Faber-Castell, 10-inch C/D graduations
| interval | mark step |
|---|---|
| 1 to <2 | 0.01 |
| 2 to <4 | 0.02 |
| 4 to 10 | 0.05 |
The printable has these same values, positioned from x = 250 log10(v), not by accumulating rounded gaps.
A calculation that leaves the screen
The Rule That Slides
Two logarithmic distances add, so two numbers multiply. Print the 250 mm scale, verify its geometry, then measure the accuracy your particular paper instrument earns.
Make six from two and three
D reads 6.00. That is 2.00 × 3.00.
If the product crosses 10, the scale wraps and you restore the decade by rough arithmetic. The rule does not place the decimal point for you.
What the manufacturers printed
These are historical anchors, not promises about this paper copy.
Cullimore for K&E, 1915
1/10 of 1% = 0.1% = 1 part in 1000
The manual assigns that performance to a “reasonably expert operator.” Its 4.67 ft example is one part in 467, not quite 1/5%. For 101.13 × 7.34 × 9.3, it rejects 6903.33606 and reports 6900 because the measured depth limits the information.
| published exercise | exact arithmetic | manual reading | difference |
|---|
The manual states 48.35 for 11.45 × 4.22. Exact arithmetic is 48.319, so the stated reading is about +0.0642%, inside 0.1%, but it is not the exact product.
Error budget, before measurement
relative error ≈ ln(10) Δx / 250. One 0.10 mm coordinate error corresponds to 0.0921%; 0.20 mm to 0.1842%; 0.50 mm to 0.4605%. If setting and reading each have independent 0.20 mm RMS uncertainty, their combined contribution is 0.2605% RMS (about 1 part in 384); if 0.20 mm is a hard bound, aligned worst-case error is 0.3684%.
Under that explicit two-placement assumption, human setting and reading are the largest quantified term. This is a model, not a measurement of your hand. Hairline width, parallax, rail clearance, assembly skew, local paper distortion and differential scaling remain unmeasured. Common horizontal scaling of both C and D largely cancels; unequal or nonlinear distortion does not. Calibration bars catch gross scaling, not local distortion.
Print two sheets, then make them earn trust
Choose A4 or US Letter in the print dialog, use 100% / Actual size, disable Fit and Shrink, and remove browser headers and footers. The long pieces run down the page; rotate the paper clockwise while cutting and using it.
Not calibrated. This page cannot vouch for a sheet it has not seen measured.
Accept only 99.5 to 100.5 mm vertically and an equivalent 149.25 to 150.75 mm horizontally, with nothing clipped. The reported correction is only an estimate, limited by roughly ±0.5 mm ruler reading. It does not repair differential or local distortion. Overlay the C and D endpoint witness lines after cutting; reject the sheet if they do not coincide.
Cut and assemble
- Use light card (160 to 220 gsm if available). Cut the 266 × 54 mm backing, 266 × 16 mm upper rail, 266 × 16 mm D rail and 266 × 20 mm C slide.
- Tape rails on the backing jig at y=0 to 16 and y=38 to 54, leaving a 22 mm channel. Insert the 20 mm slide, leaving 1 mm clearance on each side.
- Cut the 8 × 38 mm window in the 12 × 126 mm cursor sleeve. Bridge both faces with clear tape. Draw one hairline no wider than 0.25 mm at its exact 6 mm centre, fold around the 54 mm body, and tape the overlap without skew.
Safety: cut on a protected surface, away from your body. Use scissors where possible. If using a craft knife, keep fingers out of its path.
The concealed error laboratory
These ten cases are distinct from the published examples above. Read each three times without calculating it elsewhere; the key remains inside the scorer until all 30 positive readings exist. Turn the rule 180 degrees for pass 3. The result reports each scale region separately.
No score yet. Complete all 30 readings to make the regional comparison non-vacuous.
Let a coin referee
Measure one coin across twice at right angles. Multiply the mean diameter by 3.1416 on the paper rule. Wrap non-stretch sewing thread once around the edge, mark the meeting point, straighten without stretching, and measure it. Repeat the thread three times.
Waiting for all seven measurements. No universal pass band is assumed.
The check, shown
Sources: A. W. Faber-Castell 2/83 N and 62/83 N manual; Cullimore, The Use of the Slide Rule (K&E, 1915); ISO 704:2022, which identifies A4 under ISO 216 as 210 × 297 mm; NIST LC 1140, 215.9 × 279.4 mm US Letter. The coin test checks a geometric prediction, not the historical 0.1% claim.