Nomography and the Slide Rule

A rule that the reader can see

A token table lists sizes; an instrument can also show how they relate. The study begins with a 16-pixel base and changes one ratio. The same calculation sets the displayed ruler values and the reading sample’s heading size. Its value is that an editor can see the consequence of a parameter before accepting it as a rule for the page.

d’Ocagne’s 1899 Traité de nomographie is an identified historical work on graphical calculation. Nomograms can encode equations through graduated scales and alignment. A slide rule uses logarithmic scale relationships for operations such as multiplication. These traditions offer analogies for visible computation, but the current slider does not reproduce their geometry or their historical instruments.

Follow the actual calculation

For slider value v from 0 to 100, the study defines ratio r=1.05+0.0065v. At v=50, r=1.375. The size at level n is 16rⁿ pixels, so the first three levels are 22, 30.25 and 41.59375 pixels. The visible readout rounds the levels for display; rounding a readout is distinct from changing the underlying calculation.

At v=0 the ratio is 1.05; at v=100 it is 1.7. The heading sample uses level two, while its body remains 16 pixels. These inputs expose a particular teaching range. They do not establish a universal typographic optimum or imply that every token in the site derives from this one progression.

A separate logarithmic example shows the historical analogy’s boundary: log(2)+log(3)=log(6), which permits multiplication through adding positions on suitably graduated scales. The modern type slider instead evaluates powers directly. Both reveal a relationship, but they are different computational arrangements.

The number meets a word

Now put a long title in a narrow column. Its line breaks depend on the actual font’s metrics, the available width, language and content, not just its level in the progression. A mathematically consistent scale can produce an awkward title or an overlarge heading. The editor should inspect that failure rather than defend the ratio because it is elegant.

Spacing may need a different rule. A 30.25-pixel font size does not imply that every margin should be 30.25 pixels. Baseline rhythm, paragraph density and control dimensions have their own jobs. A system can use a related set of values while retaining explicit exceptions that support reading and operation.

Carry the values, then inspect the destination

The study’s laboratory link carries a base of 16 and the selected ratio into the typography workbench. The destination is another interface with its own interpretation and rounding. A successful handoff should preserve the selected values, the chosen appearance and a return route. It is a continuation of an experiment, not automatic certification of the page’s typography.

A reproducible record would save the ratio, base, font, sample text, viewport and any overrides. If a language change requires another heading level or a maximum size, save that exception too. The point is to let the next editor distinguish a deliberately adjusted composition from a broken dependency.

Let proportion remain a tool

The earlier essay treated every design token as a point on a nomogram and promised coherence at any scale. That conflated a broad analogy with a working model. This revision limits the claim to the actual proportional calculator and withdraws the universal promise.

I prefer an instrument that exposes its arithmetic and permits refusal. The rule can suggest a relationship; the sentence, column and reader can then test it. Its dignity lies in making judgment better informed, not in making judgment unnecessary.