Objective:
To multiply two values together using the W scales.
General:
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The W scales (root scales) are very powerful because these scales essentially double the natural length of the rule.
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Their combination gives increased precision.
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The Faber-Castell 63/83 and 2/83N are just two of the rules which had these scales. On some other rules, these scales may appear as R1 and R2.
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On the pocket version, Faber-Castell 63/83, W1 and W1' have the range 1 ≤ n ≤ 3.2, W2 and W2' the range 3.2 ≤ n ≤ 10.
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On the full-length Faber-Castell 2/83N, W1 and W1' have the range 0.9 ≤ n ≤ 3.5 and the W2 and W2' the range 2.8 ≤ n ≤ 11.
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Some practice is required to use these scales proficiently and although they are similar to the normal C and D scales, there are some differences in their operation.
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There are three indices on these scales; the black 1 and 10 and a red index. On the 63/83, the red index appears similar to the lower case i on W1' and W2 and an inverted lower case i on the W1 and W2' scales. On the 2/83N the red indices appear as a small upright triangle Δ on the W1 and W2' and as an inverted triangle on the W1' and W2 scales. These special indices are scaled at the square-root of ten.
Method:
There are two reasonably simple rules to remember when operating with these scales.
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If the setting is carried out using the black indices, the product is found on the body scale adjacent to the second factor.
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If the setting is carried out using the red indices, the product is found on the body scale opposite the second factor.
Example 1: Calculate 1.2 x 2.5
The setting is made with the black index, so the product is read off the body scale adjacent to the second factor.
Example 2: Calculate 1.4 x 3.6
The setting is made with the black index, so the product is read off the body scale adjacent to the second factor.
Example 3: Calculate 14 x 8.5
- Align the red index on W1' with W1:1.4
- Move the cursor to W2':8.5
- Read the result W1:119
The setting is made with the red index, so the product is read off the body scale opposite the second factor.
Example 4: Calculate 7 x 1.2
Method (a)
The setting is made with the black index, so the product is read off the body scale adjacent to the second factor.
Method (b)
The setting is made with the red index, so the product is read off the body scale opposite the second factor.
Example 5: Calculate 0.35 x 0.55
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Align W2:0.35 with the red index on W2'
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Move the cursor to W2':5.5
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Read the result W1:0.1925
The setting is made with the red index, so the product is read off the body scale opposite the second factor.
Example 6: Calculate 260 x 87.5
The setting is made with the red index, so the product is read off the body scale opposite the second factor.
On the larger 2/83N it is actually possible to read the result 227500.
Practice Questions: Calculate the following products. (The answers are calculated using the 63/83.)
- 14.5 x 5.75 (Ans: 83.4)
- 2.61 x 7.2 (Ans: 18.8)
- 2960 x 46.5 (Ans: 137600)
- 1.95 x 16 (Ans: 31.2)
- 18.5 x 0.073 (Ans: 1.35)
