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69-404: Sidereal time ("sidereal" pronounced / s aɪ ˈ d ɪər i əl , s ə -/ sy- DEER -ee-əl, sə- ) is a system of timekeeping used especially by astronomers . Using sidereal time and the celestial coordinate system , it is easy to locate the positions of celestial objects in the night sky . Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to

138-399: A r c s e c ) . {\displaystyle d(\mathrm {pc} )=1/p(\mathrm {arcsec} ).} For example, the distance to Proxima Centauri is 1/0.7687 = 1.3009 parsecs (4.243 ly). On Earth, a coincidence rangefinder or parallax rangefinder can be used to find distance to a target. In surveying , the problem of resection explores angular measurements from

207-440: A graticule , not in actual contact with the display on an oscilloscope , etc. When viewed through a stereo viewer, aerial picture pair offers a pronounced stereo effect of landscape and buildings. High buildings appear to "keel over" in the direction away from the center of the photograph. Measurements of this parallax are used to deduce the height of the buildings, provided that flying height and baseline distances are known. This

276-442: A boy". In a philosophic/geometric sense: an apparent change in the direction of an object, caused by a change in observational position that provides a new line of sight. The apparent displacement, or difference of position, of an object, as seen from two different stations, or points of view. In contemporary writing, parallax can also be the same story, or a similar story from approximately the same timeline, from one book, told from

345-499: A complete year the number of sidereal "days" is one more than the number of solar days. Solar time is measured by the apparent diurnal motion of the Sun. Local noon in apparent solar time is the moment when the Sun is exactly due south or north (depending on the observer's latitude and the season). A mean solar day (what we normally measure as a "day") is the average time between local solar noons ("average" since this varies slightly over

414-691: A different perspective in another book. The word and concept feature prominently in James Joyce 's 1922 novel, Ulysses . Orson Scott Card also used the term when referring to Ender's Shadow as compared to Ender's Game . The metaphor is invoked by Slovenian philosopher Slavoj Žižek in his 2006 book The Parallax View , borrowing the concept of "parallax view" from the Japanese philosopher and literary critic Kojin Karatani . Žižek notes The philosophical twist to be added (to parallax), of course,

483-508: A greater stellar distance, useful distances can be measured only for stars which are near enough to have a parallax larger than a few times the precision of the measurement. In the 1990s, for example, the Hipparcos mission obtained parallaxes for over a hundred thousand stars with a precision of about a milliarcsecond , providing useful distances for stars out to a few hundred parsecs. The Hubble Space Telescope 's Wide Field Camera 3 has

552-480: A known baseline for determining an unknown point's coordinates. The most important fundamental distance measurements in astronomy come from trigonometric parallax, as applied in the stellar parallax method . As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in an isosceles triangle , with 2 AU (the distance between

621-408: A ruler marked on its top surface, the thickness of the ruler will separate its markings from the ticks. If viewed from a position not exactly perpendicular to the ruler, the apparent position will shift and the reading will be less accurate than the ruler is capable of. A similar error occurs when reading the position of a pointer against a scale in an instrument such as an analog multimeter . To help

690-403: A sidereal day lasting about 243.0 Earth days, or about 1.08 times its orbital period of 224.7 Earth days; hence by the retrograde formula its solar day is about 116.8 Earth days, and it has about 1.9 solar days per orbital period. By convention, rotation periods of planets are given in sidereal terms unless otherwise specified. Timekeeper A timekeeper is a person who measures time with

759-475: A similar magnitude range, a mean parallax can be derived from statistical analysis of the proper motions relative to their radial velocities. This statistical parallax method is useful for measuring the distances of bright stars beyond 50 parsecs and giant variable stars , including Cepheids and the RR Lyrae variables . The motion of the Sun through space provides a longer baseline that will increase

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828-526: A star catalog, the time when the star should have passed through the meridian of the observatory was computed, and a correction to the time kept by the observatory clock was computed. Sidereal time was defined such that the March equinox would transit the meridian of the observatory at 0 hours local sidereal time. Beginning during the 1970s, the radio astronomy methods very-long-baseline interferometry (VLBI) and pulsar timing overtook optical instruments for

897-515: A velocity relative to the Sun that causes proper motion (transverse across the sky) and radial velocity (motion toward or away from the Sun). The former is determined by plotting the changing position of the stars over many years, while the latter comes from measuring the Doppler shift of the star's spectrum caused by motion along the line of sight. For a group of stars with the same spectral class and

966-466: A workforce so that a business can then make operational decisions to increase productivity and reduce labor costs. This standards - or measurement -related article is a stub . You can help Misplaced Pages by expanding it . This time -related article is a stub . You can help Misplaced Pages by expanding it . Parallax Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and

1035-503: A year). Earth makes one rotation around its axis each sidereal day; during that time it moves a short distance (about 1°) along its orbit around the Sun. So after a sidereal day has passed, Earth still needs to rotate slightly more before the Sun reaches local noon according to solar time. A mean solar day is, therefore, nearly 4 minutes longer than a sidereal day. The stars are so far away that Earth's movement along its orbit makes nearly no difference to their apparent direction (except for

1104-399: Is a key component of the process of photogrammetry . Parallax error can be seen when taking photos with many types of cameras, such as twin-lens reflex cameras and those including viewfinders (such as rangefinder cameras ). In such cameras, the eye sees the subject through different optics (the viewfinder, or a second lens) than the one through which the photo is taken. As the viewfinder

1173-403: Is a need to maintain definitions for sidereal time during the transition, and when working with older data and documents. Similarly to mean solar time, every location on Earth has its own local sidereal time (LST), depending on the longitude of the point. Since it is not feasible to publish tables for every longitude, astronomical tables use Greenwich sidereal time (GST), which is sidereal time on

1242-467: Is a special case of the principle of triangulation , which states that one can solve for all the sides and angles in a network of triangles if, in addition to all the angles in the network, the length of at least one side has been measured. Thus, the careful measurement of the length of one baseline can fix the scale of an entire triangulation network. In parallax, the triangle is extremely long and narrow, and by measuring both its shortest side (the motion of

1311-465: Is also an issue in image stitching , such as for panoramas. Parallax affects sighting devices of ranged weapons in many ways. On sights fitted on small arms and bows , etc., the perpendicular distance between the sight and the weapon's launch axis (e.g. the bore axis of a gun)—generally referred to as " sight height "—can induce significant aiming errors when shooting at close range, particularly when shooting at small targets. This parallax error

1380-615: Is compensated for (when needed) via calculations that also take in other variables such as bullet drop , windage , and the distance at which the target is expected to be. Sight height can be used to advantage when "sighting in" rifles for field use. A typical hunting rifle (.222 with telescopic sights) sighted in at 75m will still be useful from 50 to 200 m (55 to 219 yd) without needing further adjustment. In some reticled optical instruments such as telescopes , microscopes or in telescopic sights ("scopes") used on small arms and theodolites , parallax can create problems when

1449-449: Is exploited also in wiggle stereoscopy , computer graphics that provide depth cues through viewpoint-shifting animation rather than through binocular vision. Parallax arises due to a change in viewpoint occurring due to the motion of the observer, of the observed, or both. What is essential is relative motion. By observing parallax, measuring angles , and using geometry , one can determine distance . Distance measurement by parallax

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1518-434: Is fixed with respect to extra-galactic radio sources. Because of the great distances, these sources have no appreciable proper motion .) In this frame of reference, Earth's rotation is close to constant, but the stars appear to rotate slowly with a period of about 25,800 years. It is also in this frame of reference that the tropical year (or solar year), the year related to Earth's seasons, represents one orbit of Earth around

1587-405: Is known as stereopsis . In computer vision the effect is used for computer stereo vision , and there is a device called a parallax rangefinder that uses it to find the range, and in some variations also altitude to a target. A simple everyday example of parallax can be seen in the dashboards of motor vehicles that use a needle-style mechanical speedometer . When viewed from directly in front,

1656-433: Is measured by the angle or half-angle of inclination between those two lines. Due to foreshortening , nearby objects show a larger parallax than farther objects, so parallax can be used to determine distances. To measure large distances, such as the distance of a planet or a star from Earth , astronomers use the principle of parallax. Here, the term parallax is the semi-angle of inclination between two sight-lines to

1725-408: Is often found above the lens of the camera, photos with parallax error are often slightly lower than intended, the classic example being the image of a person with their head cropped off. This problem is addressed in single-lens reflex cameras , in which the viewfinder sees through the same lens through which the photo is taken (with the aid of a movable mirror), thus avoiding parallax error. Parallax

1794-417: Is one fewer solar day per year than there are sidereal days, similar to an observation of the coin rotation paradox . This makes a sidereal day approximately ⁠ 365.24 / 366.24 ⁠ times the length of the 24-hour solar day. Earth's rotation is not a simple rotation around an axis that remains always parallel to itself. Earth's rotational axis itself rotates about a second axis, orthogonal to

1863-483: Is that the observed distance is not simply "subjective", since the same object that exists "out there" is seen from two different stances or points of view. It is rather that, as Hegel would have put it, subject and object are inherently "mediated" so that an " epistemological " shift in the subject's point of view always reflects an " ontological " shift in the object itself. Or—to put it in Lacanese —the subject's gaze

1932-569: Is the Julian UT1 date (JD) minus 2451545.0. The linear coefficient represents the Earth's rotation speed around its own axis. ERA replaces Greenwich Apparent Sidereal Time (GAST). The origin on the celestial equator for GAST, termed the true equinox , does move, due to the movement of the equator and the ecliptic. The lack of motion of the origin of ERA is considered a significant advantage. The ERA may be converted to other units; for example,

2001-726: Is the Earth Rotation Angle, E PREC is the accumulated precession, and E 0 is equation of the origins, which represents accumulated precession and nutation. The calculation of precession and nutation was described in Chapter 6 of Urban & Seidelmann. As an example, the Astronomical Almanac for the Year 2017 gave the ERA at 0 h 1 January 2017 UT1 as 100° 37′ 12.4365″. The GAST was 6 h 43 m 20.7109 s. For GMST

2070-441: The Astronomical Almanac for the Year 2017 tabulated it in degrees, minutes, and seconds. As an example, the Astronomical Almanac for the Year 2017 gave the ERA at 0 h 1 January 2017 UT1 as 100° 37′ 12.4365″. Since Coordinated Universal Time (UTC) is within a second or two of UT1, this can be used as an anchor to give the ERA approximately for a given civil time and date. Although ERA is intended to replace sidereal time, there

2139-689: The Celestial Ephemeris Origin , that has no instantaneous motion along the equator; it was originally referred to as the non-rotating origin . This point is very close to the equinox of J2000. ERA, measured in radians , is related to UT1 by a simple linear relation: θ ( t U ) = 2 π ( 0.779 057 273 2640 + 1.002 737 811 911 354 48 ⋅ t U ) {\displaystyle \theta (t_{U})=2\pi (0.779\,057\,273\,2640+1.002\,737\,811\,911\,354\,48\cdot t_{U})} where t U

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2208-531: The IERS Reference Meridian , less precisely termed the Greenwich, or Prime meridian . There are two varieties, mean sidereal time if the mean equator and equinox of date are used, and apparent sidereal time if the apparent equator and equinox of date are used. The former ignores the effect of astronomical nutation while the latter includes it. When the choice of location is combined with

2277-465: The celestial equator , from the observer's meridian to the great circle that passes through the March equinox (the northern hemisphere's vernal equinox) and both celestial poles , and is usually expressed in hours, minutes, and seconds. (In the context of sidereal time, "March equinox" or "equinox" or "first point of Aries" is currently a direction, from the center of the Earth along the line formed by

2346-477: The fixed stars ". Viewed from the same location , a star seen at one position in the sky will be seen at the same position on another night at the same time of day (or night), if the day is defined as a sidereal day (also known as the sidereal rotation period ). This is similar to how the time kept by a sundial ( Solar time ) can be used to find the location of the Sun . Just as the Sun and Moon appear to rise in

2415-423: The ERA is a full rotation of the Earth. A sidereal day on Earth is approximately 86164.0905 seconds (23 h 56 min 4.0905 s or 23.9344696 h). (Seconds are defined as per International System of Units and are not to be confused with ephemeris seconds .) Each day, the sidereal time at any given place and time will be about four minutes shorter than local civil time (which is based on solar time), so that for

2484-475: The Sun, there is only a small difference between the length of the sidereal day and that of the solar day – the ratio of the former to the latter never being less than Earth's ratio of 0.997. But the situation is quite different for Mercury and Venus. Mercury's sidereal day is about two-thirds of its orbital period, so by the prograde formula its solar day lasts for two revolutions around the Sun – three times as long as its sidereal day. Venus rotates retrograde with

2553-407: The Sun. The precise definition of a sidereal day is the time taken for one rotation of Earth in this precessing frame of reference. During the past, time was measured by observing stars with instruments such as photographic zenith tubes and Danjon astrolabes, and the passage of stars across defined lines would be timed with the observatory clock. Then, using the right ascension of the stars from

2622-524: The accuracy of parallax measurements, known as secular parallax . For stars in the Milky Way disk, this corresponds to a mean baseline of 4 AU per year, while for halo stars the baseline is 40 AU per year. After several decades, the baseline can be orders of magnitude greater than the Earth–Sun baseline used for traditional parallax. However, secular parallax introduces a higher level of uncertainty because

2691-447: The assistance of a clock or a stopwatch . In addition, a timekeeper records time, time taken, or time remaining during events such as sports matches. Along with the game clock , a timekeeper may be needed to manage clocks other gameplay clocks, including play clocks , pitch clocks , and shot clocks . In business, a timekeeper tracks employee time, potentially using a time clock . Collecting such data gives employers insight into

2760-767: The choice of including astronomical nutation or not, the acronyms GMST, LMST, GAST, and LAST result. The following relationships are true: The new definitions of Greenwich mean and apparent sidereal time (since 2003, see above) are: G M S T ( t U , t ) = θ ( t U ) − E P R E C ( t ) {\displaystyle \mathrm {GMST} (t_{U},t)=\theta (t_{U})-E_{\mathrm {PREC} }(t)} G A S T ( t U , t ) = θ ( t U ) − E 0 ( t ) {\displaystyle \mathrm {GAST} (t_{U},t)=\theta (t_{U})-E_{0}(t)} such that θ

2829-462: The deviation of the object from sphericity. Binary stars which are both visual and spectroscopic binaries also can have their distance estimated by similar means, and do not suffer from the above geometric uncertainty. The common characteristic to these methods is that a measurement of angular motion is combined with a measurement of the absolute velocity (usually obtained via the Doppler effect ). The distance estimate comes from computing how far

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2898-500: The distance obtained for the Hyades has historically been an important step in the distance ladder. Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a supernova remnant or planetary nebula , can be observed over time, then an expansion parallax distance to that cloud can be estimated. Those measurements however suffer from uncertainties in

2967-423: The east and set in the west due to the rotation of Earth, so do the stars. Both solar time and sidereal time make use of the regularity of Earth's rotation about its polar axis: solar time is reckoned according to the position of the Sun in the sky while sidereal time is based approximately on the position of the fixed stars on the theoretical celestial sphere. More exactly, sidereal time is the angle, measured along

3036-539: The extreme positions of Earth's orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal-length legs. The amount of shift is quite small, even for the nearest stars, measuring 1 arcsecond for an object at 1 parsec's distance (3.26 light-years ), and thereafter decreasing in angular amount as the distance increases. Astronomers usually express distances in units of parsecs (parallax arcseconds); light-years are used in popular media. Because parallax becomes smaller for

3105-463: The fixed stars, completing one revolution in about 25,800 years, so the misnamed "sidereal" day ("sidereal" is derived from the Latin sidus meaning "star") is 0.0084 seconds shorter than the stellar day , Earth's actual period of rotation relative to the fixed stars. The slightly longer stellar period is measured as the Earth rotation angle (ERA), formerly the stellar angle. An increase of 360° in

3174-1116: The focus of the target image at varying distances into the same optical plane of the reticle (or vice versa). Many low-tier telescopic sights may have no parallax compensation because in practice they can still perform very acceptably without eliminating parallax shift. In this case, the scope is often set fixed at a designated parallax-free distance that best suits their intended usage. Typical standard factory parallax-free distances for hunting scopes are 100  yd (or 90 m) to make them suited for hunting shots that rarely exceed 300  yd/m. Some competition and military-style scopes without parallax compensation may be adjusted to be parallax free at ranges up to 300  yd/m to make them better suited for aiming at longer ranges. Scopes for guns with shorter practical ranges, such as airguns , rimfire rifles , shotguns , and muzzleloaders , will have parallax settings for shorter distances, commonly 50 m (55 yd) for rimfire scopes and 100 m (110 yd) for shotguns and muzzleloaders. Airgun scopes are very often found with adjustable parallax, usually in

3243-407: The form of an adjustable objective (or "AO" for short) design, and may adjust down to as near as 3 metres (3.3 yd). Non-magnifying reflector or "reflex" sights can be theoretically "parallax free". But since these sights use parallel collimated light this is only true when the target is at infinity. At finite distances, eye movement perpendicular to the device will cause parallax movement in

3312-399: The formula for a retrograde rotation, the operator of the denominator will be a plus sign (put another way, in the original formula the length of the sidereal day must be treated as negative). This is due to the solar day being shorter than the sidereal day for retrograde rotation, as the rotation of the planet would be against the direction of orbital motion. If a planet rotates prograde, and

3381-886: The hour and minute were the same but the second was 21.1060. If a certain interval I is measured in both mean solar time (UT1) and sidereal time, the numerical value will be greater in sidereal time than in UT1, because sidereal days are shorter than UT1 days. The ratio is: I m e a n s i d e r e a l I U T 1 = r ′ = 1.002 737 379 093 507 95 + 5.9006 × 10 − 11 t − 5.9 × 10 − 15 t 2 {\displaystyle {\frac {I_{\mathrm {mean\,sidereal} }}{I_{\mathrm {UT1} }}}=r'=1.002\,737\,379\,093\,507\,95+5.9006\times 10^{-11}t-5.9\times 10^{-15}t^{2}} such that t represents

3450-416: The intersection of the Earth's equator and the Earth's orbit around the Sun, toward the constellation Pisces; during ancient times it was toward the constellation Aries.) Common time on a typical clock (using mean Solar time ) measures a slightly longer cycle, affected not only by Earth's axial rotation but also by Earth's orbit around the Sun. The March equinox itself precesses slowly westward relative to

3519-493: The most precise astrometry . This resulted in the determination of UT1 (mean solar time at 0° longitude) using VLBI, a new measure of the Earth Rotation Angle, and new definitions of sidereal time. These changes became effective 1 January 2003. The Earth rotation angle ( ERA ) measures the rotation of the Earth from an origin on the celestial equator, the Celestial Intermediate Origin , also termed

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3588-432: The nearest stars if measured with extreme accuracy; see parallax ), and so they return to their highest point at the same time each sidereal day. Another way to understand this difference is to notice that, relative to the stars, as viewed from Earth, the position of the Sun at the same time each day appears to move around Earth once per year. A year has about 36 5 .24 solar days but 36 6 .24 sidereal days. Therefore, there

3657-453: The number of Julian centuries elapsed since noon 1 January 2000 Terrestrial Time . Six of the eight solar planets have prograde rotation—that is, they rotate more than once per year in the same direction as they orbit the Sun, so the Sun rises in the east. Venus and Uranus , however, have retrograde rotation. For prograde rotation, the formula relating the lengths of the sidereal and solar days is: or, equivalently: When calculating

3726-408: The object must be to make its observed absolute velocity appear with the observed angular motion. Measurements made by viewing the position of some marker relative to something to be measured are subject to parallax error if the marker is some distance away from the object of measurement and not viewed from the correct position. For example, if measuring the distance between two ticks on a line with

3795-433: The observer) and the small top angle (always less than 1  arcsecond , leaving the other two close to 90  degrees), the length of the long sides (in practice considered to be equal) can be determined. In astronomy, assuming the angle is small, the distance to a star (measured in parsecs ) is the reciprocal of the parallax (measured in arcseconds ): d ( p c ) = 1 / p (

3864-406: The plane of Earth's orbit, taking about 25,800 years to perform a complete rotation. This phenomenon is termed the precession of the equinoxes . Because of this precession, the stars appear to move around Earth in a manner more complicated than a simple constant rotation. For this reason, to simplify the description of Earth's orientation in astronomy and geodesy , it was conventional to chart

3933-497: The positions of the stars in the sky according to right ascension and declination , which are based on a frame of reference that follows Earth's precession, and to keep track of Earth's rotation, through sidereal time, relative to this frame as well. (The conventional reference frame, for purposes of star catalogues, was replaced in 1998 with the International Celestial Reference Frame , which

4002-463: The potential to provide a precision of 20 to 40 micro arcseconds, enabling reliable distance measurements up to 5,000 parsecs (16,000 ly) for small numbers of stars. The Gaia space mission provided similarly accurate distances to most stars brighter than 15th magnitude. Distances can be measured within 10% as far as the Galactic Center , about 30,000 light years away. Stars have

4071-435: The process by which the brain exploits the parallax due to the different views from the eye to gain depth perception and estimate distances to objects. Animals also use motion parallax , in which the animals (or just the head) move to gain different viewpoints. For example, pigeons (whose eyes do not have overlapping fields of view and thus cannot use stereopsis) bob their heads up and down to see depth. The motion parallax

4140-463: The relative velocity of observed stars is an additional unknown. When applied to samples of multiple stars, the uncertainty can be reduced; the uncertainty is inversely proportional to the square root of the sample size. Moving cluster parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster. Only open clusters are near enough for this technique to be useful. In particular

4209-416: The resultant apparent "floating" movements of the reticle over the target image when the user moves his/her head/eye laterally (up/down or left/right) behind the sight, i.e. an error where the reticle does not stay aligned with the user's optical axis . Some firearm scopes are equipped with a parallax compensation mechanism, which consists of a movable optical element that enables the optical system to shift

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4278-568: The reticle image in exact relationship to the eye position in the cylindrical column of light created by the collimating optics. Firearm sights, such as some red dot sights , try to correct for this via not focusing the reticle at infinity, but instead at some finite distance, a designed target range where the reticle will show very little movement due to parallax. Some manufacturers market reflector sight models they call "parallax free", but this refers to an optical system that compensates for off axis spherical aberration , an optical error induced by

4347-460: The reticle is not coincident with the focal plane of the target image. This is because when the reticle and the target are not at the same focus, the optically corresponded distances being projected through the eyepiece are also different, and the user's eye will register the difference in parallaxes between the reticle and the target (whenever eye position changes) as a relative displacement on top of each other. The term parallax shift refers to

4416-477: The sidereal day exactly equals the orbital period, then the formula above gives an infinitely long solar day ( division by zero ). This is the case for a planet in synchronous rotation ; in the case of zero eccentricity, one hemisphere experiences eternal day, the other eternal night, with a "twilight belt" separating them. All the solar planets more distant from the Sun than Earth are similar to Earth in that, since they experience many rotations per revolution around

4485-406: The speed may show exactly 60, but when viewed from the passenger seat, the needle may appear to show a slightly different speed due to the angle of viewing combined with the displacement of the needle from the plane of the numerical dial. Because the eyes of humans and other animals are in different positions on the head, they present different views simultaneously. This is the basis of stereopsis ,

4554-458: The spherical mirror used in the sight that can cause the reticle position to diverge off the sight's optical axis with change in eye position. Because of the positioning of field or naval artillery , each gun has a slightly different perspective of the target relative to the location of the fire-control system . When aiming guns at the target, the fire control system must compensate for parallax to assure that fire from each gun converges on

4623-691: The star, as observed when Earth is on opposite sides of the Sun in its orbit. These distances form the lowest rung of what is called "the cosmic distance ladder ", the first in a succession of methods by which astronomers determine the distances to celestial objects, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder. Parallax also affects optical instruments such as rifle scopes, binoculars , microscopes , and twin-lens reflex cameras that view objects from slightly different angles. Many animals, along with humans, have two eyes with overlapping visual fields that use parallax to gain depth perception ; this process

4692-536: The target. Several of Mark Renn 's sculptural works play with parallax, appearing abstract until viewed from a specific angle. One such sculpture is The Darwin Gate (pictured) in Shrewsbury , England, which from a certain angle appears to form a dome, according to Historic England , in "the form of a Saxon helmet with a Norman window... inspired by features of St Mary's Church which was attended by Charles Darwin as

4761-411: The user avoid this problem, the scale is sometimes printed above a narrow strip of mirror , and the user's eye is positioned so that the pointer obscures its reflection, guaranteeing that the user's line of sight is perpendicular to the mirror and therefore to the scale. The same effect alters the speed read on a car's speedometer by a driver in front of it and a passenger off to the side, values read from

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