Historical Science & Technology, Technology

Torquetum & Rectangulus

The above is not the name of the illest hip hop duo since OutKast. Instead, the torquetum and rectangulus are medieval astronomical instruments used for spherical trigonometry.

The Torquetum of Jabir ibn Aflah

Also known as the turquet, the torquetum is designed to measure and convert three sets of coordinates—horizontal, equatorial, and ecliptic. First developed by Spanish Muslim astronomer and mathematician Jabir “Big Jabir” ibn Aflah in the late 12th or early 13th century CE, it is essentially an analog computer.

An example of a torquetum can be seen in Swiss artist Hans “Big Hans” Holbein the Younger’s The Ambassadors (below), above the elbow of the dude on the right.

The Ambassadors, by Hans Holbein the Younger

Wallingford’s Rectangulus

Approximately a century later in 1326, English Catholic monk and mathematician Richard “Big Dick” of Wallingford developed the rectangulus. Perpetually irked by the limitations of astrolabes, Big Dick designed the device to measure the angles between planets and other astronomical bodies, as the torquetum does; however, the rectangulus is calibrated via linear scales and read by plumb lines, and resolves polar measurements directly into their Cartesian components.

Technically, the rectangulus is a form of skeleton torquetum—a series of nested angular scales that allow measurement of azimuth and elevation in direct polar coordinates relative to the ecliptic. Prior to the invention of the rectangulus, converting these coordinates required the most advanced mathematics that had yet been developed. Ye olde rectangulus simplified these and further calculations.

The original rectangulus is lost to the sands of time, but extant examples date back to the 1600s. The device was comprised of a brass pillar with numerous linear scales hinged above it. Sights on the upper arm allowed it to be easily aimed at the intended astronomical object. Plumb bob lines descending from the scales intersected with linear scales, which were themselves marked on horizontal scales. This gave measurements in trigonometric ratios, rather than angles. Math, right?!

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Historical Science & Technology

The Warren Field Calendar

The Warren Field Calendar is an archaeological excavation discovered in the Dee River Valley of Aberdeenshire, Scotland, in 2004. It was not until 2013, however, that the find was discovered to be the world’s oldest known calendar, dating back over 10,000 years.

The Mighty Mesolithic Monument of Aberdeenshire

Warren Field is located near Crathes Castle in Aberdeenshire county, in northeastern Scotland. The field itself contains a series of a dozen purpose-dug pits that are believed to correspond to the twelve phases of the Moon, as in a lunar calendar. It was discovered from the air by the Royal Commission on the Ancient and Historical Monuments of Scotland and first excavated in 2004.

Crathes Castle (no, I couldn’t find any pics of the Calendar itself–sorry!)

The twelve pits are shaped to mimic the phases of the moon, and appear to be intended to help the observer track lunar months. The pits align along the southeastern horizon, and with sunrise on the day of the Winter Solstice. This provides annual astronomical corrections to coordinate the solar year with the lunar cycles, and helps account for the asynchronous solar year (which is why we need Leap Day every four years).

The Warren Field Calendar may also have been used as a seasonal calendar to help nearby communities of the age track the migration of animals they hunted for sustenance. The fact that it was created by a society of hunter-gatherers, rather than farmers, is unique amongst historically significant ancient calendars.

Evidence indicates that the pits were carefully maintained and repeatedly reshaped in response to shifting solar and lunar cycles; the monument may have been altered hundreds of times over the 6,000 year period in which it was used.

For whatever reason, the Warren Field Calendar fell out of use approximately 4,000 years ago. The find has been dated to roughly 8000 BCE, during the Mesolithic Period (circa 10,000 to 5000 BCE). Thus, the Warren Field Calendar predates the next-oldest historically-known calendars, from Mesopotamia, by over 5,000 years.

Photo credit: -epsilon- via Foter.com / CC BY

Historical Science & Technology, Technology

Tools, Not Cocktails: A Brief History of the Screwdriver

Everybody knows the good ol’ screwdriver. It’s one of the most useful tools in any toolbox, and almost everyone, no matter how mechanically inclined or not, has at least one somewhere in the house. The screwdriver is one of those devices that is so simple, and has been around so long, that it seems like it’s always been a thing—not really invented so much as it has just existed since the dawn of civilization. Where, then, did the noble screwdriver come from?

Screwin’ Around Medieval-Style

The first historical evidence of humans using screwdrivers comes from Medieval Europe, toward the tail end of the 15th century CE. The long shared border between Germany and France makes it difficult to say for sure in which of the two countries the tool was invented. The earliest written evidence is found in the Hausbuch (“housebook”) of Wolfegg Castle, a manuscript written betwixt 1475 and 1490. In Germany, the tool was known as the Schraubendrehe (“screwturner”); in France, tournevis (“turnscrew”); English speakers, naturally, ignored these two perfectly reasonable (and more aurally pleasing) translations and went with screwdriver, for some reason.

These old-timiest of old-timey screwdrivers had pear-shaped wooden handles and were, perhaps unsurprisingly, made to fit slotted screws—what are now often called flathead screws, which were the only type of screws in existence at the time. However, very little actual evidence of screwdrivers themselves from this period exists; we only know that screwdrivers were used for the next three centuries because screws from throughout this period have been found.

Advancements in Screwdriving

One key early use of screwdrivers was in the assembly of firearms, which had only recently become a thing. In early guns, a jaw mechanism was used to hold the pyrites that ignited when struck to fire a bullet. These jaws needed to be replaced frequently, and were held in place by screws. This lead to a number of refinements in screwdriver design, though all screws remained single-slotted until the late 19th century.

It was not until the Industrial Revolution when Job “Big Job” Wyatt and his brother William “Big Willie Style” Wyatt developed a way to quickly, easily, and inexpensively produce screws that the fasteners, and therefore screwdrivers, came into popular, widespread use. With this increase in popularity came considerable refinement and diversification.

Big Pete vs. Big Hank

P.L. “Big Pete” Robertson, a Canadian inventor, developed the first commercially successful socket-head screws and, by necessity, screwdrivers, in 1908. Socket-head screws remain popular today, though they would likely be even more popular had Robertson been able to successfully market them to the then-nascent (and rapidly growing) automotive industry.

Instead, automakers struck a deal with the American Screw Company (who had themselves recently struck a deal with Henry F. “Big Hank” Phillips of Portland, Oregon, inventor of the Phillips-head screw, to mass-produce his new and improved screw), and in 1936, the Phillips screw became the standard throughout the American auto industry. Today, the Phillips-head is the most popular screw type in the world.

Photo credit: Noel C. Hankamer via Foter.com / CC BY-NC-SA

Historical Science & Technology, Technology

I Can See For Miles, Pt. II: A Brief History of Prism Binoculars

Welcome to part two of the Sandy Mountain Historical & Technological Society’s brief history of binoculars. In the gripping cliffhanger finale of part one, we introduced the prism binocular design, which was developed as a method of righting the inverted images presented by the Keplerian optical design. Today, our tale concludes with a closer look at the technology that changed the long-distance viewing game forever.

Go Go Porro Bro Bro

Porro prism binoculars are the kind of field glasses you most likely picture your grandfather using. (Go ahead and conjure up a quick mental image of that. We’ll wait.) Named for the Italian inventor who developed this particular lens configuration in 1854, Ignazio “Big Iggy” Porro, this type of binoculars uses Porro prisms (also developed by Big Iggy) arranged in a Z-pattern to flip the image the right way ‘round. By necessity, Porro prism binoculars are wide, with widely-spaced objective lenses (the ones you point toward what you’re looking at) that are offset from the ocular lenses (the ones you look through, also called eyepiece lenses).

Likely the greatest photo of Porro prism binoculars ever taken.

Likely the greatest photo of Porro prism binoculars ever taken.

One significant benefit of the Porro prism design is that its folding optical path (created by the Z-configuration of lenses and prisms) allows the binoculars to have a focal length that is longer than the physical length, sometimes significantly longer. The wider space of the objective lenses also gives the presented image a better sense of depth.

Cat On A Hot Tin Roof Prism

Developed in the 1870s by noted great-French-name-haver Achille Victor Emile “Big Vic” Daubresse, roof prism binoculars use either the Abbe-Koenig prisms (invented by German engineers Ernst Karl “Big Ern” Abbe and Albert “Big Al” Koenig, and later patented, Thomas Edison-style, by Carl Zeiss in 1905) or Schmidt-Pechan prisms, a.k.a. Pechan prism pairs to invert the image to its proper orientation. In this configuration, the objective lenses are aligned with the eyepiece lenses.

Military-grade roof prism field glasses.

Military-grade roof prism field glasses.

The roof prism design results in field glasses that are narrower and more compact than their Porro prism cousins. And, whereas Porro prism binoculars occasionally need their prisms realigned, the fixed alignment of roof prism models eliminates the need for realignment, except in extreme circumstances. However, due to the silvered surfaces of their lenses and prisms, roof prism binoculars present images that are generally 12-15 percent darker than equivalent Porro prism binocs. Additionally, due to the tighter tolerances required for proper alignment of the optical elements, roof prism binoculars tend to be more expensive than the Porro prism variety.

Top photo credit: The U.S. National Archives via Foter.com / No known copyright restrictions
Bottom photo credit: Caro’s Lines via Foter.com / CC BY-NC-SA


Historical Science & Technology, Technology

I Can See for Miles: A Brief History of Field Glasses

Binoculars. Binocs. Field glasses. The ol’ spysie eyesies. Whatever you call them, these popular, (mostly) handheld, binocular telescopes have been around for centuries, essentially since the invention of the boring ol’ monocular telescope (commonly known as the telescope). Which makes sense, since, really, just put two regular telescopes side by side and you’ve pretty much got binoculars.


“Whaddaya see out there, Mildred?”

Galileo Figaro!

The earliest field glasses utilized “Galilean optics”—a convex objective lens (the one you point at what you’re looking at) paired with a concave eyepiece lens (the one you look through, also called the ocular lens). While Galilean optics do present magnified images oriented in the correct direction, unlike the camera obscura and other optical devices that present upside-down images, they provide only a very narrow field of view, and cannot provide particularly high magnification.

The same basic design is still used in modern opera glasses and el cheapo kiddie binoculars, as well as surgical and jewelers’ loupes that don’t require high magnification. The technology remains popular for such applications because they can be very short and produce clear, upright images through a simple design.

Put Some Kepler in Your Step

A significant improvement was made through the use of Keplerian optics, a design used in the first refracting ocular telescopes. Because the image formed by the objective lens is viewed through a positive eyepiece lens, Keplerian optics provide higher magnification and a clearer image. However, this configuration does produce an inverted image, and requires an additional lens or lenses to present a correctly-oriented image.

Erecting Lenses (Oh, Hush…)

Aprismatic field glasses using Keplerian optics have either one or two additional relay lenses betwixt the objective and ocular lenses. By necessity, the design of these binoculars made them too long for practical use. They became obsolete with the invention of prism binoculars (see below) in the late 19th century CE and quickly fell out of use.

Prism Isn’t Just A Disappointing Katy Perry Album

The new-and-improved binoc design, known as prism binoculars, utilize prisms to invert the image so that it is presented right side up. There are two common prism binocular variations: porro prism and roof-prism. Tune in next week to learn about these game-changing field glasses.

Photo credit: MLazarevski via Foter.com / CC BY-ND