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List of Scales and Scale Marks: Difference between revisions
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(Created page with "Slide rules consist of a set of analogue Scales which are set against one another to perform operations. Many scales exist and have different functions. Most slide rules also have marks that denote particular values that aid in calculations. Below is a list of common scales and marks on most slide rules. ==Scales== The primary scales of a slide rule are C and D. unless otherwise specified, other scales are related to ("keyed" to) them. When...") |
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Slide rules consist of a set of analogue [[Scales (Slide Rule)|Scales]] which are set against one another to perform operations. Many scales exist and have different functions. Most slide rules also have marks that denote particular values that aid in calculations. Below is a list of | Slide rules consist of a set of analogue [[Scales (Slide Rule)|Scales]] which are set against one another to perform operations. Many scales exist and have different functions. Most slide rules also have marks that denote particular values that aid in calculations. Below is a list of scales and marks on many slide rules. While most common scales and marks have standardized names, rarer elements may not have such standards, and alternate names will be given. | ||
==Scales== | ==Scales== | ||
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|Body, usually same side as A and B on duplex rules | |Body, usually same side as A and B on duplex rules | ||
|"three decade" scale, from 1 to 1000 in one line. Unlike A, does not usually have companion scales. | |"three decade" scale, from 1 to 1000 in one line. Unlike A, does not usually have companion scales. | ||
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|R (√, W/W') | |||
|Square root scale (√x) | |||
|Body, usually on the same side as A | |||
|the relationship R:C is the same as the relationship C:B, any numbers on R will have their associated square on C. This scale is necessarily split at √10 into two halves, usually right next to each other. On certain specialty rules which forego A and B, this scale is duplicated and set adjacent to each other just like C and D, which allow for the accuracy of a double length slide rule in a smaller package. In these cases, it is often called "W<sub>1/2</sub>" on the body and "W'<sub>1/2</sub>" on the slide. When used in conjunction with A or B, it can act to easily find 4th powers. | |||
|- | |||
|∛ | |||
|Cube root scale (∛x) | |||
|Body, usually on the same side as K | |||
|The relationship ∛:C is the same as the relationship C:K, any number on the cube root scale will have its cube on C. This scale is necessarily split into three parts, at ∛10 and ∛100 respectively. Using this in combination with other power scales allow for various exponents, such as 6th powers or 9th powers with a single setting. | |||
|- | |- | ||
|DF | |DF | ||
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|Lower body or center of slide (with other trig scales) | |Lower body or center of slide (with other trig scales) | ||
|The first, and most common of the trig scales. Trig scales generally are read by finding the angle (in degrees) on the trig scale, then reading the associated value on C or D. The S scale has a range from 5.7° (0.1 radians) to 90°, either in DMS or decimal degrees. Sine (and cosine) is always less than or equal to 1, so all readings on C and D are the decimal portion. | |The first, and most common of the trig scales. Trig scales generally are read by finding the angle (in degrees) on the trig scale, then reading the associated value on C or D. The S scale has a range from 5.7° (0.1 radians) to 90°, either in DMS or decimal degrees. Sine (and cosine) is always less than or equal to 1, so all readings on C and D are the decimal portion. | ||
|- | |||
|<span style="color:red">Cos</span> | |||
|cosine scale (arccos(x)) | |||
|marked on same divisions as S | |||
|for convenience, S scales often have the complements of their values printed in red to allow for easy reading of cosine values. | |||
|- | |- | ||
|T | |T | ||
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|usually next to T | |usually next to T | ||
|In some cases, a separate T scale from 45° to 84.3° will be provided which can be read with the C or D scales. | |In some cases, a separate T scale from 45° to 84.3° will be provided which can be read with the C or D scales. | ||
|- | |||
|P | |||
|Pythagorean scale (√(1-x²)) | |||
|often directly adjacent to S | |||
|Popular on European rules, most commonly the Darmstadt simplex layout. Allows for higher precision of both cosine and sine values in the more cramped range of the S scale. Functions as its own inverse, so can be used in flexible ways. | |||
|- | |||
|S<sub>a</sub> (S) | |||
|Sine scale (arcsin(x²)) | |||
|commonly on the back of the slide of Mannheim rules | |||
|A combination of S and ST which is keyed to the A scale, meaning values are read on A instead of C. This allowed for an extended low range that eliminated the need for an ST scale, at the cost of some precision in the high range. | |||
|- | |||
|Sh | |||
|Hyperbolic Sine scale (asinh(x)) | |||
|uncommon, usually near LL scales | |||
|Set up such that reading the argument on Sh gives the result on C or D. Usually split into two scales adjacent to one another for higher accuracy. for an argument a > 3, sinh(a)≈e<sup>a</sup>/2, which can be found on the LL scales with the further approximation sinh(a)≈exp(a-0.7). Can be used with Th to calculate Cosh(x) | |||
|- | |||
|Th | |||
|Hyperbolic Tangent scale (atanh(x)) | |||
|Usually adjacent to Sh | |||
|Often found in pairings with Sh. Similarly set up such that the argument read on Th has result on C or D. Can be used to calculate Cosh(x) with the formula sinh(x)/tanh(x)=cosh(x) | |||
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