In 1977, Andrewes moved to the United States to head the Time Museum, in Rockford, Illinois, at the invitation of its founder, Seth G. Atwood, a manufacturer of hardware and automobile parts. At the museum, housed in a hotel Atwood owned then called the Clock Tower Inn, Andrewes looked after hourglasses, water clocks, fire clocks, incense clocks, oil lamp clocks, electric clocks and atomic clocks, in addition to many marvelous mechanical clocks, 65 of which were kept running abreast of time, meaning they had to be set forward an hour every spring and turned back an hour in the fall.
The museum contained about 100 sundials. They ranged from a fifth-century Greco-Byzantine vertical dial to a brass and silvered-brass mechanical equinoctial standing ring dial, made by Richard Glynne about 1720 for Archibald Campbell, the Earl of Ilay, whose arms and initials were elaborately incorporated into its shining design, and which told the time with a focused pinhole of light instead of a shadow.
Andrewes modeled his business card on a sundial devised by 15-century astronomer Johannes Müller, or Regiomontanus. Andrewes' folded card, which exceeded the usual business-card dimensions even before it was opened, allowed recipients to convert it into a working sundial with the addition of a needle and thread according to directions printed on the back. Later, when Atwood's daughter announced her engagement, Andrewes designed a toast-rack sundial as a wedding present. "It was a square dial of the horizontal type," he recalls. "Instead of numbers, it was inlaid with different woods that helped you count the hours, and its triangular gnomon was cut with vertical slots, to hold your toast."
Toward the end of 1986, Atwood curtailed the museum's collecting and publishing activities. "Seth Atwood is the only person I know who was infected by the horological virus and later recovered," Andrewes says. "For most collectors, death is the only cure." The next year, Andrewes was appointed curator of Harvard's historic scientific instrument collection. The wealth of sundials there—more than 700—exceeded anything he had previously overseen. In 1992, Andrewes supervised the publication of a catalog covering a small subset of these: Ivory Diptych Sundials 1570-1750, with text by Steven Lloyd and hundreds of photographs, describing 82 tiny folding contrivances gathered from Germany, France, Italy and other countries, each bearing its own time design in blue, red, green and brown, with a string for a gnomon and a built-in compass to point it north. The following year, Andrewes organized a Longitude Symposium that drew 500 participants from 17 countries to celebrate the tercentenary of John Harrison's birth, and later he published an annotated edition of the proceedings, The Quest for Longitude.
His delving into that subject helped revive Andrewes' own sundial idea, what he calls the Longitude Dial. His original inspiration came from a 1610 map that University of Wisconsin cartographer David Woodward had once shown him. That map and others by the mathematician Franz Ritter are the oldest known examples of a gnomonic projection. They appear in Ritter's how-to book on sundials, Speculum Solis (Mirror of the Sun), published in Nuremberg, Germany. Ritter's map placed Nuremberg at the center of the Western Hemisphere. The farthest reaches of the map's landmasses look grossly distorted as a result, but the novel perspective causes the meridians of longitude to radiate out from the North Pole in straight lines, so they can double as the hour lines of a sundial. Ritter's innovative pairing of time and place might well have impressed any dialist, but it struck Andrewes with the force of a revelation. And although Ritter intended his gnomonic projection as the basis for a novel sundial, he seems never to have built one. Andrewes knew of no such dial anywhere. But he determined to make one.
It's a measure of the astonishing recent progress in computing that the first gnomonic projection that Andrewes commissioned—in 1979—was such an onerous undertaking that it was created on the University of Wisconsin's supercomputer, by Woodward. By the time Andrewes returned to dialing in earnest more than 20 years later, a gnomonic projection map could be drafted at home on a laptop in just minutes, thanks to Geocart, a cartography program developed by Daniel Strebe of Mapthematics in Renton, Washington. (Today, the gnomonic projection finds its most common application in aviation.) With Geocart, Andrewes realized he could design a dial plate for any location in the world. As a test, he created a paper-and-cardboard prototype for the coordinates of the hotel in which he and his family planned to vacation in Crete. "Everyone else was sunbathing," Cathy Andrewes recalled of that 2002 summer vacation. "William was balancing paper sundials on trash cans at the beach, trying to keep them from blowing away." Even after sunset he busied himself with the dial, since he had fitted it with an attachment, called a lunar volvelle, for telling time by moonlight. By August, he had convinced himself that the basic design was sound.
Inspired by the look of his favorite historical instruments, Andrewes arrayed the Roman numerals for the hours in a ring around the map, by hand, drawing their vertical strokes so they all pointed to the North Pole, and rendering their serifs concentric with the center of the dial. He wanted the small Arabic numerals that counted off ten-minute intervals to bow and tilt according to their longitude, and likewise the tiers of tiny tick marks subdividing the larger intervals into individual minutes. Decorative flourishes shaped like tridents or fleurs-de-lis, inserted at the half-hour points, would change their orientation and shape according to their distance from the pole. Andrewes appealed to Strebe, who, with his colleague Paul Messmer, created a "sundial plug-in" for Adobe Illustrator that lets Andrewes automatically adapt his hour-ring artwork to any number of locations with only minor adjustments.
Then he cast about for the right stone. "I thought it had to be bright stone," he recalled. "Most sundials are made of light-colored materials because those show off a shadow to best advantage. I'd gone down to see this wonderful chap in Newport, one of the great monument stonecutters in America. I wanted him to cut a dial for me by hand in granite. He took one look at the design—the map, the numerals, the precision constraints for the minute ticks—and said, ‘You must be mad.'" Andrewes turned to establishments where stonecutting had been mechanized and modernized, namely the manufacturers of cemetery memorials. On a visit to Rock of Ages in Methuen, New Hampshire, he learned that black gabbro stone could be etched by laser. What's more, it displayed the unusual property of turning white where laser-etched, so that every incision appeared both cut-in and painted-on. "That was the turning point," Andrewes said. The map's white continents would stand out from dark seas, and decorations too delicate to be chiseled in stone could be transferred to it from pen-and-ink drawings by a carbon-dioxide laser's white light. The finished dial plate, polished to a mirror-like luster and water-sealed, would show off a gnomon shadow as well as any pale-colored stone could do. Gary Hahn, a stone artisan in New Hampshire, has since become Andrewes' collaborator. Together they found a source of superior gabbro from China. Andrewes' friend and colleague Linn Hobbs, a materials scientist and nuclear engineer at MIT, advised him on how best to attach metal parts to the dial and pedestal.
Andrewes has built ten Longitude Dials in the past two years and delivered these to clients in England, Spain, Connecticut, Maryland, New York State and California. Each is a precision timepiece without hands—a wheel of polished black stone bearing a laser-etched map that centers its intended location inside a private time universe, where the hours pass visibly minute by minute on a ring of Roman numerals reminiscent of an elegant 18th-century watch face. In addition to giving the correct time, each dial acknowledges an important moment in its owner's life—a wedding anniversary, a birthday—by casting an annual commemorative shadow along a customized date line. "It's a magnificent thing, a unique type of instrument that does not seem to have been built ever before," says Bruce Chandler, a mathematician at the City University of New York.
Andrewes builds his signature dial in three sizes, the largest of which is nearly four feet across and costs at least $50,000 with its pedestal and base. The smaller, garden dial also stands on a permanent pedestal and base, and starts at about $30,000. The petite terrace dial, only a foot in diameter, has adjustable brass feet, along with a tiny spirit level tucked in a drawer underneath, that help it accommodate to a slanting tabletop or a sloping porch. In its handmade wooden presentation box, it starts at $15,500.