Thompson (13) provides some details on eighteenth century practice. First, the disks were cast in approximately the desired curve, to minimize the amount of subsequent grinding and polishing (speculum metal was notoriously difficult to work). The grinding was done with a convex iron tool, and emery or sand as the abrasive. The polishing was with a pitch lap, and rouge.

  In view of the tendency of speculum metal to tarnish, it might be wise to take a piece of modern window glass and use it to close off the "business end" of the reflector (Texereau 189).

  Improvisations

  Eyeglasses. Could the eyeglasses of deceased Grantville residents be recycled for use in telescopes? Obviously, eyeglass lenses are typically singlets, not achromatic doublets. But we are comparing them, for now, not with even Doland's lenses, but with those available in the early seventeenth century. By down-time standards, they're marvelously clear.

  About 80% of eyeglass lenses are plastic, and the remainder are glass. Plastic lens can be impact-resistant polycarbonate, "CR39," or a "High Index" plastic.

  A telescope lens is likely to be larger, thicker, and more accurately ground than one for eyeglasses. (MadeHow).

  The first impediment to the recycling of eyeglasses for astronomical use is their small size. I haven't found any statistics, but the effective diameter of ophthalmic lenses (that is, the longest line from edge to edge, and thus the minimum diameter of the original lens blank) seems to run 40-75 mm. If the lens isn't circular, then when the lens is cut down to circular for telescope use, it will be narrower. For example, my eyeglasses have an effective diameter of 50 mm and a height of only 38 mm. That is not much of an improvement on the Galilean lenses.

  Another issue is focal length. Pope says "a sharply curved eyeglass lens is not expected to perform as well as one of flatter shape." All else being equal, the more sharply curved the glass, the shorter its focal length.

  To minimize spherical and chromatic aberration (and with singlet lenses, you worry about both) you would want to use a high f-ratio. And that usually means a relatively high focal length. Even with modern refractors, a typical ratio is 15:1 ("f/15"). Thus, if you were using a 50mm diameter eyeglass lens as the objective, the desired focal length would be 750mm.

  Unfortunately, you are probably going to have a hard time finding that long a focal length in an eyeglass. Opticians don't usually talk about focal length; they refer instead to refractive power, measured in Diopters. The focal length is the reciprocal of the refractive power, so a 2.0D lens has a 500 mm focal length. And you would need a 1.33D lens to get 750 mm.

  Myopia (short-sightedness) is corrected with a concave (negative) lens and hyperopia with a convex (positive) lens. (Bear in mind that concave and convex are relative to the light source, so you can convert a negative lens into a positive one by flipping it.)

  Low myopia is 0-3D, medium is 3-6D, and high is 6 or worse. Among Americans at least forty years old, 25.4% are 1D or worse, and 4.5% 5D or worse. The milder the myopia, the less likely it is to be corrected. A 3D lens would have a focal length of only 333 mm.

  Hyperopia usually isn't corrected unless it is at least 3D. Among the same population, 9.9% had hyperopia of 3D or greater. (Kempen)

  A myopic patient may also have astigmatism, and if the lens corrects for the latter, it isn't going to be useful for astronomy because it will then introduce astigmatism.

  All in all, it looks like prescription eyeglass lenses are likely to prove too small and too short in focal length to be useful as objectives—even in competition with seventeenth-century lenses.

  Curiously, the most useful eyeglasses are probably those cheap 1-3 diopter reading glasses you can buy in a drugstore. People in their forties might want one diopter glasses, and as they age, the required goes up about 0.5 diopter per decade (Duenwald). A one diopter 50 mm eyeglass would provide a nice f/20 objective, albeit a rather small one.

  Eyeglass diameter is not a problem for eyepieces. Unfortunately, focal length is. If a refractor had an objective with a focal length of 1000 mm, then a 3D eyepiece (333 mm) would yield a magnification of only 3x. To match the maximum magnification of Galileo's scopes (30x), you would need to couple that eyepiece to an objective with a focal length of 10,000 mm—over thirty feet! You could keep the objective at 1000 mm if you could find an eyeglass which was just 33 mm focal length—but that would correspond to a refractive power of 30D!

  Fixing up Department Store Telescopes. In general, the worst parts on these scopes are the eyepieces (mostly plastic, narrow field of view, poor eye relief, non-standard barrels, and a low focal length chosen to provide absurdly high magnification) the mounts ("sag city"), and the finder scope. So the key is to replace the eyepiece, mount and finder scope with something better (Portuesi, Trott).

  The eyepiece is the trickiest part to fix. Trott suggests salvaging the eyepieces from an inexpensive or broken pair of binoculars. He warns that these have to be prism style binoculars ("Z" shape); the straight binoculars are Galilean refractors.

  Telescope Prices

  James Short, in the late eighteenth century (multiply by 0.8 for 1632 equivalent), had a catalogue offering his Gregorian and Newtonian telescopes for sale. Here are his Gregorian prices:

  (Thompson, 14)

  Herschel borrowed a 4.5 incher, but couldn't afford to buy one. That led him to teach himself the arcane art of telescope making. He started with refractors and, finding that too difficult, turned to reflectors (Bell 32). Eventually, he sold his own scopes, a 6.5 inch reflector for 100 guineas and an 8.8 inch for 200-300.

  Dolland, in the mid-eighteenth century (prices within 10% of 1632) sold a refractor with a two inch achromatic objective, and 24 inch focal length, for 2 guineas. One with a simple objective sold for about one-sixth the price.

  (See Thompson 14-18.)

  Practical Use of Astronomical Telescopes

  In the introduction, I discussed the philosophical value of the telescope as a tool for convincing the intelligentsia of Europe to accept the teachings of twentieth-century science. But the telescopes, especially with up-time inspired improvements, are of some immediate practical value.

  Telescopes can be used to accurately map the heavens, with benefits for those traveling long distances by land, sea or air.

  While some up-time star position information is available, it is anachronistic because of almost four centuries of precession. In "Soundings and Sextants," I expressed the opinion that the late-sixteenth century Tycho Brahe data for the northern hemisphere stars would be more useful in 163x than "back-precessed" data from the typical twentieth century "star guide." (If astronomy software with a good precession algorithms are available to the up-timers, then I will have to retract that statement.) In any event, there will be a demand for "current" star positions determined with the precision which up-time inspired telescope designs would make possible. That is especially true for southern hemisphere stars, which are poorly covered by Brahe.

  In addition, the telescope can be used to determine the "current" (163x) orbital elements of the moon and planets, and thus to predict the future positions of these celestial bodies.

  And of course the Sun, too.

  Thus, the telescope will facilitate the creation of accurate ephemerides, and hence lead to improvements in the art of navigation.

  When traveling, we need to know not only where we are, but also where we are going. The telescope will play an important role in mapping. It is true that the latitudes and longitudes of many locations will be deducible from up-time maps, by interpolation between the drawn latitude and longitude lines. The accuracy of the interpolation will be dependent on the scale of the map, and on the accuracy of the tool used to measure the distance between the location and the nearest line. For example, the grid for the Hammond Citation Atlas map of Germany uses lines which are two degrees apart. We can probably determine latitude and longitude of the locations shown on this map with an accuracy of a few arc-minutes.

  To achieve greater accuracy, or to determine the latitude or longitude of unmapped locations, we will need to make telescopic observations.

  For example, the telescope can also be used, at least on land, to observe the moons of Jupiter. The changing orientations of the moons provides a reference time which, when compared with the local time indicated by the movement of the Sun, yields the longitude of the point of observation.

  Telescopes can also be put to terrestrial use, such as surveying, communications (reading flag or light signals), and navigation (seeing landmarks or hazards). Of course, for these purposes, you need an erect image, such as that offered by the Galilean refractor (which is why that design persists in opera glasses) or the Cassegrain reflector. The inverted image of the Kepler refractor or Newtonian reflector can be reverted by a lens or mirror, but at the cost of additional light loss.

  Conclusion

  I have not yet commented on the social value of the telescope, as a tool for increasing interest in science. For the Florentine court, Galileo was as much an entertainer as a scientist; he gave telescope demonstrations at parties. Herschel, after discovering Uranus, got treatment similar to that of a modern rock star. Many of the seventeenth- and eighteenth-century intelligentsia dabbled in astronomy (Bell 19).

  In 1584, Giordano Bruno wrote, "God is infinite, so His universe must be too. Thus is the excellence of God magnified and the greatness of His kingdom made manifest: He is glorified not in one but countless suns; not in a single world but in a thousand thousand I say in an infinity of worlds."

  Telescopes show us a myriad of stars and other wonders which are not visible to the naked eye.

  Bibliography

  Summerlin, Chemical Demonstrations: A Sourcebook for Teachers (1985).

  Biringuccio, Pirotechnica, Book IX, Chap. 12 (1959).

  Bell, The Telescope (1922, 1982).

  Charles, Practical Astrophotography (2000).

  Doherty, Building and Using an Astronomical Observatory (1986).

  Howard, Standard Handbook for Telescope Making (1959).

  Levenson, How to Buy and Understand Refracting Telescopes (1981).

  Thompson, Making Your Own Telescope (2003).

  Texereau, How to Make a Telescope (1984).

  Berry, Build Your Own Telescope (2000).

  "Telescope," "Aberration in Optical Systems," "Glass," "Objective," "Diffraction," Encyclopedia Britannica (1911).

  Panek, Seeing and Believing (1998).

  Learner, Richard, Astronomy Through the Telescope(1981).

  Wilson, R.N., Reflecting Telescope Optics, vol. I (Springer-Verlag: 1996).

  Martinez, Observer's Guide to Astronomy (1994)

  Gregory, Mirrors in Mind (1996)

  Dijksterhuis, Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics (2004)

  Newton, Optics, Book I, Part I, Proposition 7, Theorem 6 ("Great Books" edition)

  Zebrowski, Ernest, A History of the Circle, 113 (Free Association Books: 1999).

  White, Michael, Newton: The Last Sorceror 169 (Perseus Books: 1997).

  Kempen, "The prevalence of refractive errors among adults in the United States, Western Europe, and Australia," Arch Ophthalmol. 2004 Apr;122(4):495-505

  Internet sources—

  Portuesi, "Fixing the Department Store Telescope,"

  http://www.jotabout.com/portuesi/astro/ds_scope.html

  Van Helden, "Galileo's Telescope,"

  http://cnx.org/content/m11932/latest/

  Abraham, "The Testing of Telescope Optics in Historic Times,"

  http://www.europa.com/~telscope/histtest.txt

  Nagler, Choosing Your Telescope's Magnification

  http://www.televue.com/engine/page.asp?ID=140

  Pope, "Optics of the Singlet Refractor: Galileo Vs. Kepler,"

  http://www.pacifier.com/~tpope/Galilean_Optics_Page.htm

  Petit, "A Telescope of Galileo," Astron. Soc'y Pacific 147 (1939), available online at

  http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1939PASP...51..147P&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

  Smith, "Design Musings: Mountings," http://home.earthlink.net/~indig/DesignMusings/text/Design_Mountings.html

  Rubski, "Important Astronomers, their Instruments and Discoveries, Part 3", http://www.seds.org/billa/psc/hist3.html

  Hong, Sungook, "Optics and Light," http://www.chass.utoronto.ca/~sungook/hps311/optics.htm

  Zoom Inventors and Inventions, Inventors and Inventions from the 1600's - the Seventeenth Century, "James Gregory", http://www.enchantedlearning.com/inventors/1600.shtml

  Zoom Inventors and Inventions, Inventors and Inventions from the 1600's - the Seventeenth Century, "Cassegrain Telescope", http://www.enchantedlearning.com/inventors/1600.shtml

  [TRIPOD] "Astronomical Instruments", http://members.tripod.com/~worldsite/astronomy/astroinst.html

  Swadha, Tools of the Trade, Lecture 2, The Telescope, Part 2, http://members.ozemail.com.au/~swadhwa/m2c2lect2.html

  [SKYHOUND] "Scenario: Georgium Sidus", http://www.skyhound.com/george.htm

  [WEASNER] "From James Gregory to John Gregory: The 300 Year Evolution of the Maksutov-Cassegrain Telescope", http://www.weasner.com/etx/guests/mak/MAKSTO.HTM

  [GEOCITIES] "Astronomical Instruments," http://www.geocities.com/Area51/Shadowlands/6583/observatory.html

  Kramer, Jack, A Short History of the Telescope, http://homepage.interaccess.com/~purcellm/lcas/Articles/telehist.htm

  [MadeHow] "Eyeglass Lens,"

  http://www.madehow.com/Volume-1/Eyeglass-Lens.html

  Duenwald, "Need Reading Glasses? Welcome to Middle Age," New York Times (June 8, 2004), http://query.nytimes.com/gst/fullpage.html?res=9500E3D91E31F93BA35755C0A9629C8B63

  [Birdwatching] "Birding Binoculars: Birding Scopes Test Results at a Glance" (Jan. 2000)

  http://www.birdwatching.com/optics/scopes2000table.html

  Savard, "Telescope Mountings," http://www.hypermaths.org/quadibloc/science/opt03.htm

  [AST110] "Telescopes Mounts" http://www.utm.utoronto.ca/~astro/ast110/lectures/tel_mounts.html

  Slotegraaf, "Visual Astronomy," http://www.fortunecity.com/roswell/borley/49/visual.htm

  [HAO] High Altitude Observatory, "Johannes Hevelius,"

  http://www.hao.ucar.edu/Public/education/bios/hevelius.html

  [CoO] College of Optometrists, "Newton and the Colour of Light,"

  http://www.college-optometrists.org/index.aspx/pcms/site.college.What_We_Do.museyeum.online_exhibitions.observatory.newton/

  "Medicean Skies,"

  http://www.imss.firenze.it/news/cielimedicei/eespos.html

  Woods, "Clear as Glass,"

  http://www.memagazine.org/oct06/features/clearas/clearas.html

  Optics Planet, "How to choose a Riflescope,"

  http://www.opticsplanet.net/how-to-choose-riflescope.html

  Unintended Consequences: Dealing with the Population Density Explosion

  Written by Walt Boyes

  The reconstruction of Magdeburg brings to mind issues in population density. Although relatively large cities existed in 1634 in OTL, none of them qualifies as a really modern city, as the up-timers would recognize them. The up-timers will cause an unparalleled population density explosion, based on the technologies and the social systems that were developed in the late nineteenth and in the twentieth centuries to handle the growth of the megalopolis.

  None of the large cities of Europe or Asia qualified as metropolitan until nearly the end of the nineteenth century. Why? To handle large scale urban populations of the density of even a twenty-first-century Hamburg, you require a combination of the effects of the development of five things. You need the germ theory of disease and epidemiology, centrifugal pumps and the associated high pressure piping, electricity, and the modern safety elevator. What, you say? They had pumps, they had running water . . . All that's true, but this is a synergism. You need all of them to make a modern metropolis work.

  So, what's a large, modern city? Here are the 2007 top five:

  By Population

 

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