title: Sundial

text: The formulas shown in the paragraphs below allow the positions of the hour-lines to be calculated for various types of sundial. In some cases, the calculations are simple; in others they are extremely complicated. There is an alternative, simple method of finding the positions of the hour-lines which can be used for many types of sundial, and saves a lot of work in cases where the calculations are complex. This is an empirical procedure in which the position of the shadow of the gnomon of a real sundial is marked at hourly intervals. The equation of time must be taken into account to ensure that the positions of the hour-lines are independent of the time of year when they are marked. An easy way to do this is to set a clock or watch so it shows "sundial time" which is standard time, plus the equation of time on the day in question. The hour-lines on the sundial are marked to show the positions of the shadow of the style when this clock shows whole numbers of hours, and are labelled with these numbers of hours. For example, when the clock reads 5:00, the shadow of the style is marked, and labelled "5" (or "V" in Roman numerals). If the hour-lines are not all marked in a single day, the clock must be adjusted every day or two to take account of the variation of the equation of time.


title: Sundial

text: The distinguishing characteristic of the "equatorial dial" (also called the "equinoctial dial") is the planar surface that receives the shadow, which is exactly perpendicular to the gnomon's style. This plane is called equatorial, because it is parallel to the equator of the Earth and of the celestial sphere. If the gnomon is fixed and aligned with the Earth's rotational axis, the sun's apparent rotation about the Earth casts a uniformly rotating sheet of shadow from the gnomon; this produces a uniformly rotating line of shadow on the equatorial plane. Since the Earth rotates 360° in 24 hours, the hour-lines on an equatorial dial are all spaced 15° apart (360/24).


title: Sundial

text: The uniformity of their spacing makes this type of sundial easy to construct. If the dial plate material is opaque, both sides of the equatorial dial must be marked, since the shadow will be cast from below in winter and from above in summer. With translucent dial plates (e.g. glass) the hour angles need only be marked on the sun-facing side, although the hour numberings (if used) need be made on both sides of the dial, owing to the differing hour schema on the sun-facing and sun-backing sides.


title: Sundial

text: Another major advantage of this dial is that equation of time (EoT) and daylight saving time (DST) corrections can be made by simply rotating the dial plate by the appropriate angle each day. This is because the hour angles are equally spaced around the dial. For this reason, an equatorial dial is often a useful choice when the dial is for public display and it is desirable to have it show the true local time to reasonable accuracy. The EoT correction is made via the relation


title: Sundial

text: Near the equinoxes in spring and autumn, the sun moves on a circle that is nearly the same as the equatorial plane; hence, no clear shadow is produced on the equatorial dial at those times of year, a drawback of the design.


title: Sundial

text: A "nodus" is sometimes added to equatorial sundials, which allows the sundial to tell the time of year. On any given day, the shadow of the nodus moves on a circle on the equatorial plane, and the radius of the circle measures the declination of the sun. The ends of the gnomon bar may be used as the nodus, or some feature along its length. An ancient variant of the equatorial sundial has only a nodus (no style) and the concentric circular hour-lines are arranged to resemble a spider-web.


title: Sundial

text: In the "horizontal sundial" (also called a "garden sundial"), the plane that receives the shadow is aligned horizontally, rather than being perpendicular to the style as in the equatorial dial. Hence, the line of shadow does not rotate uniformly on the dial face; rather, the hour lines are spaced according to the rule.


title: Sundial

text: where L is the sundial's geographical latitude (and the angle the gnomon makes with the dial plate), formula_5 is the angle between a given hour-line and the noon hour-line (which always points towards true North) on the plane, and "t" is the number of hours before or after noon. For example, the angle formula_5 of the 3pm hour-line would equal the arctangent of sin L, since tan 45° = 1. When L equals 90° (at the North Pole), the horizontal sundial becomes an equatorial sundial; the style points straight up (vertically), and the horizontal plane is aligned with the equatorial plane; the hour-line formula becomes formula_5 = 15° × t, as for an equatorial dial. A horizontal sundial at the Earth's equator, where L equals 0°, would require a (raised) horizontal style and would be an example of a polar sundial (see below).


title: Sundial

text: The chief advantages of the horizontal sundial are that it is easy to read, and the sunlight lights the face throughout the year. All the hour-lines intersect at the point where the gnomon's style crosses the horizontal plane. Since the style is aligned with the Earth's rotational axis, the style points true North and its angle with the horizontal equals the sundial's geographical latitude L. A sundial designed for one latitude can be adjusted for use at another latitude by tilting its base upwards or downwards by an angle equal to the difference in latitude. For example, a sundial designed for a latitude of 40° can be used at a latitude of 45°, if the sundial plane is tilted upwards by 5°, thus aligning the style with the Earth's rotational axis.


title: Sundial

text: Many ornamental sundials are designed to be used at 45 degrees north. Some mass-produced garden sundials fail to correctly calculate the "hourlines" and so can never be corrected. A local standard time zone is nominally 15 degrees wide, but may be modified to follow geographic or political boundaries. A sundial can be rotated around its style (which must remain pointed at the celestial pole) to adjust to the local time zone. In most cases, a rotation in the range of 7.5 degrees east to 23 degrees west suffices. This will introduce error in sundials that do not have equal hour angles. To correct for daylight saving time, a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer, and in cool colors for winter. Since the hour angles are not evenly spaced, the equation of time corrections cannot be made via rotating the dial plate about the gnomon axis. These types of dials usually have an equation of time correction tabulation engraved on their pedestals or close by. Horizontal dials are commonly seen in gardens, churchyards and in public areas.


title: Sundial

text: In the common "vertical dial", the shadow-receiving plane is aligned vertically; as usual, the gnomon's style is aligned with the Earth's axis of rotation. As in the horizontal dial, the line of shadow does not move uniformly on the face; the sundial is not "equiangular". If the face of the vertical dial points directly south, the angle of the hour-lines is instead described by the formula


title: Sundial

text: where L is the sundial's geographical latitude, formula_9 is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and "t" is the number of hours before or after noon. For example, the angle formula_9 of the 3pm hour-line would equal the arctangent of cos L, since tan 45° = 1. The shadow moves "counter-clockwise" on a south-facing vertical dial, whereas it runs clockwise on horizontal and equatorial north-facing dials.


title: Sundial

text: Dials with faces perpendicular to the ground and which face directly South, North, East, or West are called "vertical direct dials". It is widely believed, and stated in respectable publications, that a vertical dial cannot receive more than twelve hours of sunlight a day, no matter how many hours of daylight there are. However, there is an exception. Vertical sundials in the tropics which face the nearer pole (e.g. north facing in the zone between the Equator and the Tropic of Cancer) can actually receive sunlight for more than 12 hours from sunrise to sunset for a short period around the time of the summer solstice. For example, at latitude 20 degrees North, on June 21, the sun shines on a north-facing vertical wall for 13 hours, 21 minutes. Vertical sundials which do "not" face directly South (in the northern hemisphere) may receive significantly less than twelve hours of sunlight per day, depending on the direction they do face, and on the time of year. For example, a vertical dial that faces due East can tell time only in the morning hours; in the afternoon, the sun does not shine on its face. Vertical dials that face due East or West are "polar dials", which will be described below. Vertical dials that face North are uncommon, because they tell time only during the spring and summer, and do not show the midday hours except in tropical latitudes (and even there, only around midsummer). For non-direct vertical dials—those that face in non-cardinal directions—the mathematics of arranging the style and the hour-lines becomes more complicated; it may be easier to mark the hour lines by observation, but the placement of the style, at least, must be calculated first; such dials are said to be "declining dials".


title: Sundial

text: Vertical dials are commonly mounted on the walls of buildings, such as town-halls, cupolas and church-towers, where they are easy to see from far away. In some cases, vertical dials are placed on all four sides of a rectangular tower, providing the time throughout the day. The face may be painted on the wall, or displayed in inlaid stone; the gnomon is often a single metal bar, or a tripod of metal bars for rigidity. If the wall of the building faces "toward" the South, but does not face due South, the gnomon will not lie along the noon line, and the hour lines must be corrected. Since the gnomon's style must be parallel to the Earth's axis, it always "points" true North and its angle with the horizontal will equal the sundial's geographical latitude; on a direct south dial, its angle with the vertical face of the dial will equal the colatitude, or 90° minus the latitude.


title: Sundial

text: Thus, the shadow slides sideways over the surface, moving perpendicularly to itself as the Sun rotates about the style. As with the gnomon, the hour-lines are all aligned with the Earth's rotational axis. When the Sun's rays are nearly parallel to the plane, the shadow moves very quickly and the hour lines are spaced far apart. The direct East- and West-facing dials are examples of a polar dial. However, the face of a polar dial need not be vertical; it need only be parallel to the gnomon. Thus, a plane inclined at the angle of latitude (relative to horizontal) under the similarly inclined gnomon will be a polar dial. The perpendicular spacing "X" of the hour-lines in the plane is described by the formula


title: Sundial

text: where "H" is the height of the style above the plane, and "t" is the time (in hours) before or after the center-time for the polar dial. The center time is the time when the style's shadow falls directly down on the plane; for an East-facing dial, the center time will be 6am, for a West-facing dial, this will be 6pm, and for the inclined dial described above, it will be noon. When "t" approaches ±6 hours away from the center time, the spacing "X" diverges to +∞; this occurs when the Sun's rays become parallel to the plane.


title: Sundial

text: A "declining dial" is any non-horizontal, planar dial that does not face in a cardinal direction, such as (true) North, South, East or West. As usual, the gnomon's style is aligned with the Earth's rotational axis, but the hour-lines are not symmetrical about the noon hour-line. For a vertical dial, the angle formula_12 between the noon hour-line and another hour-line is given by the formula below. Note that formula_12 is defined positive in the clockwise sense w.r.t. the upper vertical hour angle; and that its conversion to the equivalent solar hour requires careful consideration of which quadrant of the sundial that it belongs in.


title: Sundial

text: where formula_15 is the sundial's geographical latitude; "t" is the time before or after noon; formula_16 is the angle of declination from true south, defined as positive when east of south; and formula_17 is a switch integer for the dial orientation. A partly south-facing dial has an formula_17 value of + 1; those partly north-facing, a value of -1. When such a dial faces South (formula_19), this formula reduces to the formula given above for vertical south-facing dials, i.e.


title: Sundial

text: When a sundial is not aligned with a cardinal direction, the substyle of its gnomon is not aligned with the noon hour-line. The angle formula_21 between the substyle and the noon hour-line is given by the formula


title: Sundial

text: If a vertical sundial faces true South or North (formula_23 or formula_24, respectively), the angle formula_25 and the substyle is aligned with the noon hour-line.


title: Sundial

text: The sundials described above have gnomons that are aligned with the Earth's rotational axis and cast their shadow onto a plane. If the plane is neither vertical nor horizontal nor equatorial, the sundial is said to be "reclining" or "inclining". Such a sundial might be located on a South-facing roof, for example. The hour-lines for such a sundial can be calculated by slightly correcting the horizontal formula above


title: Sundial

text: where formula_29 is the desired angle of reclining relative to the local vertical, L is the sundial's geographical latitude, formula_30 is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and "t" is the number of hours before or after noon. For example, the angle formula_30 of the 3pm hour-line would equal the arctangent of cos(L + R), since tan 45° = 1. When R equals 0° (in other words, a South-facing vertical dial), we obtain the vertical dial formula above.


title: Sundial

text: Some authors use a more specific nomenclature to describe the orientation of the shadow-receiving plane. If the plane's face points downwards towards the ground, it is said to be "proclining" or "inclining", whereas a dial is said to be "reclining" when the dial face is pointing away from the ground. Many authors also often refer to reclined, proclined and inclined sundials in general as inclined sundials. It is also common in the latter case to measure the angle of inclination relative to the horizontal plane on the sun side of the dial.


title: Sundial

text: Some sundials both decline and recline, in that their shadow-receiving plane is not oriented with a cardinal direction (such as true North or true South) and is neither horizontal nor vertical nor equatorial. For example, such a sundial might be found on a roof that was not oriented in a cardinal direction.


title: Sundial

text: The formulae describing the spacing of the hour-lines on such dials are rather more complicated than those for simpler dials.


title: Sundial

text: There are various solution approaches, including some using the methods of rotation matrices, and some making a 3D model of the reclined-declined plane and its vertical declined counterpart plane, extracting the geometrical relationships between the hour angle components on both these planes and then reducing the trigonometric algebra.


title: Sundial

text: The angle formula_35 between the noon hour-line and another hour-line is given by the formula below. Note that formula_35 advances counterclockwise with respect to the zero hour angle for those dials that are partly south-facing and clockwise for those that are north-facing.


title: Sundial

text: Or, if preferring to use inclination angle, formula_40, rather than the reclination, formula_29, where formula_42 :


title: Sundial

text: Here formula_46 is the sundial's geographical latitude; formula_17 is the orientation switch integer; "t" is the time in hours before or after noon; and formula_29 and formula_16 are the angles of reclination and declination, respectively.


title: Sundial

text: Note that formula_29 is measured with reference to the vertical. It is positive when the dial leans back towards the horizon behind the dial and negative when the dial leans forward to the horizon on the Sun's side. Declination angle formula_16 is defined as positive when moving east of true south.


title: Sundial

text: Dials facing fully or partly south have formula_17 = +1, while those partly or fully north-facing have an formula_17 value of -1.


title: Sundial

text: Since the above expression gives the hour angle as an arctan function, due consideration must be given to which quadrant of the sundial each hour belongs to before assigning the correct hour angle.


title: Sundial

text: Unlike the simpler vertical declining sundial, this type of dial does not always show hour angles on its sunside face for all declinations between east and west. When a northern hemisphere partly south-facing dial reclines back (i.e. away from the Sun) from the vertical, the gnomon will become co-planar with the dial plate at declinations less than due east or due west. Likewise for southern hemisphere dials that are partly north-facing.


title: Sundial

text: Were these dials reclining forward, the range of declination would actually exceed due east and due west.


title: Sundial

text: In a similar way, northern hemisphere dials that are partly north-facing and southern hemisphere dials that are south-facing, and which lean forward toward their upward pointing gnomons, will have a similar restriction on the range of declination that is possible for a given reclination value.


title: Sundial

text: The critical declination formula_54 is a geometrical constraint which depends on the value of both the dial's reclination and its latitude :


title: Sundial

text: As with the vertical declined dial, the gnomon's substyle is not aligned with the noon hour-line. The general formula for the angle formula_21, between the substyle and the noon-line is given by :


title: Sundial

text: Because of the complexity of the above calculations, using them for the practical purpose of designing a dial of this type is difficult and prone to error. It has been suggested that it is better to locate the hour lines empirically, marking the positions of the shadow of a style on a real sundial at hourly intervals as shown by a clock and adding/deducting that day's equation of time adjustment. See Empirical hour-line marking, above.


title: Sundial

text: The surface receiving the shadow need not be a plane, but can have any shape, provided that the sundial maker is willing to mark the hour-lines. If the style is aligned with the Earth's rotational axis, a spherical shape is convenient since the hour-lines are equally spaced, as they are on the equatorial dial shown here; the sundial is "equiangular". This is the principle behind the armillary sphere and the equatorial bow sundial. However, some equiangular sundials—such as the Lambert dial described below—are based on other principles.


title: Sundial

text: In the "equatorial bow sundial", the gnomon is a bar, slot or stretched wire parallel to the celestial axis. The face is a semicircle, corresponding to the equator of the sphere, with markings on the inner surface. This pattern, built a couple of meters wide out of temperature-invariant steel invar, was used to keep the trains running on time in France before World War I.


title: Sundial

text: Among the most precise sundials ever made are two equatorial bows constructed of marble found in Yantra mandir. This collection of sundials and other astronomical instruments was built by Maharaja Jai Singh II at his then-new capital of Jaipur, India between 1727 and 1733. The larger equatorial bow is called the "Samrat Yantra" (The Supreme Instrument); standing at 27 meters, its shadow moves visibly at 1 mm per second, or roughly a hand's breadth (6 cm) every minute.


title: Sundial

text: As an elegant alternative, the style (which could be created by a hole or slit in the circumference) may be located on the circumference of a cylinder or sphere, rather than at its central axis of symmetry.


title: Sundial

text: In that case, the hour lines are again spaced equally, but at "twice" the usual angle, due to the geometrical inscribed angle theorem. This is the basis of some modern sundials, but it was also used in ancient times;


title: Sundial

text: In another variation of the polar-axis-aligned cylindrical, a cylindrical dial could be rendered as a helical ribbon-like surface, with a thin gnomon located either along its center or at its periphery.


title: Sundial

text: Sundials can be designed with a gnomon that is placed in a different position each day throughout the year. In other words, the position of the gnomon relative to the centre of the hour lines varies. The gnomon need not be aligned with the celestial poles and may even be perfectly vertical (the analemmatic dial). These dials, when combined with fixed-gnomon sundials, allow the user to determine true North with no other aid; the two sundials are correctly aligned if and only if they both show the same time.


title: Sundial

text: A "universal equinoctial ring dial" (sometimes called a "ring dial" for brevity, although the term is ambiguous), is a portable version of an armillary sundial, or was inspired by the mariner's astrolabe. It was likely invented by William Oughtred around 1600 and became common throughout Europe.


title: Sundial

text: In its simplest form, the style is a thin slit that allows the Sun's rays to fall on the hour-lines of an equatorial ring. As usual, the style is aligned with the Earth's axis; to do this, the user may orient the dial towards true North and suspend the ring dial vertically from the appropriate point on the meridian ring. Such dials may be made self-aligning with the addition of a more complicated central bar, instead of a simple slit-style. These bars are sometimes an addition to a set of Gemma's rings. This bar could pivot about its end points and held a perforated slider that was positioned to the month and day according to a scale scribed on the bar. The time was determined by rotating the bar towards the Sun so that the light shining through the hole fell on the equatorial ring. This forced the user to rotate the instrument, which had the effect of aligning the instrument's vertical ring with the meridian.


title: Sundial

text: In 1610, Edward Wright created the sea ring, which mounted a universal ring dial over a magnetic compass. This permitted mariners to determine the time and magnetic variation in a single step.


title: Sundial

text: Analemmatic sundials are a type of horizontal sundial that has a vertical gnomon and hour markers positioned in an elliptical pattern. There are no hour lines on the dial and the time of day is read on the ellipse. The gnomon is not fixed and must change position daily to accurately indicate time of day.


title: Sundial

text: Analemmatic sundials are sometimes designed with a human as the gnomon. Human gnomon analemmatic sundials are not practical at lower latitudes where a human shadow is quite short during the summer months. A 66 inch tall person casts a 4-inch shadow at 27 deg latitude on the summer solstice.


title: Sundial

text: The Foster-Lambert dial is another movable-gnomon sundial. In contrast to the elliptical analemmatic dial, the Lambert dial is circular with evenly spaced hour lines, making it an "equiangular sundial", similar to the equatorial, spherical, cylindrical and conical dials described above. The gnomon of a Foster-Lambert dial is neither vertical nor aligned with the Earth's rotational axis; rather, it is tilted northwards by an angle α = 45° - (Φ/2), where Φ is the geographical latitude. Thus, a Foster-Lambert dial located at latitude 40° would have a gnomon tilted away from vertical by 25° in a northerly direction. To read the correct time, the gnomon must also be moved northwards by a distance


title: Sundial

text: where "R" is the radius of the Foster-Lambert dial and δ again indicates the Sun's declination for that time of year.


title: Sundial

text: Altitude dials measure the height of the Sun in the sky, rather than directly measuring its hour-angle about the Earth's axis. They are not oriented towards true North, but rather towards the Sun and generally held vertically. The Sun's elevation is indicated by the position of a nodus, either the shadow-tip of a gnomon, or a spot of light.


title: Sundial

text: In altitude dials, the time is read from where the nodus falls on a set of hour-curves that vary with the time of year. Many such altitude-dials' construction is calculation-intensive, as also the case with many azimuth dials. But the capuchin dials (described below) are constructed and used graphically.


title: Sundial

text: Since the Sun's altitude is the same at times equally spaced about noon (e.g., 9am and 3pm), the user had to know whether it was morning or afternoon. At, say, 3:00 pm, that isn't a problem. But when the dial indicates a time 15 minutes from noon, the user likely won't have a way of distinguishing 11:45 from 12:15.


title: Sundial

text: Additionally, altitude dials are less accurate near noon, because the sun's altitude isn't changing rapidly then.


title: Sundial

text: Many of these dials are portable and simple to use. As is often the case with other sundials, many altitude dials are designed for only one latitude. But the capuchin dial (described below) has a version that's adjustable for latitude.


title: Sundial

text: The length of a human shadow (or of any vertical object) can be used to measure the sun's elevation and, thence, the time. The Venerable Bede gave a table for estimating the time from the length of one's shadow in feet, on the assumption that a monk's height is six times the length of his foot. Such shadow lengths will vary with the geographical latitude and with the time of year. For example, the shadow length at noon is short in summer months, and long in winter months.


title: Sundial

text: A shepherd's dial – also known as a "shepherd's column dial", "pillar dial", "cylinder dial" or "chilindre" – is a portable cylindrical sundial with a knife-like gnomon that juts out perpendicularly. It is normally dangled from a rope or string so the cylinder is vertical. The gnomon can be twisted to be above a month or day indication on the face of the cylinder. This corrects the sundial for the equation of time. The entire sundial is then twisted on its string so that the gnomon aims toward the Sun, while the cylinder remains vertical. The tip of the shadow indicates the time on the cylinder. The hour curves inscribed on the cylinder permit one to read the time. Shepherd's dials are sometimes hollow, so that the gnomon can fold within when not in use.


title: Sundial

text: The shepherd's dial is evoked in Shakespeare's "Henry VI, Part 3" (Act 2, Scene 5, Lines 21-29), among other works of literature.


title: Sundial

text: The cylindrical shepherd's dial can be unrolled into a flat plate. In one simple version, the front and back of the plate each have three columns, corresponding to pairs of months with roughly the same solar declination (June–July, May–August, April–September, March–October, February–November, and January–December). The top of each column has a hole for inserting the shadow-casting gnomon, a peg. Often only two times are marked on the column below, one for noon and the other for mid-morning/mid-afternoon.


title: Sundial

text: Timesticks, "clock spear", or "shepherds' time stick", are based on the same principles as dials. The time stick is carved with eight vertical time scales for a different period of the year, each bearing a time scale calculated according to the relative amount of daylight during the different months of the year. Any reading depends not only on the time of day but also on the latitude and time of year.


title: Sundial

text: A peg gnomon is inserted at the top in the appropriate hole or face for the season of the year, and turned to the Sun so that the shadow falls directly down the scale. Its end displays the time.


title: Sundial

text: In a ring dial (also known as an "Aquitaine" or a "perforated ring dial"), the ring is hung vertically and oriented sideways towards the sun. A beam of light passes through a small hole in the ring and falls on hour-curves that are inscribed on the inside of the ring. To adjust for the equation of time, the hole is usually on a loose ring within the ring so that the hole can be adjusted to reflect the current month.


title: Sundial

text: Card dials are another form of altitude dial. A card is aligned edge-on with the sun and tilted so that a ray of light passes through an aperture onto a specified spot, thus determining the sun's altitude. A weighted string hangs vertically downwards from a hole in the card, and carries a bead or knot. The position of the bead on the hour-lines of the card gives the time. In more sophisticated versions such as the Capuchin dial, there is only one set of hour-lines, i.e., the hour lines do not vary with the seasons. Instead, the position of the hole from which the weighted string hangs is varied according to the season.


title: Sundial

text: The Capuchin sundials are constructed and used graphically, as opposed the direct hour-angle measurements of horizontal or equatorial dials; or the calculated hour angle lines of some altitude and azimuth dials.


title: Sundial

text: In addition to the ordinary Capuchin dial, there is a universal Capuchin dial, adjustable for latitude.


title: Sundial

text: A navicula de Venetiis or "little ship of Venice" was an altitude dial used to tell time and which was shaped like a little ship. The cursor (with a plumb line attached) was slid up/down the mast to the correct latitude. The user then sighted the Sun through the pair of sighting holes at either end of the "ship's deck". The plumb line then marked what hour of the day it was.


title: Sundial

text: Another type of sundial follows the motion of a single point of light or shadow, which may be called the "nodus". For example, the sundial may follow the sharp tip of a gnomon's shadow, e.g., the shadow-tip of a vertical obelisk (e.g., the "Solarium Augusti") or the tip of the horizontal marker in a shepherd's dial. Alternatively, sunlight may be allowed to pass through a small hole or reflected from a small (e.g., coin-sized) circular mirror, forming a small spot of light whose position may be followed. In such cases, the rays of light trace out a cone over the course of a day; when the rays fall on a surface, the path followed is the intersection of the cone with that surface. Most commonly, the receiving surface is a geometrical plane, so that the path of the shadow-tip or light-spot (called "declination line") traces out a conic section such as a hyperbola or an ellipse. The collection of hyperbolae was called a "pelekonon" (axe) by the Greeks, because it resembles a double-bladed ax, narrow in the center (near the noonline) and flaring out at the ends (early morning and late evening hours).


title: Sundial

text: There is a simple verification of hyperbolic declination lines on a sundial: the distance from the origin to the equinox line should be equal to harmonic mean of distances from the origin to summer and winter solstice lines.


title: Sundial

text: Nodus-based sundials may use a small hole or mirror to isolate a single ray of light; the former are sometimes called "aperture dials". The oldest example is perhaps the antiborean sundial ("antiboreum"), a spherical nodus-based sundial that faces true North; a ray of sunlight enters from the South through a small hole located at the sphere's pole and falls on the hour and date lines inscribed within the sphere, which resemble lines of longitude and latitude, respectively, on a globe.


title: Sundial

text: Isaac Newton developed a convenient and inexpensive sundial, in which a small mirror is placed on the sill of a south-facing window. The mirror acts like a nodus, casting a single spot of light on the ceiling. Depending on the geographical latitude and time of year, the light-spot follows a conic section, such as the hyperbolae of the pelikonon. If the mirror is parallel to the Earth's equator, and the ceiling is horizontal, then the resulting angles are those of a conventional horizontal sundial. Using the ceiling as a sundial surface exploits unused space, and the dial may be large enough to be very accurate.


title: Sundial

text: Sundials are sometimes combined into multiple dials. If two or more dials that operate on different principles — such as an analemmatic dial and a horizontal or vertical dial — are combined, the resulting multiple dial becomes self-aligning, most of the time. Both dials need to output both time and declination. In other words, the direction of true North need not be determined; the dials are oriented correctly when they read the same time and declination. However, the most common forms combine dials are based on the same principle and the analemmatic does not normally output the declination of the sun, thus are not self-aligning.


title: Sundial

text: The diptych consisted of two small flat faces, joined by a hinge. Diptychs usually folded into little flat boxes suitable for a pocket. The gnomon was a string between the two faces. When the string was tight, the two faces formed both a vertical and horizontal sundial. These were made of white ivory, inlaid with black lacquer markings. The gnomons were black braided silk, linen or hemp string. With a knot or bead on the string as a nodus, and the correct markings, a diptych (really any sundial large enough) can keep a calendar well-enough to plant crops. A common error describes the diptych dial as self-aligning. This is not correct for diptych dials consisting of a horizontal and vertical dial using a string gnomon between faces, no matter the orientation of the dial faces. Since the string gnomon is continuous, the shadows must meet at the hinge; hence, "any" orientation of the dial will show the same time on both dials.


title: Sundial

text: A common type of multiple dial has sundials on every face of a Platonic solid (regular polyhedron), usually a cube.


title: Sundial

text: Extremely ornate sundials can be composed in this way, by applying a sundial to every surface of a solid object.


title: Sundial

text: In some cases, the sundials are formed as hollows in a solid object, e.g., a cylindrical hollow aligned with the Earth's rotational axis (in which the edges play the role of styles) or a spherical hollow in the ancient tradition of the "hemisphaerium" or the "antiboreum". (See the History section above.) In some cases, these multiface dials are small enough to sit on a desk, whereas in others, they are large stone monuments.


title: Sundial

text: A Polyhedral's dial faces can be designed to give the time for different time-zones simultaneously. Examples include the Scottish sundial of the 17th and 18th century, which was often an extremely complex shape of polyhedral, and even convex, faces.


title: Sundial

text: Prismatic dials are a special case of polar dials, in which the sharp edges of a prism of a concave polygon serve as the styles and the sides of the prism receive the shadow. Examples include a three-dimensional cross or star of David on gravestones.


title: Sundial

text: The Benoy dial was invented by Walter Gordon Benoy of Collingham, Nottinghamshire, England. Whereas a gnomon casts a sheet of shadow, his invention creates an equivalent sheet of light by allowing the Sun's rays through a thin slit, reflecting them from a long, slim mirror (usually half-cylindrical), or focusing them through a cylindrical lens. Examples of Benoy dials can be found in the United Kingdom at:


title: Sundial

text: Invented by the German mathematician Hugo Michnik in 1922, the bifilar sundial has two non-intersecting threads parallel to the dial. Usually the second thread is orthogonal to the first.


title: Sundial

text: A digital sundial indicates the current time with numerals formed by the sunlight striking it. Sundials of this type are installed in the Deutsches Museum in Munich and in the Sundial Park in Genk (Belgium), and a small version is available commercially. There is a patent for this type of sundial.


title: Sundial

text: The globe dial is a sphere aligned with the Earth's rotational axis, and equipped with a spherical vane. Similar to sundials with a fixed axial style, a globe dial determines the time from the Sun's azimuthal angle in its apparent rotation about the earth. This angle can be determined by rotating the vane to give the smallest shadow.


title: Sundial

text: The simplest sundials do not give the hours, but rather note the exact moment of 12:00 noon. In centuries past, such dials were used to set mechanical clocks, which were sometimes so inaccurate as to lose or gain significant time in a single day. The simplest noon-marks have a shadow that passes a mark. Then, an almanac can translate from local solar time and date to civil time. The civil time is used to set the clock. Some noon-marks include a figure-eight that embodies the equation of time, so that no almanac is needed.


title: Sundial

text: In some U.S. colonial-era houses, a noon-mark might be carved into a floor or windowsill. Such marks indicate local noon, and provide a simple and accurate time reference for households to set their clocks. Some Asian countries had post offices set their clocks from a precision noon-mark. These in turn provided the times for the rest of the society. The typical noon-mark sundial was a lens set above an analemmatic plate. The plate has an engraved figure-eight shape, which corresponds to the equation of time (described above) versus the solar declination. When the edge of the Sun's image touches the part of the shape for the current month, this indicates that it is 12:00 noon.


title: Sundial

text: A sundial cannon, sometimes called a 'meridian cannon', is a specialized sundial that is designed to create an 'audible noonmark', by automatically igniting a quantity of gunpowder at noon. These were novelties rather than precision sundials, sometimes installed in parks in Europe mainly in the late 18th or early 19th century. They typically consist of a horizontal sundial, which has in addition to a gnomon a suitably mounted lens, set to focus the rays of the sun at exactly noon on the firing pan of a miniature cannon loaded with gunpowder (but no ball). To function properly the position and angle of the lens must be adjusted seasonally.


title: Sundial

text: A horizontal line aligned on a meridian with a gnomon facing the noon-sun is termed a meridian line and does not indicate the time, but instead the day of the year. Historically they were used to accurately determine the length of the solar year. Examples are the Bianchini meridian line in Santa Maria degli Angeli e dei Martiri in Rome, and the Cassini line in San Petronio Basilica at Bologna.


title: Sundial

text: The association of sundials with time has inspired their designers over the centuries to display mottoes as part of the design. Often these cast the device in the role of "memento mori", inviting the observer to reflect on the transience of the world and the inevitability of death. "Do not kill time, for it will surely kill thee." Other mottoes are more whimsical: "I count only the sunny hours," and "I am a sundial and I make a botch / of what is done far better by a watch." Collections of sundial mottoes have often been published through the centuries.


title: Sundial

text: If a horizontal-plate sundial is made for the latitude in which it is being used, and if it is mounted with its plate horizontal and its gnomon pointing to the celestial pole that is above the horizon, then it shows the correct time in apparent solar time. Conversely, if the directions of the cardinal points are initially unknown, but the sundial is aligned so it shows the correct apparent solar time as calculated from the reading of a clock, its gnomon shows the direction of True North or South, allowing the sundial to be used as a compass. The sundial can be placed on a horizontal surface, and rotated about a vertical axis until it shows the correct time. The gnomon will then be pointing to the North, in the northern hemisphere, or to the South in the southern hemisphere. This method is much more accurate than using a watch as a compass (see Cardinal direction#Watch face) and can be used in places where the magnetic declination is large, making a magnetic compass unreliable. An alternative method uses two sundials of different designs. (See #Multiple dials, above.) The dials are attached to and aligned with each other, and are oriented so they show the same time. This allows the directions of the cardinal points and the apparent solar time to be determined simultaneously, without requiring a clock.


title: Last Chance U

text: Last Chance U is an American documentary streaming television series that is produced and premiered by Netflix. The six-episode first season explores the football program at East Mississippi Community College, which features several collegiate athletes that have had trouble in their lives and struggled with finding structure. The players are then required to perform at the junior college (JUCO) level, under the stewardship of coach Buddy Stephens, in order to prove themselves and return to Division I.


title: Last Chance U

text: The series' second season returned to Mississippi, but transitioned to Independence Community College in Kansas for the show's third season, which premiered on July 21, 2018. This was followed by a return to Independence for the fourth season; it debuted on July 19, 2019. The final season took place at Laney College in Oakland, California and premiered on July 28, 2020. In 2020, it was announced that a scripted drama based on the first two seasons would be produced by and starring Courteney Cox.


title: Last Chance U

text: The first two seasons focus on all aspects of the football program at East Mississippi Community College, one of the most successful JUCO programs in the country. Major themes include the academic struggles of the players – some of whom have come from severely disadvantaged backgrounds. This is set against an overall redemption and coming-of-age “last chance” theme for the group of men struggling to find their place. Team academic advisor Brittany Wagner is featured prominently as she is tasked with getting all team members to graduate on time. Head coach Buddy Stephens' struggles with controlling his temper is also a major theme, which is often juxtaposed with his devout Christian faith that he attempts to impart on the team.


title: Last Chance U

text: The crew followed the EMCC Lions during their 2015 season as they attempted to capture their fourth JUCO national title. While the team appeared dominant for much of the year, their season was derailed after a brawl broke out during their game with Mississippi Delta. EMCC was disqualified from the state playoffs and a potential berth to the national championship game.


title: Last Chance U

text: Netflix returned to Scooba to follow their 2016 season. Once again holding national championship aspirations, the team faced a major hurdle in that only 32 of their players were eligible for their opening game with Jones County Junior College due to suspensions related to the previous season's brawl. EMCC lost that game, 27–25, their first season-opening loss since 2010. The Lions would go on to win the rest of their games, but were left out of the national championship game when they finished the season ranked No. 3 in the polls.


title: Last Chance U

text: Despite being invited back to EMCC for a third season, producers decided to move the show to Independence Community College of Kansas. The new location is different in that ICC has historically had much lower expectations than EMCC; in 2016, it ended the season 5–4, its first winning season in ten years. The ICC Pirates had a very successful recruiting campaign for the 2017 season, landing many acclaimed players who began at NCAA Division I schools.


title: Last Chance U

text: Jeff Carpenter, the long-time Voice of the Indy Pirates delivers the back story of the team and the town of Independence, KS.


title: Last Chance U

text: The fourth season continues in Independence, where the team fails to live up to high preseason expectations, finishing 2–8. After the season, Coach Brown is forced to resign for insensitive remarks. The season received the 2020 Emmy Award for Outstanding Serialized Sports Documentary.


title: Last Chance U

text: The fifth season takes place in Oakland, California at Laney College alongside football head coach John Beam. It premiered in July 2020.


title: Last Chance U

text: The series was given a positive review by "SB Nation"s Jason Kirk, who summed it up as a "carefully crafted drama with personalities to care about." Critical aggregator website Metacritic awarded the series a score of 79, indicating "generally favorable reviews".


title: Last Chance U

text: On March 10, 2021, a spin-off series "Last Chance U: Basketball" premiered on Netflix, introducing a new sport for the award-winning documentary series to follow. The eight-episode first season explores the basketball program at East Los Angeles College, which features a once faltering junior college team that has become a title contender under head coach John Mosley. Through his strong convictions, Coach Mosley leads young men who hope to fulfill their major college potential. On September 10, 2021, the series was renewed for a second season. The second season premiered on December 13, 2022.


title: Last Chance U

text: Mosley's Huskies enjoyed their best season in ELAC history during the 2019–20 season. The team had their eyes on the CCCAA State Title, entering the Championship Tournament with a program-best 29–1 record while being ranked the second-best team in the state. Their season was cancelled, however, due to the COVID-19 pandemic.


title: Ludlow Massacre

text: The Ludlow Massacre was a mass killing perpetrated by anti-striker militia during the Colorado Coalfield War. Soldiers from the Colorado National Guard and private guards employed by Colorado Fuel and Iron Company (CF&I) attacked a tent colony of roughly 1,200 striking coal miners and their families in Ludlow, Colorado, on April 20, 1914. Approximately 21 people, including miners' wives and children, were killed. John D. Rockefeller Jr., a part-owner of CF&I who had recently appeared before a United States congressional hearing on the strikes, was widely blamed for having orchestrated the massacre.


title: Ludlow Massacre

text: The massacre was the seminal event of the 1913–1914 Colorado Coalfield War, which began with a general United Mine Workers of America strike against poor labor conditions in CF&I's southern Colorado coal mines. The strike was organized by miners working for the Rocky Mountain Fuel Company and Victor-American Fuel Company. Ludlow was the deadliest single incident during the Colorado Coalfield War and spurred a ten-day period of heightened violence throughout Colorado. In retaliation for the massacre at Ludlow, bands of armed miners attacked dozens of anti-union establishments, destroying property and engaging in several skirmishes with the Colorado National Guard along a front from Trinidad to Louisville. From the strike's beginning in September 1913 to intervention by federal soldiers under President Woodrow Wilson's orders on April 29, 1914, an estimated 69 to 199 people were killed during the strike. Historian Thomas G. Andrews has called it the "deadliest strike in the history of the United States."


title: Ludlow Massacre

text: The Ludlow Massacre was a watershed moment in American labor relations. Socialist historian Howard Zinn described it as "the culminating act of perhaps the most violent struggle between corporate power and laboring men in American history". Congress responded to public outrage by directing the House Committee on Mines and Mining to investigate the events. Its report, published in 1915, was influential in promoting child labor laws and an eight-hour work day. The Ludlow townsite and the adjacent location of the tent colony, northwest of Trinidad, Colorado, is now a ghost town. The massacre site is owned by the United Mine Workers of America, which erected a granite monument in memory of those who died that day. The Ludlow tent colony site was designated a National Historic Landmark on January 16, 2009, and dedicated on June 28, 2009. Subsequent investigations immediately following the massacre and modern archeological efforts largely support some of the strikers' accounts of the event.


title: Ludlow Massacre

text: Areas of the Rocky Mountains have veins of coal close to the surface, providing significant and relatively accessible reserves. In 1867 these coal deposits caught the attention of William Jackson Palmer, then leading a survey team planning the route of the Kansas Pacific Railway. The rapid expansion of rail transport in the United States made coal a highly valued commodity, and it was rapidly commercialized.


title: Ludlow Massacre

text: At its peak in 1910, the coal mining industry of Colorado employed 15,864 people, 10% of jobs in the state. Colorado's coal industry was dominated by a handful of operators. Colorado Fuel and Iron was the largest coal operator in the west and one of the nation's most powerful corporations, at one point employing 7,050 people and controlling of coal land. John D. Rockefeller purchased a controlling stake in the Colorado Fuel & Iron Company in 1902, and nine years later he turned over his controlling interest in the company to his son, John D. Rockefeller Jr., who managed the company from his offices at 26 Broadway in New York.


title: Ludlow Massacre

text: Mining was dangerous and difficult work. Colliers in Colorado were constantly threatened by explosions, suffocation, and collapsing mine walls. In 1912 the death rate in Colorado's mines was 7.055 per 1,000 employees, compared to a national rate of 3.15. In 1914 the United States House Committee on Mines and Mining reported:


title: Ludlow Massacre

text: Colorado has good mining laws and such that ought to afford protection to the miners as to safety in the mine if they were enforced, yet in this State the percentage of fatalities is larger than any other, showing there is undoubtedly something wrong in reference to the management of its coal mines.


title: Ludlow Massacre

text: Miners were generally paid according to tonnage of coal produced, while so-called "dead work", such as shoring up unstable roofs, was often unpaid. The tonnage system drove many poor and ambitious colliers to gamble with their lives by neglecting precautions and taking on risk, with consequences that were often fatal.Between 1884 and 1912 mining accidents claimed the lives of more than 1,700 in Colorado. In 1913 alone 110 men died in mine-related accidents.


title: Ludlow Massacre

text: Colliers had little opportunity to air their grievances. Many resided in company towns, in which all land, real estate, and amenities were owned by the mine operator, and which were expressly designed to inculcate loyalty and squelch dissent. Welfare capitalists believed that anger and unrest among the workers could be placated by raising colliers' standard of living, while subsuming it under company management. Company towns indeed brought tangible improvements to many colliers' lives, including larger houses, better medical care, and broader access to education. But owning the towns gave companies considerable control over all aspects of workers' lives, and they did not always use this power to augment public welfare. Historian Philip S. Foner has described company towns as "feudal domain[s], with the company acting as lord and master. ... The 'law' consisted of the company rules. Curfews were imposed. Company guards—brutal thugs armed with machine guns and rifles loaded with soft-point bullets—would not admit any 'suspicious' stranger into the camp and would not permit any miner to leave." Miners who came into conflict with the company were often summarily evicted from their homes.


title: Ludlow Massacre

text: Frustrated by working conditions they found unsafe and unjust, colliers increasingly turned to unionism. Nationwide, organized mines boasted 40% fewer fatalities than nonunion mines. Colorado miners repeatedly attempted to unionize after the state's first strike in 1883. The Western Federation of Miners organized primarily hard-rock miners in the gold and silver camps during the 1890s.


title: Ludlow Massacre

text: Beginning in 1900, the United Mine Workers of America began organizing coal miners in the western states, including southern Colorado. The union decided to focus on the Colorado Fuel & Iron Company because of its harsh management tactics under the conservative and distant Rockefellers and other investors. To break or prevent strikes, the coal companies hired strike breakers, mainly from Mexico and southern and eastern Europe. The Colorado Fuel & Iron Company mixed immigrants of different nationalities in the mines to discourage communication that might lead to organization.


title: Ludlow Massacre

text: Despite attempts to suppress union activity, the United Mine Workers of America secretly continued its unionization efforts in the years leading up to 1913. Eventually, the union presented a list of seven demands:


title: Ludlow Massacre

text: The major coal companies rejected the demands. In September 1913 the United Mine Workers of America called a strike. Those who went on strike were evicted from their company homes and moved to tent villages prepared by the union. The tents were built on wood platforms and furnished with cast-iron stoves on land the union had leased in preparation for a strike.


title: Ludlow Massacre

text: When leasing the sites, the union had selected locations near the mouths of canyons that led to the coal camps in order to block any strikebreakers' traffic. The company hired the Baldwin–Felts Detective Agency to protect the new workers and harass the strikers.


title: Ludlow Massacre

text: Baldwin–Felts had a reputation for aggressive strike breaking. Agents shone searchlights on the tent villages at night and fired bullets into the tents at random, occasionally killing and maiming people. They used an improvised armored car, mounted with a machine gun the union called the "", to patrol the camp's perimeters. The steel-covered car was built at the Colorado Fuel & Iron Company plant in Pueblo, Colorado, from the chassis of a large touring sedan. Confrontations between striking miners and working miners, whom the union called scabs, sometimes resulted in deaths. Frequent sniper attacks on the tent colonies drove the miners to dig pits beneath the tents to hide in. Armed battles also occurred between (mostly Greek) strikers and sheriffs recently deputized to suppress the strike: this was the Colorado Coalfield War.


title: Ludlow Massacre

text: As strike-related violence mounted, Colorado governor Elias M. Ammons called in the Colorado National Guard on October 28. At first, the Guard's appearance calmed the situation, but the Guard leaders' sympathies lay with company management. Guard Adjutant-General John Chase, who had served during the violent Cripple Creek strike 10 years earlier, imposed a harsh regime. On March 10, 1914, a replacement worker's body was found on the railroad tracks near Forbes, Colorado. The National Guard said the strikers had murdered the man. In retaliation, Chase ordered the Forbes tent colony destroyed. The attack was launched while the residents were attending a funeral of two infants who had died a few days earlier. Photographer Lou Dold witnessed the attack, and his images of the destruction often appear in accounts of the strike.


title: Ludlow Massacre

text: The strikers persevered until the spring of 1914. By then, according to historian Anthony DeStefanis, the National Guard had largely broken the strike by helping the mine operators bring in non-union workers. The state had also run out of money to maintain the Guard, and Ammons decided to recall them. He and the mining companies, fearing a breakdown in order, left one company of Guardsmen in southern Colorado. They formed a new company called "Troop A", which consisted largely of Colorado Fuel & Iron Company mine camp guards and mine guards hired by Baldwin–Felts, who were given National Guard uniforms.


title: Ludlow Massacre

text: On the morning of April 20, the day after some in the tent colony celebrated Orthodox Easter, three Guardsmen appeared at the camp ordering the release of a man they claimed was being held against his will. The camp leader, Louis Tikas, left to meet with Major Patrick J. Hamrock at the train station in Ludlow village, from the colony. While this meeting was progressing, two militias installed a machine gun on a ridge near the camp and took positions along a rail route about half a mile south of Ludlow. Simultaneously, armed Greek miners began flanking to an arroyo. When two of the militias' dynamite explosions–detonated to draw support from the National Guard units at Berwind and Cedar Hill–alerted the Ludlow tent colony, the miners took up positions at the bottom of the hill. When the militia opened fire, hundreds of miners and their families ran for cover.


title: Ludlow Massacre

text: The fighting raged for the entire day. The militia was reinforced by non-uniformed mine guards later in the afternoon. At dusk a passing freight train stopped on the tracks in front of the Guards' machine-gun placements, allowing many of the miners and their families to escape to an outcrop of hills to the east called the Black Hills. By 7 p.m., the camp was in flames, and the militia descended on it and began to search and loot it. Tikas had remained in the camp the entire day and was still there when the fire started. He and two other men were captured by the militia. Tikas and Lt. Karl Linderfelt, commander of one of two Guard companies, had confronted each other several times in the previous months. While two militiamen held Tikas, Linderfelt broke a rifle butt over his head. Tikas and the other two captured miners were later found shot dead. Tikas had been shot in the back. Their bodies lay along the Colorado and Southern Railway tracks for three days in full view of passing trains. The militia officers refused to allow them to be moved until a local of a railway union demanded they be taken away for burial.


title: Ludlow Massacre

text: During the battle, four women and 11 children hid in a pit beneath one tent, where they were trapped when the tent above them was set on fire. Two of the women and all the children suffocated. These deaths became a rallying cry for the United Mine Workers of America, who called the incident the Ludlow Massacre.


title: Ludlow Massacre

text: Julia May Courtney reported different numbers in her contemporaneous article "Remember Ludlow!" for the magazine "Mother Earth". She said that, in addition to men who were killed, a total of 55 women and children had died in the massacre. According to her account, the militia:


title: Ludlow Massacre

text: Some reports say a second machine gun was brought in to support the estimated 200 Guardsmen who participated in the engagement, and that a Colorado and Southern train's operators purposely put their engine between a machine gun and the strikers as a shield against National Guard fire.


title: Ludlow Massacre

text: A board of Colorado military officers described the events as beginning with the killing of Tikas and other strikers in custody, with gunfire largely emanating from the southwestern corner of the Ludlow Colony. Guardsmen stationed on "Water Tank Hill"—the name for the machine gun position—fired into the camp. The Guardsmen reported having seen women and children withdrawing the morning before the battle and said they thought the strikers would not have begun firing if they had women still with them. The board's official report commended the "truly heroic behavior" of Linderfelt, the guardsmen, and the militia during the battle and blamed the strikers for any civilian casualties during the engagement, despite those killed being family members of the strikers. The report also blamed the looting that occurred afterward on "Troop 'A'", a unit composed largely of non-uniformed mine guards who had been integrated into the Guard.


title: Ludlow Massacre

text: In addition to the miners and their family members, three regular members of the National Guard and one other militiaman were reported killed in the day's fighting by contemporary accounts. However, modern historians assert that only one of the militia's number, a private named Martin of the National Guard, was killed. Martin was fatally shot in the neck, presumably by strikers.


title: Ludlow Massacre

text: In the aftermath of the massacre came the Ten Day War, part of the wider Colorado Coalfield War. As news of the deaths of women and children spread, the leaders of organized labor issued a call to arms. They urged union members to get "all the arms and ammunition legally available". Subsequently, the coal miners began a large-scale guerrilla war against the mine guards and facilities throughout Colorado's southern coalfields. In the town of Trinidad, the United Mine Workers of America openly and officially distributed arms and ammunition to strikers at union headquarters. Over the next ten days, 700 to 1,000 strikers "attacked mine after mine, driving off or killing the guards and setting fire to the buildings." At least 50 people, including those at Ludlow, were killed during the ten days of fighting between the guards and miners. Hundreds of state militia reinforcements were rushed to the coalfields to regain control of the situation. The fighting ended only after President Woodrow Wilson sent in federal troops. The troops disarmed both sides, displacing and often arresting the militia in the process. The Colorado Coalfield War produced a total death toll of approximately 75.


title: Ludlow Massacre

text: The United Mine Workers of America finally ran out of money, and called off the strike on December 10, 1914. In the end, the strikers' demands were not met, the union did not obtain recognition, and many striking workers were replaced. 408 strikers were arrested, 332 of whom were indicted for murder.


title: Ludlow Massacre

text: Of those present at Ludlow during the massacre, only John R. Lawson, leader of the strike, was convicted of murder, and the Colorado Supreme Court eventually overturned the conviction. Twenty-two National Guardsmen, including 10 officers, were court-martialed. While Linderfelt was found responsible for the deaths of Tikas and other strikers that exhibited execution-style injuries, he and all others were acquitted.


title: Ludlow Massacre

text: An Episcopalian minister, Reverend John O. Ferris, pastored Trinity Church in Trinidad and another church in Aguilar. He was one of the few pastors in Trinidad permitted to search and provide Christian burials to the deceased victims of the Ludlow Massacre.


title: Ludlow Massacre

text: The massacre sparked nationwide reproach for the Rockefellers, especially in New York, where protesters demonstrated outside of the Rockefeller building in New York City. Protesters led by Ferrer Center anarchists Alexander Berkman and Carlo Tresca followed when Rockefeller Jr. fled upstate to the family estate near Tarrytown. In early July, a failed bomb plot on the Tarrytown estate ended with a dynamite explosion in East Harlem and three dead anarchists. The New York City Police Department inaugurated its bomb squad within a month. Bomb plots continued throughout the rest of the year.


title: Ludlow Massacre

text: Although the UMWA failed to win recognition from the company, the strike had a lasting effect both on conditions at the Colorado mines and on labor relations nationally. John D. Rockefeller Jr. engaged W. L. Mackenzie King, a labor relations expert and future Canadian Prime Minister, to help him develop reforms for the mines and towns. Improvements included paved roads and recreational facilities, as well as worker representation on committees dealing with working conditions, safety, health, and recreation. He prohibited discrimination against workers who had belonged to unions and ordered the establishment of a company union. The miners voted to accept the Rockefeller plan.


title: Ludlow Massacre

text: Rockefeller Jr. also brought in pioneer public relations expert Ivy Lee, who warned that the Rockefellers were losing public support and developed a strategy that Rockefeller followed to repair it. Rockefeller had to overcome his shyness, go to Colorado to meet the miners and their families, inspect the homes and the factories, attend social events, and listen closely to the grievances. This was novel advice, and attracted widespread media attention. The Rockefellers were able both to resolve the conflict, and present a more humanized versions of their leaders.


title: Ludlow Massacre

text: Over time, Ludlow has assumed "a striking centrality in the interpretation of the nation's history developed by several of the most important left-leaning thinkers of the 20th century." Historian Howard Zinn, noted for his controversial reframing of U.S. history, wrote his master's thesis and several book chapters on Ludlow. George McGovern wrote his doctoral dissertation on the subject. In 1972, the same year as his U.S. presidential campaign, he published this dissertation with the help of historian Leonard Guttridge under the title "The Great Coalfield War".


title: Ludlow Massacre

text: A United States Commission on Industrial Relations (CIR), headed by labor lawyer Frank Walsh, conducted hearings in Washington, DC, collecting information and taking testimony from all the principals, including Rockefeller Sr., who testified that, even after knowing that guards in his pay had committed atrocities against the strikers, he "would have taken no action" to prevent his hirelings from attacking them. The commission's report endorsed many of the reforms the unions sought, and provided support for bills establishing a national eight-hour workday and a ban on child labor.


title: Ludlow Massacre

text: The last survivor of the Ludlow Massacre, Ermenia "Marie" Padilla Daley, was 3 months old during the event. Her father was a miner and she was born in the camp. Her mother took her and her siblings away as violence escalated; they traveled by train to Trinidad, Colorado. The evacuation resulted in the family having to split up afterward. Daley was cared for by various families and also placed for a time in orphanages in Pueblo and Denver. She worked as a housekeeper, then married a consultant whose work allowed them to travel the world. Daley died on March 14, 2019, at age 105.


title: Ludlow Massacre

text: Several popular songs have been written and recorded about the events at Ludlow. Among them are American folk singer Woody Guthrie's "Ludlow Massacre", Red Dirt country singer Jason Boland's "Ludlow", and Irish musician Andy Irvine's "The Monument (Lest We Forget)".


title: Ludlow Massacre

text: Upton Sinclair's novel "King Coal" is loosely based on the origin and aftermath of the Ludlow Massacre. Thomas Pynchon's 2006 novel "Against the Day" contains a chapter on the massacre.


title: Ludlow Massacre

text: American writer and Colorado Poet Laureate David Mason wrote what he calls a verse-novel, "Ludlow" (2007), inspired by the labor dispute. Composer Lori Laitman's opera "Ludlow" is based on Mason's book. The University of Colorado's New Opera Works presented Act I of the opera in June 2012, directed by Beth Greenberg.


title: Ludlow Massacre

text: In 1916, the United Mine Workers of America bought the site of the Ludlow tent colony. Two years later, they erected the Ludlow Monument to commemorate those who died during the strike. It was fabricated by the Jones Brothers Company of Barre, Vermont using local granite was commissioned by Sam Falsetto, president of the United Mine Workers of Trinidad, Colorado. The Springfield Granite Company served as the contractor. The monument was damaged in May 2003 by unknown vandals. The repaired monument was unveiled on June 5, 2005, with slightly altered faces on the statues.


title: Ludlow Massacre

text: The tent colony site was listed on the National Register of Historic Places in 1985, was designated a U.S. National Historic Landmark in 2009. Although the area continued to be occupied by mine workers and their families after the events of May 1914, they relocated, leaving the original encampment site relatively undisturbed. The site is consequently one of the best-preserved archaeological remains of such an encampment, and the monument is one of the earliest to commemorate a labor action of this type. The site is the first of its kind to be investigated by archeologists.


title: Ludlow Massacre

text: On May 7, 2003, vandals attacked the monument cutting off the sold granite/marble head of the male figure and the arm of the female figure. The missing parts were never recovered but replaced in 2005 with funding from private donations.


title: Ludlow Massacre

text: On April 19, 2013, Colorado Governor John Hickenlooper signed an executive order to create the Ludlow Centennial Commemoration Commission. The group worked to develop programming in the state, such as lectures and exhibits, to commemorate the Ludlow workers' struggle and raise awareness of the massacre. It worked with Colorado museums, historical societies, churches and art galleries, and supplied programming in 2014.


title: Ludlow Massacre

text: In 1996, the 1913–1914 Colorado Coalfield War Project began under the leadership of Randall H. McGuire of Binghamton University, Dean Saitta of University of Denver, and Philip Duke of Fort Lewis College, who later formed the Ludlow Collective. Their team conducted excavations of the territory of the former tent colony and surrounding areas.


title: Reverse engineering

text: Reverse engineering (also known as backwards engineering or back engineering) is a process or method through which one attempts to understand through deductive reasoning how a previously made device, process, system, or piece of software accomplishes a task with very little (if any) insight into exactly how it does so. It is essentially the process of opening up or dissecting a system to see how it works, in order to duplicate or enhance it. Depending on the system under consideration and the technologies employed, the knowledge gained during reverse engineering can help with repurposing obsolete objects, doing security analysis, or learning how something works.


title: Reverse engineering

text: Although the process is specific to the object on which it is being performed, all reverse engineering processes consist of three basic steps: Information extraction, Modeling, and Review. Information extraction refers to the practice of gathering all relevant information for performing the operation. Modeling refers to the practice of combining the gathered information into an abstract model, which can be used as a guide for designing the new object or system. Review refers to the testing of the model to ensure the validity of the chosen abstract. Reverse engineering is applicable in the fields of computer engineering, mechanical engineering, design, electronic engineering, software engineering, chemical engineering, and systems biology.


title: Reverse engineering

text: There are many reasons for performing reverse engineering in various fields. Reverse engineering has its origins in the analysis of hardware for commercial or military advantage. However, the reverse engineering process, as such, is not concerned with creating a copy or changing the artifact in some way. It is only an analysis to deduce design features from products with little or no additional knowledge about the procedures involved in their original production.


title: Reverse engineering

text: In some cases, the goal of the reverse engineering process can simply be a redocumentation of legacy systems. Even when the reverse-engineered product is that of a competitor, the goal may not be to copy it but to perform competitor analysis. Reverse engineering may also be used to create interoperable products and despite some narrowly-tailored United States and European Union legislation, the legality of using specific reverse engineering techniques for that purpose has been hotly contested in courts worldwide for more than two decades.


title: Reverse engineering

text: Software reverse engineering can help to improve the understanding of the underlying source code for the maintenance and improvement of the software, relevant information can be extracted to make a decision for software development and graphical representations of the code can provide alternate views regarding the source code, which can help to detect and fix a software bug or vulnerability. Frequently, as some software develops, its design information and improvements are often lost over time, but that lost information can usually be recovered with reverse engineering. The process can also help to cut down the time required to understand the source code, thus reducing the overall cost of the software development. Reverse engineering can also help to detect and to eliminate a malicious code written to the software with better code detectors. Reversing a source code can be used to find alternate uses of the source code, such as detecting the unauthorized replication of the source code where it was not intended to be used, or revealing how a competitor's product was built. That process is commonly used for "cracking" software and media to remove their copy protection, or to create a possibly-improved copy or even a knockoff, which is usually the goal of a competitor or a hacker.


title: Reverse engineering

text: Malware developers often use reverse engineering techniques to find vulnerabilities in an operating system to build a computer virus that can exploit the system vulnerabilities. Reverse engineering is also being used in cryptanalysis to find vulnerabilities in substitution cipher, symmetric-key algorithm or public-key cryptography.


title: Reverse engineering

text: As computer-aided design (CAD) has become more popular, reverse engineering has become a viable method to create a 3D virtual model of an existing physical part for use in 3D CAD, CAM, CAE, or other software. The reverse-engineering process involves measuring an object and then reconstructing it as a 3D model. The physical object can be measured using 3D scanning technologies like CMMs, laser scanners, structured light digitizers, or industrial CT scanning (computed tomography). The measured data alone, usually represented as a point cloud, lacks topological information and design intent. The former may be recovered by converting the point cloud to a triangular-faced mesh. Reverse engineering aims to go beyond producing such a mesh and to recover the design intent in terms of simple analytical surfaces where appropriate (planes, cylinders, etc.) as well as possibly NURBS surfaces to produce a boundary-representation CAD model. Recovery of such a model allows a design to be modified to meet new requirements, a manufacturing plan to be generated, etc.


title: Reverse engineering

text: Hybrid modeling is a commonly used term when NURBS and parametric modeling are implemented together. Using a combination of geometric and freeform surfaces can provide a powerful method of 3D modeling. Areas of freeform data can be combined with exact geometric surfaces to create a hybrid model. A typical example of this would be the reverse engineering of a cylinder head, which includes freeform cast features, such as water jackets and high-tolerance machined areas.


title: Reverse engineering

text: Reverse engineering is also used by businesses to bring existing physical geometry into digital product development environments, to make a digital 3D record of their own products, or to assess competitors' products. It is used to analyze how a product works, what it does, what components it has; estimate costs; identify potential patent infringement; etc.


title: Reverse engineering

text: Value engineering, a related activity that is also used by businesses, involves deconstructing and analyzing products. However, the objective is to find opportunities for cost-cutting.


title: Reverse engineering

text: Reverse engineering of printed circuit boards involves recreating fabrication data for a particular circuit board. This is done to allow benchmarking, and support for legacy systems.


title: Reverse engineering

text: In 1990, the Institute of Electrical and Electronics Engineers (IEEE) defined (software) reverse engineering (SRE) as "the process of analyzing a


title: Reverse engineering

text: subject system to identify the system's components and their interrelationships and to create representations of the system in another form or at a higher


title: Reverse engineering

text: level of abstraction" in which the "subject system" is the end product of software development. Reverse engineering is a process of examination only, and the software system under consideration is not modified, which would otherwise be re-engineering or restructuring. Reverse engineering can be performed from any stage of the product cycle, not necessarily from the functional end product.


title: Reverse engineering

text: There are two components in reverse engineering: redocumentation and design recovery. Redocumentation is the creation of new representation of the computer code so that it is easier to understand. Meanwhile, design recovery is the use of deduction or reasoning from general knowledge or personal experience of the product to understand the product's functionality fully. It can also be seen as "going backwards through the development cycle." In this model, the output of the implementation phase (in source code form) is reverse-engineered back to the analysis phase, in an inversion of the traditional waterfall model. Another term for this technique is program comprehension. The Working Conference on Reverse Engineering (WCRE) has been held yearly to explore and expand the techniques of reverse engineering. Computer-aided software engineering (CASE) and automated code generation have contributed greatly in the field of reverse engineering.


title: Reverse engineering

text: Software anti-tamper technology like obfuscation is used to deter both reverse engineering and re-engineering of proprietary software and software-powered systems. In practice, two main types of reverse engineering emerge. In the first case, source code is already available for the software, but higher-level aspects of the program, which are perhaps poorly documented or documented but no longer valid, are discovered. In the second case, there is no source code available for the software, and any efforts towards discovering one possible source code for the software are regarded as reverse engineering. The second usage of the term is more familiar to most people. Reverse engineering of software can make use of the clean room design technique to avoid copyright infringement.


title: Reverse engineering

text: On a related note, black box testing in software engineering has a lot in common with reverse engineering. The tester usually has the API but has the goals to find bugs and undocumented features by bashing the product from outside.


title: Reverse engineering

text: Other purposes of reverse engineering include security auditing, removal of copy protection ("cracking"), circumvention of access restrictions often present in consumer electronics, customization of embedded systems (such as engine management systems), in-house repairs or retrofits, enabling of additional features on low-cost "crippled" hardware (such as some graphics card chip-sets), or even mere satisfaction of curiosity.


title: Reverse engineering

text: Binary reverse engineering is performed if source code for a software is unavailable. This process is sometimes termed "reverse code engineering", or RCE. For example, decompilation of binaries for the Java platform can be accomplished by using Jad. One famous case of reverse engineering was the first non-IBM implementation of the PC BIOS, which launched the historic IBM PC compatible industry that has been the overwhelmingly-dominant computer hardware platform for many years. Reverse engineering of software is protected in the US by the fair use exception in copyright law. The Samba software, which allows systems that do not run Microsoft Windows systems to share files with systems that run it, is a classic example of software reverse engineering since the Samba project had to reverse-engineer unpublished information about how Windows file sharing worked so that non-Windows computers could emulate it. The Wine project does the same thing for the Windows API, and OpenOffice.org is one party doing that for the Microsoft Office file formats. The ReactOS project is even more ambitious in its goals by striving to provide binary (ABI and API) compatibility with the current Windows operating systems of the NT branch, which allows software and drivers written for Windows to run on a clean-room reverse-engineered free software (GPL) counterpart. WindowsSCOPE allows for reverse-engineering the full contents of a Windows system's live memory including a binary-level, graphical reverse engineering of all running processes.


title: Reverse engineering

text: Another classic, if not well-known, example is that in 1987 Bell Laboratories reverse-engineered the Mac OS System 4.1, originally running on the Apple Macintosh SE, so that it could run it on RISC machines of their own.


title: Reverse engineering

text: Software classification is the process of identifying similarities between different software binaries (such as two different versions of the same binary) used to detect code relations between software samples. The task was traditionally done manually for several reasons (such as patch analysis for vulnerability detection and copyright infringement), but it can now be done somewhat automatically for large numbers of samples.


title: Reverse engineering

text: This method is being used mostly for long and thorough reverse engineering tasks (complete analysis of a complex algorithm or big piece of software). In general, statistical classification is considered to be a hard problem, which is also true for software classification, and so few solutions/tools that handle this task well.


title: Reverse engineering

text: A number of UML tools refer to the process of importing and analysing source code to generate UML diagrams as "reverse engineering." See List of UML tools.


title: Reverse engineering

text: Although UML is one approach in providing "reverse engineering" more recent advances in international standards activities have resulted in the development of the Knowledge Discovery Metamodel (KDM). The standard delivers an ontology for the intermediate (or abstracted) representation of programming language constructs and their interrelationships. An Object Management Group standard (on its way to becoming an ISO standard as well), KDM has started to take hold in industry with the development of tools and analysis environments that can deliver the extraction and analysis of source, binary, and byte code. For source code analysis, KDM's granular standards' architecture enables the extraction of software system flows (data, control, and call maps), architectures, and business layer knowledge (rules, terms, and process). The standard enables the use of a common data format (XMI) enabling the correlation of the various layers of system knowledge for either detailed analysis (such as root cause, impact) or derived analysis (such as business process extraction). Although efforts to represent language constructs can be never-ending because of the number of languages, the continuous evolution of software languages, and the development of new languages, the standard does allow for the use of extensions to support the broad language set as well as evolution. KDM is compatible with UML, BPMN, RDF, and other standards enabling migration into other environments and thus leverage system knowledge for efforts such as software system transformation and enterprise business layer analysis.


title: Reverse engineering

text: Protocols are sets of rules that describe message formats and how messages are exchanged: the protocol state machine. Accordingly, the problem of protocol reverse-engineering can be partitioned into two subproblems: message format and state-machine reverse-engineering.


title: Reverse engineering

text: The message formats have traditionally been reverse-engineered by a tedious manual process, which involved analysis of how protocol implementations process messages, but recent research proposed a number of automatic solutions. Typically, the automatic approaches group observe messages into clusters by using various clustering analyses, or they emulate the protocol implementation tracing the message processing.


title: Reverse engineering

text: There has been less work on reverse-engineering of state-machines of protocols. In general, the protocol state-machines can be learned either through a process of offline learning, which passively observes communication and attempts to build the most general state-machine accepting all observed sequences of messages, and online learning, which allows interactive generation of probing sequences of messages and listening to responses to those probing sequences. In general, offline learning of small state-machines is known to be NP-complete, but online learning can be done in polynomial time. An automatic offline approach has been demonstrated by Comparetti et al. and an online approach by Cho et al.


title: Reverse engineering

text: Other components of typical protocols, like encryption and hash functions, can be reverse-engineered automatically as well. Typically, the automatic approaches trace the execution of protocol implementations and try to detect buffers in memory holding unencrypted packets.


title: Reverse engineering

text: Reverse engineering is an invasive and destructive form of analyzing a smart card. The attacker uses chemicals to etch away layer after layer of the smart card and takes pictures with a scanning electron microscope (SEM). That technique can reveal the complete hardware and software part of the smart card. The major problem for the attacker is to bring everything into the right order to find out how everything works. The makers of the card try to hide keys and operations by mixing up memory positions, such as by bus scrambling.


title: Reverse engineering

text: In some cases, it is even possible to attach a probe to measure voltages while the smart card is still operational. The makers of the card employ sensors to detect and prevent that attack. That attack is not very common because it requires both a large investment in effort and special equipment that is generally available only to large chip manufacturers. Furthermore, the payoff from this attack is low since other security techniques are often used such as shadow accounts. It is still uncertain whether attacks against chip-and-PIN cards to replicate encryption data and then to crack PINs would provide a cost-effective attack on multifactor authentication.


title: Reverse engineering

text: The first step after images have been taken with a SEM is stitching the images together, which is necessary because each layer cannot be captured by a single shot. A SEM needs to sweep across the area of the circuit and take several hundred images to cover the entire layer. Image stitching takes as input several hundred pictures and outputs a single properly-overlapped picture of the complete layer.


title: Reverse engineering

text: Next, the stitched layers need to be aligned because the sample, after etching, cannot be put into the exact same position relative to the SEM each time. Therefore, the stitched versions will not overlap in the correct fashion, as on the real circuit. Usually, three corresponding points are selected, and a transformation applied on the basis of that.


title: Reverse engineering

text: To extract the circuit structure, the aligned, stitched images need to be segmented, which highlights the important circuitry and separates it from the uninteresting background and insulating materials.


title: Reverse engineering

text: Finally, the wires can be traced from one layer to the next, and the netlist of the circuit, which contains all of the circuit's information, can be reconstructed.


title: Reverse engineering

text: Reverse engineering is often used by people to copy other nations' technologies, devices, or information that have been obtained by regular troops in the fields or by intelligence operations. It was often used during the Second World War and the Cold War. Here are well-known examples from the Second World War and later:


title: Reverse engineering

text: Reverse engineering concepts have been applied to biology as well, specifically to the task of understanding the structure and function of gene regulatory networks. They regulate almost every aspect of biological behavior and allow cells to carry out physiological processes and responses to perturbations. Understanding the structure and the dynamic behavior of gene networks is therefore one of the paramount challenges of systems biology, with immediate practical repercussions in several applications that are beyond basic research.


title: Reverse engineering

text: There are several methods for reverse engineering gene regulatory networks by using molecular biology and data science methods. They have been generally divided into six classes:


title: Reverse engineering

text: Often, gene network reliability is tested by genetic perturbation experiments followed by dynamic modelling, based on the principle that removing one network node has predictable effects on the functioning of the remaining nodes of the network.


title: Reverse engineering

text: Applications of the reverse engineering of gene networks range from understanding mechanisms of plant physiology to the highlighting of new targets for anticancer therapy.


title: Reverse engineering

text: Reverse engineering applies primarily to gaining understanding of a process or artifact in which the manner of its construction, use, or internal processes has not been made clear by its creator.


title: Reverse engineering

text: Patented items do not of themselves have to be reverse-engineered to be studied, for the essence of a patent is that inventors provide a detailed public disclosure themselves, and in return receive legal protection of the invention that is involved. However, an item produced under one or more patents could also include other technology that is not patented and not disclosed. Indeed, one common motivation of reverse engineering is to determine whether a competitor's product contains patent infringement or copyright infringement.


title: Reverse engineering

text: In the United States, even if an artifact or process is protected by trade secrets, reverse-engineering the artifact or process is often lawful if it has been legitimately obtained.


title: Reverse engineering

text: Reverse engineering of computer software often falls under both contract law as a breach of contract as well as any other relevant laws. That is because most end-user license agreements specifically prohibit it, and US courts have ruled that if such terms are present, they override the copyright law that expressly permits it (see "Bowers v. Baystate Technologies"). According to Section 103(f) of the Digital Millennium Copyright Act (17 U.S.C. § 1201 (f)), a person in legal possession of a program may reverse-engineer and circumvent its protection if that is necessary to achieve "interoperability," a term that broadly covers other devices and programs that can interact with it, make use of it, and to use and transfer data to and from it in useful ways. A limited exemption exists that allows the knowledge thus gained to be shared and used for interoperability purposes.


title: Reverse engineering

text: EU Directive 2009/24 on the legal protection of computer programs, which superseded an earlier (1991) directive, governs reverse engineering in the European Union.


title: The Natural (film)

text: The Natural is a 1984 American sports film based on Bernard Malamud's 1952 novel of the same name, directed by Barry Levinson and starring Robert Redford, Glenn Close, and Robert Duvall. Like the book, the film recounts the experiences of Roy Hobbs, an individual with great "natural" baseball talent, spanning the decades of Roy's career. In direct contrast to the book, the film ends in a positive tone. It was the first film produced by TriStar Pictures.


title: The Natural (film)

text: The film was nominated for four Academy Awards, including Best Supporting Actress (Close), and it was nominated for a Golden Globe Award for Best Supporting Actress (Kim Basinger). Many of the baseball scenes were filmed in 1983 at War Memorial Stadium in Buffalo, New York, built in 1937 and demolished in 1988. All-High Stadium, also in Buffalo, stood in for Chicago's Wrigley Field in a key scene.


title: The Natural (film)

text: In 1910s Nebraska, a young Roy Hobbs learns to play baseball from his father. After Hobbs Sr. suffers an early fatal heart attack, lightning strikes the tree he died next to. Hobbs makes a baseball bat from the splintered wood, burning a lightning bolt and the name “Wonderboy” into the barrel.


title: The Natural (film)

text: Now 19 years old, Hobbs heads to Chicago for a tryout with the Chicago Cubs, leaving behind his girlfriend, Iris. While on the train, he meets legendary ballplayer "the Whammer" (based on Babe Ruth), sportswriter Max Mercy, and Harriet Bird, a mysterious young woman following the Whammer. At a carnival during a stopover, Hobbs wins a bet that he can strike out the Whammer with just three pitches. Later Hobbs meets Bird in Chicago, and she asks if Hobbs's boast that he can be "the best there ever was," is true. Hobbs answers yes, and Harriet shoots him in the abdomen and then commits suicide.


title: The Natural (film)

text: Sixteen years later, in 1939, Hobbs is signed as a rookie to the New York Knights, a struggling club in last place. Manager Pop Fisher is furious that Hobbs was signed without his approval, believing him too old, and suspects the owner's motives. He refuses to play Hobbs but later relents, electing him to pinch hit, where he knocks the cover off the ball. Hobbs becomes a sensation and the Knights' fortunes turn around. Max Mercy finds Hobbs familiar but fails to recognize him.


title: The Natural (film)

text: Assistant manager Red Blow tells Hobbs that if Pop loses the pennant this year, his Knights ownership share will revert to the Judge, the team's majority owner. The Judge offers Hobbs $5,000 () to throw the season. Hobbs, unlike Bump Bailey, refuses the bribe. While watching Hobbs pitch during a practice session, Mercy suddenly remembers him and introduces Hobbs to Gus Sands, a bookie who places large bets against Hobbs. He also meets Pop's beautiful niece, Memo Paris, who was Bump's girlfriend. Their budding romance causes a distracted Hobbs' game to slump.


title: The Natural (film)

text: Hobbs' slump continues until during a game, he sees a woman dressed in white and then hits a home run shattering the scoreboard clock. The woman is Iris, and they later meet at a diner. She tells Hobbs she has a teenage son whose father lives in New York City. Their reunion restores Hobbs' hitting prowess, and the Knights surge into first place. However, at a team party, Hobbs collapses in pain and awakens in the hospital. A silver bullet removed from his stomach has caused long-term damage; the doctor warns him it could prove fatal if Hobbs continues playing baseball without giving the wound time to heal.


title: The Natural (film)

text: With Hobbs hospitalized, the Knights lose three games in a row, setting up a one-game playoff against the Pittsburgh Pirates. The Judge comes to the hospital and offers Hobbs an even bigger bribe to throw the game, threatening to expose his involvement with Harriet Bird to the press. Memo visits Hobbs and urges him to accept the Judge's offer and to walk away. Later, Iris also visits and assures Hobbs he is a great ballplayer.


title: The Natural (film)

text: Still recovering, Hobbs rejects the bribe and returns to the team. Watching from the stands, Iris sends a note to Hobbs in the dugout, saying she has brought their son to the game. In the ninth inning, the Knights are trailing. The Pirates bring in a young, hard-throwing pitcher, who, exploiting Hobbs' condition, throws inside, attempting to harm him. Hobbs hits a foul that splits his bat, Wonderboy, in two. Batboy Bobby Savoy brings him his own bat, the "Savoy Special", which Hobbs helped him make. Hobbs, down to his last strike, his wound bleeding through his jersey, smashes the ball into the stadium lights, winning the game and the National League pennant. The victory secures Pop's share of the team and the Knights advance to the World Series.


title: The Natural (film)

text: Later, back in Nebraska, Iris looks on as Hobbs plays catch with his son in the same field where he and his father once played.


title: The Natural (film)

text: Malcolm Kahn and Robert Bean acquired the rights to Bernard Malamud's 1952 novel "The Natural" in 1976. Phil Dusenberry wrote the first adaptation. In October 1981, Roger Towne, a Columbia Pictures story editor and brother of Robert Towne, quit to produce and write the screenplay, with Bean set to direct and Kahn co-producing.


title: The Natural (film)

text: In 1983, newly formed Tri-Star Pictures acquired the rights to the film adaptation, its first production. It was Robert Redford's first acting role in three years.


title: The Natural (film)

text: The film's producers stated in the DVD extras that the film was not intended to be a literal adaptation of the novel, but was merely "based on" the novel. Malamud's daughter said on one of the DVD extras that her father had seen the film, and his take on it was that it had "legitimized him as a writer."