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The Slide Rule Canon
The notion of a canon is that of an elite subgroup that represents the best, or the essential that the group has to offer. Traditionally, the term has applied to works of literature that are considered the basis for a classical, or liberal, education in the Arts. In a theological context, it generally denotes those elements of ancient scripture that have been determined to represent relevatory information of a Divine nature. Of late, the term has found application in other areas, and I have been inspired to take a stab at forming a Canon for the "Slide Rule Arts". Admittedly, this undertaking has a bit of a 'half-baked' quality. Please be encouraged to make suggestions for additions, categories or to offer argument for the deletion of an item that has already been elevated here.
Classification of Slide Rules
Canonical Slide Rules
A Slide Rule Primer
- Classification of Slide Rules -
"Basic" Slide Rules
A Basic Slide Rule is typically a linear design, although it might be circular or otherwise. It has several scales, probably seven or less, the majority of which are graded logarithmically in a range from 1 to 10 (although the ten is almost universally represented by a '1', signifying the relativity of the decimal point reference). These scales are traditionally designated 'C' (on the slide), and 'D' (stator). Variations of these are common, especially the 'CI' scale, which is simply the 'C' scale running backwards to provide reciprocal (I is for "inverse") of the number indicated on C (and D if the C and D scales are aligned, or "registered"). There may also be "square" scales with a two-decade range (1 - 100) to facilitate the calculation of squares of numbers (traditionally designated 'A' and 'B', they are usually paired across the stator-slide interface) and, often, a "cube" scale, or three-decade logarithmic scale that will be the cube of whatever number is indicated on the single-decade scale (typically designated 'K').
The next level of complexity is usually achieved by adding trigonometric capability. Such rules will have 12-15 number of scales. SOme of the increase is due to duplication of the C and D scales on the back of the rule as the trig rule will ofter be duplex and the basic, simplex.
"Log Log" Slide Rules
I'm going to have to go soon, so this is sort of petering out. But adding 3-4 decades of log log and inverse log log sclaes gets us into the next category. This is your typical "technical professional" slide rule.
- Canonical Slide Rules -
K+E Log Log Duplex Decitrig
Dietzgen Decimal Trig Type Log Log Slide Rule
- Slide Rule Primer -
Part One: Slide Rule Types
Complexity- Except for special purpose rules (such as electrical), about 99% of all slide rules are the same with different levels of complexity or number of scales. The most basic type has a C, D, A, B, CI, CIF, etc. scales which are variations on the log scale and for multiplying and dividing numbers. Usually there is an L scale which is a linear scale that corresponds to the base 10 log of the other scales (which are logarithmic). The next level is the trig rule which typically has sine, tangent and another "st" scale that is for both functions at small angles. The next level is the log-log which are base "e" logs of the base 10 log scale (hence "log-log") and are nice for taking powers, roots of arbitrary values. And that's pretty much it. Some rules have hyperbolic scales on top of all that.
The basic rule will usually be one-sided. The archetype is the "Mannheim" (named after a French Army officer that designed it) which may be one-sided but usually is a sort of "quasi-duplex" or (I think there's a word for this type but I don't know what it is) a sort of ruler shape with a beveled edge for a measuring scale and where most of the scales are on the top but a few are on the back of the slide. For an example, look at the Post 1452 under "Quality "Pre-owned" Rules: - Frederick Post" on my webpage. Almost ALL log-log rules are duplex with 20 or more scales.
Materials: Wood is certainly the nicest aesthetically but worst for aging. Plastic is durable and ages well (except the early plastics like cellulose nitrate that K+E built all of their cursors with in the 30's; they're all falling apart now). But generally, plastic is a good practical material. And some plastic rules, especially the later (50' - 60's) K+E are very pretty. Pickett made their first rules of magnesium but it doesn't age well; it oxidizes and bubbles form under the paint and the whole thing becomes hard to read. They switched to aluminum in the 60's (or thereabouts) and it does oxidize, but more slowly. To some extent, rule composition dictates cursor as well: wood rules will tend to have glass cursors, plastic and aluminum will have plastic. Plastic is more durable but softer and hence more prone to scratching, but this isn't usually much of a problem with a well-cared-for rule.
Length: "standard" rules are 10" or 25 cm. (scale length, overall rule length will be greater and vary somewhat depending on the rule). Other common lengths include 5" (half the resolution of 10") and 20" (with double resolution of the standard). K+E used a suffix to denote the scale length: a "-3" was used for 10 inch. "-5" for 20 inch and "-1" for 5 inch. The less common 8 and 16 inch versions were denoted by "-2" and "-4", respectively.
Part Two: How Slide Rules Multiply
Well, you see, um, usually a girl slide rule and a boy slide rule find a quiet desk drawer. Then the ... oh no! never mind... this is what I wanted to say:
Multiplication and Division: Slide rules, as the name suggests, are rules that slide. The rules measure distances using logarithmic scales. The numbers on a logarithmic scale correspond to the numbers on a linear scale in the following way - the logarithm is the exponent to which a certain "base" number must be raised to realize the number on the linear scale. The base can be any number. The most common base is 10, in fact, logarithms based on 10 are called "common logarithms". But any number will work, as long as it is used consistently. For example, the number 3 is the base 2 log of 8 - since 2x2x2 = 8. The base 2 log of 16 is 4, etc.
And you thought I was going to tell you how to multiply with a slide rule. Actually, I want to explain HOW a slide rule multiplies, and logarithms are the key. You see, they enable us to multiply numbers by adding their lengths together - to multiply 4x8, we align the end of segment of length 4 with the beginning of a segment of length 8. Normally, we would expect the combined length of the two segments to be the sum of their individual lengths, or 12. Instead, it is a case of the "whole is greater that the sum of it's parts", but in a different way than is normally meant by the phrase. Because the distance proportions of the scales correspond to the logarithms of the numbers imprinted on them, we are adding their logarithmic, not linear lengths. In our example above, the length of 8 would be it's log, or 3. The length of 16 would be 4. Adding 3+4 yields 7. You don't read a 7, but it's antilog, 2 to the 7th power, or 128, the product of 8 and 16. It works with all of the numbers in between the integers, as well. I'm using integers here because it makes it easier to see - fractional powers are less intuitive.
And that's all that there is to it! Division works the same way, only in reverse, To divide, you subtract the length of the divisor from the dividend to obtain the quotient.
Part Three: Log of Logs
To be continued ...
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