A graduation is a marking used to indicate points on a visual

scale Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number ...

, which can be present on a

container A container is any receptacle or enclosure for holding a product used in storage, packaging, and transportation, including shipping. Things kept inside of a container are protected on several sides by being inside of its structure. The term ...

, a measuring device, or the axes of a

line plot A line chart or line graph or curve chart is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a sc ...

, usually one of many along a line or curve, each in the form of short line segments perpendicular to the line or curve. Often, some of these line segments are longer and marked with a numeral, such as every fifth or tenth graduation. The scale itself can be linear (the graduations are spaced at a constant distance apart) or nonlinear. Linear graduation of a scale occurs mainly (but not exclusively) on straight measuring devices, such as a

rule Rule or ruling may refer to: Education * Royal University of Law and Economics (RULE), a university in Cambodia Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pert ...

or measuring tape, using units such as

inch Measuring tape with inches The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelft ...

es or

millimetre 330px, Different lengths as in respect to the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 meter to 1 millimeter. The millimetre (American and British English spelling differences#-re, -er, ...

s. Graduations can also be spaced at varying spatial intervals, such as when using a

logarithmic Logarithmic can refer to: * Logarithm, a transcendental function in mathematics * Logarithmic scale, the use of the logarithmic function to describe measurements * Logarithmic spiral, * Logarithmic growth * Logarithmic distribution, a discrete pr ...

, for instance on a

measuring cup A measuring cup is a kitchen utensil used primarily to measure the volume of liquid or bulk solid cooking ingredients such as flour and sugar, especially for volumes from about 50 mL (2 fl oz) upwards. Measuring cups are also use ...

, can vary in scale due to the container's non-

cylindrical A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an in ...

shape.

Graduations along a curve

Circular graduations of a scale occur on a circular arc or

limb Limb may refer to: Science and technology * Limb (anatomy), an appendage of a human or animal *Limb, a large or main branch of a tree *Limb, in astronomy, the curved edge of the apparent disk of a celestial body, e.g. lunar limb *Limb, in botany, ...

of an instrument. In some cases, non-circular curves are graduated in instruments. A typical circular arc graduation is the division into angular measurements, such as degrees, minutes and seconds. These types of graduated markings are traditionally seen on devices ranging from

compasses A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses ...

and clock faces to alidades found on such instruments as

telescopes A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to obser ...

, theodolites, inclinometers,

astrolabes An astrolabe ( grc, ἀστρολάβος ; ar, ٱلأَسْطُرلاب ; persian, ستاره‌یاب ) is an ancient astronomical instrument that was a handheld model of the universe. Its various functions also make it an elaborate inclin ...

armillary spheres An armillary sphere (variations are known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (on the celestial sphere), consisting of a spherical framework of rings, centered on Earth or the Sun, that represent lines of ...

, and

celestial spheres The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed stars ...

. There can also be non-uniform graduations such as logarithmic or other scales such as seen on circular slide rules and graduated cylinders. Slide rule scales back

Manufacture of graduations

Graduations can be placed on an instrument by

etching Etching is traditionally the process of using strong acid or mordant to cut into the unprotected parts of a metal surface to create a design in intaglio (incised) in the metal. In modern manufacturing, other chemicals may be used on other type ...

, scribing or engraving,

painting Painting is the practice of applying paint, pigment, color or other medium to a solid surface (called the "matrix" or "support"). The medium is commonly applied to the base with a brush, but other implements, such as knives, sponges, and ai ...

printing Printing is a process for mass reproducing text and images using a master form or template. The earliest non-paper products involving printing include cylinder seals and objects such as the Cyrus Cylinder and the Cylinders of Nabonidus. The ...

or other means. For durability and accuracy, etched or scribed marks are usually preferable to surface coatings such as paints and inks. Markings can be a combination of both physical marks such as a scribed line and a paint or other marking material. For example, it is common for black ink or paint to fill the grooves cut in a scribed rule. Inexpensive plastic devices can be molded and painted or molded with two or more colors of plastic used. Some rather high-quality devices can be manufactured with plastic and reveal high-precision graduations. Graduations traditionally have been scribed into an instrument by hand with a sharp, hard

tool A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates ba ...

.Daumas, Maurice, ''Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers'', Portman Books, London 1989 Later developments in devices such as

dividing engine A dividing engine is a device employed to mark graduations on measuring instruments to allow for reading smaller measurements than can be allowed by directly engraving them. The well-known vernier scale and micrometer screw-gauge are classic exa ...

s allowed the process to be automated with greater precision. Modern devices can be stamped, cut on a

milling machine Milling is the process of machining using rotary cutters to remove material by advancing a cutter into a workpiece. This may be done by varying direction on one or several axes, cutter head speed, and pressure. Milling covers a wide variety of d ...

or with a

CNC Numerical control (also computer numerical control, and commonly called CNC) is the automated control of machining tools (such as drills, lathes, mills, grinders, routers and 3D printers) by means of a computer. A CNC machine processes a pie ...

machine. In the case of stamping, the master has the precision built into itself and the stamped device is as accurate as the stamping process allows. Similarly, molding of plastic can be as precise as the mold process. With proper concern for such effects as thermal expansion or contraction and shrinkage, the precision can be very high.

US graduation style

The US graduation style of an instrument was a Federal standard for codes used by manufacturers to quickly determine which types of scales are marked on the instrument. Other commonly recognized styles are:{{Citation needed, date=February 2019 * 30–1 mm, 0.5 mm *31–1 mm, 0.5 mm, 1/32″, 1/64″ *34–1 mm, 0.5 mm, 1/10″, 1/50″ *35–1 mm, 0.5 mm on both sides *35E—1 mm, 0.5 mm on both sides, plus mm on both ends on one side *36—1/32″ and 1 mm on one side; 1/64″ and 1 mm on other side *37–1 mm, 0.5 mm *37E—1 mm, 0.5 mm on both sides, plus mm on both ends on one side, Single row inch figure *E/M—edge 1: 1/10″, edge 2: 1/100″, edge 3: 1.0 mm, edge 4: 0.5 mm *3R—1/64″, 1/50″, 1/32″, 1/10″ * 4R—1/64″, 1/32″, 1/16″, 1/8″ * 5R—1/100″, 1/64″, 1/32″, 1/10″ * 6R—1/32″, 1/64″, 1/10″, 1/100″ * 7R—1/100″,1/64″, 1/32″, 1/16″ *9R—1/16″, 1/32″, 1/64″ *10R—1/32″, 1/64″ (quick-reading) *10R/D—1/64″, 1/32″, Decimal Equivalency Table Graduation * 12R—1/100″, 1/64″, 1/50″, 1/32″ * 16R—1/100″, 1/64″, 1/50″, 1/32″ Suffix key: * R = Rapid Read (32nd & 64th graduations marked with number values) * E = End Graduations (Graduations appear on end edge/edges) * ME = Metric/English (Metric units in preferred position) * E/M = English/Metric (English units in preferred position)

References

Measuring instruments Signage

Graduations along a curve

Manufacture of graduations

US graduation style

See also

References