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In most projections, scale varies with latitude, so on small scale maps, covering large areas and a wide range of latitudes, the linear scale must show the scale for the range of latitudes covered by the map. One of these is shown below. Since most nautical charts are constructed using the Mercator projection whose scale varies substantially ...
Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each unit of length is a multiple of some base value raised to a power, and corresponds to the multiplication of the previous value in the scale by the base value. In common use, logarithmic scales are in base 10 (unless otherwise specified).
Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right). In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes.
For example, aligning the rightmost 1 on the C scale with 2 on the LL2 scale, 3 on the C scale lines up with 8 on the LL3 scale. To extract a cube root using a slide rule with only C/D and A/B scales, align 1 on the B cursor with the base number on the A scale (taking care as always to distinguish between the lower and upper halves of the A scale).
A vernier scale (/ v ə r ˈ n iː ˈ ə r / ver-NEE-er), named after Pierre Vernier, is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation, thereby increasing resolution and reducing measurement uncertainty by using vernier acuity to reduce human
A description of linear interpolation can be found in the ancient Chinese mathematical text called The Nine Chapters on the Mathematical Art (九章算術), [1] dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. The basic operation of linear interpolation between two values is commonly used in computer graphics.
The vernier scales may include metric measurements on the lower part of the scale and inch measurements on the upper, or vice versa, in countries that use inches. Vernier calipers commonly used in industry provide a precision to 0.01 mm (10 micrometres ), or one thousandth of an inch.
In slide rule terminology, "folded" means a scale that starts and finishes at values offset from a power of 10. Often folded scales start at π but may be extended lengthways to, say, 3.0 and 35.0. Folded scales with the code subscripted with "M" start and finish at log 10 e to simplify conversion between base-10 and natural logarithms. When ...