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Topics: patented, patent, scientific, electric, apparatus, patents, caisson, tbe, scientific american, Topics: scientific, automobile, machine, american, tion, center, device, electric, moving pictures, Topics: motor, boat, scientific, electric, engine, gasoline, speed, american, scientific american, Topics: scientific, machine, air, tion, steam, buy, engine, american, tie plate, scientific american, Topics: scientific, electric, american, munn, automobile, motor, patent, steam, steam turbine, scientific Topics: scientific, automobile, tion, device, traction, machine, motor, patent, traction engine, scientific Topics: scientific, patent, tion, american, object, machine, device, apparatus, cylinder head, scientific Topics: scientific, ties, apparatus, tion, orinoco, device, american, patent, scientific american, steam, Topics: patent, steam, scientific, feet, patents, inches, american, patented, scientific american, iron, Topics: tbe, steam, scientific, patented, water, steel, iron, vessel, ocean steamers, locomotive, motive Topics: scientific, american, steam, automobile, tion, supplement, yarn, feet, scientific american, steel, Topics: scientific, american, tion, construction, apparatus, railroad, patent, speed, average speed, Topics: claim, combination, purpose, patent, manner, arranged, constructed, set, purpose set, steam, beet Topics: patent, steam, iron, assignor, patents, machine, tion, scientific, molten iron, surface, infusorial Topics: scientific, american, patent, apparatus, going, people, tion, mars, scientific american, munn, Topics: scientific, automobile, american, electric, motor, device, eclipse, apparatus, scientific american, Topics: scientific, american, colorado, catalog, feet, river, machine, tion, scientific american, patent, Topics: scientific, american, tion, supplement, device, electric, railroad, artificial, scientific Topics: scientific, naval, guns, american, speed, feet, ships, inches, armor, gun, residuary resistance, Topics: steam, patented, patent, shaft, boiler, improved, scientific, iron, scientific american, electric, Topics: inches, armor, scientific, naval, steel, torpedo, feet, guns, main deck, scientific american, Topics: patent, patented, silk, apparatus, tlie, improved, scientific, steam, scientific american, tbe, Topics: pewter, scientific, electric, torpedo, radium, printing, apparatus, automobile, scientific Topics: scientific, american, supplement, electric, tion, steam, tbe, exposition, american supplement, Topics: patent, scientific, vapor, apparatus, steam, patents, tion, patented, scientific american, Topics: rear, scientific, clutch, transmission, engine, american, automobile, shaft, scientific american, Topics: scientific, eclipse, american, arc, machine, tion, motor, patent, scientific american, feet, Topics: steam, patent, scientific, iron, truck, consists, improved, center, scientific american, feet, Topics: feet, scientific, york, steel, american, dam, city, construction, scientific american, railroad, They studied every inch of plaster to see where it had fallen off, whether it was holding together or holding to the wall, and whether it had cracked; they also looked for places where rock fragments were jutting through the plaster.
Ear- lier efforts at restoration had tried, unsuccessfully, to stem the damage by holding the plaster in place with gauze above, bot- tom. This time the approach was thorough: conservators re- moved the salt crystals, reattached the plaster to the walls and cleaned the paintings right. At the same time, the team recorded the extent of the salt crystallization on the surface of the paintings and be- tween the rock face and the plaster.
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Finally, they located the earlier interventions: the places where paintings had been re- touched, holes patched, and facing—such as gauze or adhe- sive tape—applied. The Moras and their colleagues started by taking minute pigment samples from the paintings as well as samples of the plaster underneath. In the interim, they prevented further degra- dation by applying strips of Japanese mulberry bark paper to the plaster, which kept it from falling off the walls and which could be easily removed once they were ready to begin work.
The binding medium— which holds the pigments together—was largely gum arabic, a natural resin from a local acacia tree. The plaster was composed of gypsum, anhydrite and Nile silt, with some crushed limestone mixed in; wheat straw had been used to reinforce it and to prevent it from cracking as it dried. Once they knew what they were dealing with, the team members could set about the work. It was critically important that these efforts not affect the original colors. So before they even started any of this con- servation work, Michael Schilling of the Getty Conservation Institute made 1, color measurements at locations throughout the tomb.
He used a chromometer in this case, a Minolta CR to assess exact hue. These records not only helped to guide the process by demonstrating that no shift in the color had occurred but also will aid ongoing monitoring of the paintings. Keeping the Salt Out Concern about the future of these paintings centers on the most obvious threat: salt. When work began on the tomb, thick, millimeter 0.
The salt came from Theban limestone, the marine sediment into which the tomb was cut. Salt is not a worry in most tombs, because the extremely dry Egyptian climate serves as a powerful preserva- tive, keeping mummies and their artifacts sere and intact. Not everyone who has worked on the project agrees—even today, after years of study—about where exactly the water came from. That moisture, however, would not have caused thick layers of crystals to form.
A more probable explanation is the very occasional, but very heavy, rain that falls about every 50 years on aver- age. To monitor humidity and temperature, one of us Maekawa recorded both the external climate and the microclimate of the tomb over several years and seasons. These outside conditions could af- fect the tomb because of leaks at the entrance, but for the most part, the internal temperature remained about 29 degrees C and humidity was stable at 50 percent. This movement caused the paintings and plaster to stay dry. When visitors entered the tomb, how- ever, humidity rose sharply.
Maekawa had to take into account the fact that peak tourist season falls primarily during the summer—just when air is not circulating back outside and humidity could easily become trapped in the tomb.
Shin Maekawa used a solar-powered system to study the microclimate of the tomb left ; he determined that the number of visitors had to be carefully regulated so that the temperature and humidity in the tomb did not catalyze the growth of salt crystals again. No more than tourists are allowed in per day below. Carbon dioxide can also react with moisture in the air, pro- ducing carbonic acid, which can discolor the wall paintings. Maekawa found that ambient levels of parts per million ppm surged to 2, ppm when tourists visited the tomb.
For health reasons, levels should not get higher than 1, ppm.
The Edge of the Sky
They installed lights that gave off very little heat. Since late a maximum of people a day, in groups of 10 to 15, have been allowed in for no more than 15 minutes. Despite this careful monitoring, the potential damage of these visitors needs to be considered carefully and periodically evalu- ated.
Because damage is irreversible and cumulative—and because we seem to be able to destroy in just a few decades what has survived for millennia—it may not be right for ev- eryone to have the access they expect. After all, that is what Ramses II intended for his wife: a peaceful, sealed existence. Stanley Mayes.
Walker, Edited by M. Corzo and M. Getty Conservation Institute, Los Angeles, Daily Life in Ancient Egypt. Andrea G. McDowell in Scientific American, Vol. House of Eternity, the Tomb of Nefertari. John K.
McDon- ald. Paul Getty Museum, Los Angeles, Agnew, who received his doctorate in chemistry, is group director for information and communications at the GCI. Maekawa, who specializes in environ- mental monitoring and the control of microenvironments, is a se- nior scientist at the institute. Maekawa developed the oxygen-free display cases for pharaonic mummies that are used in the Egyptian Museum in Cairo. Their continued survival depends on striking a careful balance be- tween public access and protection of the paintings.
From to , Japan lived in strict, self-im- posed isolation from the West.
Devotees of math, evidently samurai, merchants and farmers, would solve a wide variety of geometry problems, in- scribe their efforts in delicately colored wooden tablets and hang the works un- der the roofs of religious buildings. These sangaku, a word that literally means mathematical tablet, may have been acts of homage—a thanks to a guiding spirit— or they may have been brazen challeng- es to other worshipers: Solve this one if you can! For the most part, sangaku deal with ordinary Euclidean geometry. But the problems are strikingly different from those found in a typical high school ge- ometry course.
Circles and ellipses play a far more prominent role than in West- ern problems: circles within ellipses, el- lipses within circles. One problem reproduces the Descartes circle theorem. Many of the tablets are exceptionally beautiful and can be regarded as works of art. Pleasing the Kami It is natural to wonder who created the sangaku and when, but it is easier to ask such questions than to answer them. The custom of hanging tablets at shrines was established in Japan cen- turies before sangaku came into exis- tence.
Because the kami, it was said, love horses, those worshipers who could not present a living horse as an offering to the shrine might instead give a likeness drawn on wood. As a re- sult, many tablets dating from the 15th century and earlier depict horses.
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Of the sangaku themselves, the oldest surviving tablet has been found in To- chigi Prefecture and dates from Another tablet, from Kyoto, is dated , and a third is from The 19th-century travel diary of the mathe- matician Kazu Yamaguchi refers to an even earlier tablet—now lost—dated Other collections followed throughout the 18th and 19th centuries.
These books were either hand- written or printed with wooden blocks and are remarkably beautiful. Today more than tablets survive, with ref- erences to hundreds of others in the various collections. From a survey of the extant sangaku, the tablets seem to have been distributed fairly uniformly throughout Japan, in both rural and ur- ban districts, with about twice as many found in Shinto shrines as in Buddhist temples. Most of the surviving sangaku con- tain more than one theorem and are fre- quently brightly colored. The proof of the theorem is usually not given, only the result.
Other information typically includes the name of the presenter and the date. Not all the problems deal sole- ly with geometry. Some ask for the vol- umes of various solids and thus require calculus. This point raises the interest- ing question of what techniques the practitioners brought into play; some speculations will be offered in the fol- lowing discussion. Other tablets con- tain Diophantine problems—that is, al- gebraic equations requiring solutions in integers. In modern times the sangaku have been largely forgotten but for a few devotees of traditional Japanese mathe- matics.
Among them is Hidetoshi Fu- kagawa, a high school teacher in Aichi Prefecture, roughly halfway between Tokyo and Osaka. A mention of the math tablets in an old library book greatly astonished him, for he had never heard of such a thing. Since then, Fukagawa, who holds a Ph. This problem is from a sangaku, or mathematical wood- en tablet, dated in Tokyo Prefecture. It asks for the radius of the nth largest blue circle in terms of r, the radius of the green circle.