought; that is 3/32", or 6 3/4 points, so dealing with that case doesn't make matters overly complicated, it would just mean that the obvious accomodation would be to allow steps of 1/4 of a point instead of just 1/2 of a point.
In addition to 4-line mathematics, another area in which this feature would come in handy would be to allow the typewriter to work with elements for the Arabic script, particularly as used with the Urdu and Farsi languages, in the Nastaliq style.
It was noted above that a platen circumference of 5 1/2", as used on IBM's electric typewriters with conventional typebars that preceded the Selectric, allowed a platen diameter to be chosen based on the 22/7 approximation for pi.
Could one go even further?
An even better approximation for pi, one that is remarkably good, is 355/113.
If one chooses to use a 71-tooth ratchet gear to advance the paper 1/6" at a time, then the circumference of the platen is 71 times 1/6", or 11 5/6". That is just a bit longer than the 11" height of a normal sheet of writing paper. One could cut the size requred by half by using a 71-tooth ratchet to advance the paper by half a line at a time, or 1/12", but in that case, the option of having a ratchet that only allowed full line spacing would not be available.
Half of 71 is, of course, 35.5. So the platen circumference would be almost right if the platen diameter was 11.3... times 1/3", which works out to 3 23/30".
For an 11 5/6" platen circumference, a 63-tooth ratchet would advance the paper at a rate of 5 23/71 lines per inch (one line: 0.18783068783... inches), which would be the approximation to Executive line spacing for this case; note that it's closer to that of the Mag Card Executive than that of the original Executive, but it does lie between the two.
Given, though, that a sheet of paper is about 0.004" thick, accounting for that would normally mean that the use of so close an approximation to pi is lost; one has to decrease the diameter of the platen by twice the thickness of a sheet of paper.
Still, as it happens, 3 23/30" less .008" is very close to 9.547 centimetres.