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Faber-Castell 2/83N · Volume 3

Faber-Castell 2/83N Novo-Duplex — Volume 3 — Using It, and Caring for It

Worked examples on the scales only this rule has, and how to clean and keep a Geroplast rule without losing its colours

Figure 1 — The front face of a Faber-Castell 2/83N Novo-Duplex with the cursor at the centre.
Figure 1 — The front face of a Faber-Castell 2/83N Novo-Duplex with the cursor at the centre.

Figure 1 — The front of a 2/83N, with the cursor near the middle of the rule. Image: “Fc 91 2-83n front” by Larque1957, public domain, via Wikimedia Commons, https://commons.wikimedia.org/wiki/File:Fc_91_2-83n_front.jpg.

3.1 About This Volume

The first half of this volume works through examples that show what the 2/83N does beyond an ordinary duplex rule: folded-scale multiplication without resetting, the doubled-length W scales, the Pythagorean P scale, decimal-degree trigonometry and the eight log-log scales. Each example follows the method in Faber-Castell’s own instructions, and every number has been checked by calculation; where the rule’s reading differs from the exact value, both are given. The second half covers cleaning, lubrication, cursor care and storage for a Geroplast rule. General technique — reading graduations, placing the decimal point — is in the Using Slide Rules unit, Vols 1–4.

3.2 Multiplication: C/D, and the Folded Scales

2.45 × 3 = 7.35. Set the left index of C (C 1) over 2.45 on D. Move the hairline to 3 on C. Read 7.35 on D under the hairline. This is the ordinary method, and the instructions use it as their first example.

2.91 × 4 = 11.64, without resetting the slide. Set C 1 over 2.91 on D, as before. Now 4 on C lies beyond the right-hand end of D, because the product, 11.64, has run past the end of the decade. On most rules the slide would have to be run back and the right index used instead. On the 2/83N, move the hairline to 4 on CF instead and read 11.64 on DF. The folded scales are shifted by the same amount as C and D, so the product appears on them; because they are folded at π, their middle lies under the ends of C and D and the reading is always on the rule (Faber-Castell, Instructions 2/83N). Exact: 2.91 × 4 = 11.64.

A chain of factors with CI: 0.66 × 20.25 × 2.38. Put the hairline on 6.6 on D and bring 2.025 on CI under it. The slide now stands with C 1 over the first product, 13.37, on D (exact 13.365) — multiplying by the reciprocal is dividing. Without reading that intermediate, move the hairline to 2.38 on C and read 31.8 on D. Exact: 31.81. Alternating “CI under the hairline” and “hairline to C” multiplies any number of factors with one slide movement per pair.

3.3 The W Scales: Fifty-Centimetre Precision

The W scales need a slightly different habit, set out in the instructions as two rules: with the black index, the product is on the fixed W scale adjacent to the second factor; with the red index mark, it is on the fixed W scale opposite it (Faber-Castell, Instructions 2/83N).

1.635 × 5.365. On the back, set the black index 1 of W1′ over 1.635 on W1. Move the hairline to 5.365 on W2′ and read the product on the adjacent fixed scale, W2: 8.77. Exact: 8.7718. On C and D the same product reads about 8.77 too, but with the third figure an estimate; on W2 the graduation between 8 and 9 is divided into 0.02 steps and 8.772 can be placed with confidence.

√56 = 7.483. Put the hairline on 56 on D (in its second decade, 5.6). On the back, under the same hairline, W2 reads 7.483. Exact: 7.4833. Because every number from 1 to 10 has its root on one of the two W scales, square roots on the 2/83N need none of the “which half of A?” care that the A/B method demands — numbers whose integer part has an even number of digits fall on W2, odd on W1.

3.4 The Pythagorean Scale

Sine to cosine without the angle. With the slide at zero (indexes aligned), set the hairline on 13° on S. D reads sin 13° = 0.225 (exact 0.22495) and, under the same hairline, P reads cos 13° = 0.974 (exact 0.97437). The cosine of a small angle is the reading that ordinary scales handle worst; P spreads that end of the range out.

Active and reactive current. A circuit draws 35 A at a power factor cos φ = 0.8. Set 3.5 on C over the right index (10) of D. Move the hairline to 8 on D: C reads the active current, 28 A. Under the same hairline P reads sin φ = 0.6. Move the hairline to 6 on D and C reads the reactive current, 21 A. Exact: 35 × 0.8 = 28; √(1 − 0.8²) = 0.6; 35 × 0.6 = 21 (Faber-Castell, Instructions 2/83N).

Reactive power from apparent and real power. Apparent power 530 kVA, real power 428 kW. Set 5.3 on C over D 10, move the hairline to 4.28 on C and read cos φ = 0.808 on D (exact 0.8075). Under the hairline P gives sin φ = 0.590 (exact 0.5898). Move the hairline to 0.590 on D and read 313 on C — that is 313 kvar of reactive power. Exact: 312.6. (The English booklet labels the answer “kW”; it is reactive power, kvar.)

A right-angled triangle. Legs a = 2 and b = 3; find the angle α opposite a and the hypotenuse c. Set C 1 over 2 on D and move the hairline to 3 on CI; D now holds 2/3, and T1 under the hairline reads α = 33.7° (exact 33.69°). Move the hairline to 33.7° on S; CI under it reads c = 3.61 (exact 3.606). The second step works because, with the slide where it is, CI at the hairline gives a ÷ sin α.

3.5 Trigonometry in Decimal Degrees

With the slide at zero, the trigonometric scales are tables read on D (Faber-Castell, Instructions 2/83N):

Table 1 — With the slide at zero, the trigonometric scales are tables read on D (Faber-Castell, Instructions 2/83N)

WantedSet hairline onReadRuleExact
sin 13°S 13 (black)D0.2250.22495
sin 76°S 76 (red)P0.9700.97030
cos 78°S 78 (red)D0.2080.20791
tan 32°T1 32 (black)D0.6250.62487
tan 57°T2 57 (black)D1.5401.53986
cot 18°T2 18 (red)D3.083.0777

Small angles. For angles between about 0.57° and 5.7°, sin α, tan α and the angle in radians agree to three figures, and ST gives all three: the hairline on 2.5° on ST reads 0.0436 on D (sin 2.5° = 0.04362, tan 2.5° = 0.04366, 2.5° = 0.04363 rad). Between 4° and 6° use the correction marks: tan 4° is read at the short mark just right of the 4° graduation, giving 0.0699 (exact 0.06993). For a run of conversions, set C 1 over the ρ mark on D and every angle on C has its radian value below it on D.

3.6 The Log-Log Scales

e^1.61 = 5.00. Put the hairline on 1.61 on D and read 5.00 on LL3. Exact: 5.0028. The same setting reads e^0.161 = 1.175 on LL2 and e^0.0161 = 1.0162 on LL1 — the decimal point of the exponent selects the scale. On the red scales, LL03 under the same hairline reads e^−1.61 = 0.200 (exact 0.19989).

3.75^2.96 = 50.0. Put the hairline on 3.75 on LL3 and bring C 1 under it. Move the hairline to 2.96 on C and read 50.0 on LL3. Exact: 50.019.

Fifth root of 0.5 = 0.8706. Put the hairline on 0.5 on LL02, bring 5 on C under it, then move the hairline to the index of C and read 0.8706 on LL02. Exact: 0.87055.

3.7 Cursor Marks in Use

Area of a circle. Set the central hairline on the diameter 4.8 (cm) on D. Under the short upper-left marks, A reads 18.1 cm². Exact: π × 4.8²/4 = 18.096.

Kilowatts to PS. Set the kW mark over 20 on D; the PS mark stands over 27.2. Exact: 20 ÷ 0.7355 = 27.19 PS. (Reverse the procedure for PS to kW.)

3.8 Caring for a Geroplast Rule

The 2/83N is made of polystyrene, which Faber-Castell called Geroplast (Vol 1). The material itself is stable: it does not swell with damp the way wood does, and it does not yellow and shrink like celluloid. What is fragile is the colour — the black and red figures and graduations and the pale-blue and green bands — and the acrylic cursor windows. Faber-Castell’s own care note is the best starting point:

“These slide rules should nevertheless not be allowed to come in contact with corrosive liquids or powerful solvents, which are at all events liable to attack the colouring-agents applied to the graduation-marks, even if they do not actually harm the material itself. If necessary, the smooth movement of the slide can be improved by the use of Vaseline or silicon oil. … The scales and the cursor should be protected from dirt and scratches and should be cleaned with the special cleaning agents CASTELL No. 211 (liquid), or No. 212 (cleaning paste).” — Faber-Castell, Instructions 2/83N

The Castell 211 and 212 cleaners are long out of production. The procedure below follows the maker’s cautions with materials that are safe on polystyrene and acrylic.

3.8.1 Cleaning the body and slide

  1. Dust first, dry. Brush along the graduations with a soft brush (a clean make-up or lens brush), and blow out the slide channels. Grit dragged across the scales by a wet cloth is the most common cause of fine scratches.
  2. Take the slide out, and if the cursor needs cleaning, take it off as described below. Do not loosen the end-brace screws for cleaning; they set the alignment.
  3. Wash with mild soap and lukewarm water — a drop of washing-up liquid in a bowl — on a soft cloth or cotton bud that is damp, not wet. Work along the scales, not across them. Rinse the cloth and wipe again with clean water, then dry at once with a soft lint-free cloth.
  4. Keep water out of the end braces. The screws and metal brackets should be wiped, not soaked; never immerse the rule.
  5. Stubborn marks (pencil, ink, sticky residue) can be lifted with a little more soap and patience. If something stronger is unavoidable, test it first on the plain unprinted plastic at an end and on the very edge of one graduation.

Do not use:

  • Solvents — acetone, nail-polish remover, MEK, lacquer thinner, toluene, xylene, petrol, cellulose thinners, ethyl acetate. Polystyrene crazes and dissolves in many of these, and they strip the colour.
  • Alcohol (methylated spirit, isopropanol, surgical spirit, alcohol wipes) on the printed scales. It may not harm the polystyrene quickly, but it can lift the colour and it crazes the cursor’s acrylic.
  • Abrasives — scouring cream, toothpaste, “magic eraser” melamine sponges, metal polish, car polish with cutting compound. They wear the colour off the graduations and leave the surface dull. The coloured bands are especially easy to thin.
  • Bleach, ammonia, oven cleaner or other alkaline or oxidising cleaners.
  • Heat — a dishwasher, hot tap water, a radiator top, a closed car in summer or sustained direct sun. Polystyrene softens well below boiling, and a long thin moulding bends readily; Vorkoetter’s readers report rules arriving slightly bent after warm shipping.

3.8.2 The cursor

The windows are acrylic (Plexiglas), which scratches more easily than glass and crazes in alcohol and solvents. Clean them only with water and a trace of mild soap, dry them with a microfibre cloth, and never use spirit-based glass or lens cleaners. Acrylic picks up static and attracts dust (a common complaint on 2/83Ns); a slightly damp final wipe reduces it.

To remove the cursor, follow the maker’s method: press the two cheeks apart at the notched lower edge, pulling the side of the cheek down with a thumb to release the fastening, then bend the windows apart only as far as needed to slide the cursor off over the top. When refitting, the window carrying the five index marks goes on the front of the rule (Faber-Castell, Instructions 2/83N). The windows are not designed to flex far; spread them as little as possible.

If the front and back hairlines no longer agree — set a value on C front and check the same value on C back — the four screws in the cursor bars allow the windows to be realigned: loosen them slightly, align the hairlines against the C and D scales on both faces, and tighten gently. Over-tightening a screw into plastic cracks it.

3.8.3 Lubrication

A clean 2/83N slide usually runs smoothly dry. If it is stiff after cleaning, Faber-Castell recommends pure Vaseline or silicone oil — the tiniest amount, wiped onto the tongue-and-groove edges of the slide and then wiped off again so that only a film remains. Owners note that petroleum jelly helps only briefly and attracts dirt, so less is better. Never put oil or grease on the scale faces or the cursor, and never use penetrating oils or spray lubricants with solvent carriers.

3.8.4 Alignment

If the slide is loose or binds along its length, or the C and D scales do not meet the A/B and back scales at the same index, the two stator halves may have shifted. Loosen the end-brace screws a little at both ends, set the slide at zero, square the stator halves to the slide so the indexes line up on both faces, and tighten the screws evenly. A bent rule is a different matter: gentle warmth may tempt, but reshaping polystyrene by heat risks distorting the scales and is best left alone.

3.8.5 Storage

Keep the rule in its case, flat, at room temperature and out of sunlight; light fades the red figures first, and faded or low-contrast red markings are reported on some examples (Vorkoetter, readers’ reports). The clear case’s hinge pins can work loose — keep them, since replacements are not made. Store the booklet and card separately from the rule so that the paper does not trap moisture against the plastic.

Sources

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