Seeing the Heavens

“The soul without imagination is what an observatory would be without a telescope,” according to Henry Ward Beecher. In the seventeenth century, solar system astronomy lay at the center of the debates as to place of mankind in the universe, and the relationship of religion and science. The telescope played a decisive role in these debates.

It is true that the Church and the royal courts have access to the books from the future, and know what they say about the Solar System. Certainly, the Pope in 1634: The Galileo Affair is aware of those teachings and hence anxious to find a way to minimize the repercussions of the Galileo Trial.

It might seem that, with all the astronomy and physics books in Grantville, there is no dire need for improved telescopes. However, it is one thing to read something, and another to observe it for yourself.

Astronomers in Canon

None of the up-timers has a degree in astronomy. However, several have degrees in physics: John McDougal “Mac” Clements (M.S.), Charnock Fielder (1931–1634)(M.S.), James Michael “Jim” McNally and James Victor Saluzzo. Eve Zibarth was six semester hours short of a second major in physics, and Frederic Swisher studied some physics before he dropped out of college. There are also mathematicians in Grantville.

Any of the college grads could have taken an astronomy class or two. In fact, it is not exactly unusual for math-allergic liberal arts majors to satisfy their “science distribution requirement” by taking an astronomy class.

There are astronomy clubs in several West Virginia towns: Wheeling, Clarksburg, Charleston, Huntington, Athens, White Sulphur Springs, Tridelphia, and Morgantown.

The Morgantown (WVU) club presently has twenty-five members, and the club is affiliated with the WVU Physics department. It meets every other Wednesday (around the first and third quarter moons). On the Friday and Saturday nights near new moon the club often has a star party in Chestnut Ridge Park. The Physics department has the “Tomchin Planetarium and Observatory,” with a Spitz A3P Planetarium Projector and a 14-inch Celestron telescope. This equipment is available to club members.

The other club reasonably close to Mannington (Grantville) is the Central Appalachian Astronomy Club in Clarksburg (south of Fairmont). Note that Fairmont State University has a satellite campus in Clarksburg. The CAAC owns the Good Hope Observatory, ten miles south of Clarksburg, which is equipped with a piggybacked Meade 16″ F/10 LX 200 GPS Schmidt-Cassegrain with a Takahashi 4″ FS-102 II, and a Williams Optics Zenithstar 80mm F/6. They also have a 14″ F/10 LX 200 GPS Schmidt-Cassegrain, and, for solar observing, a Coronado Max Scope 60.

Unfortunately, I have not found any specific evidence that anyone from Mannington was a member of either of these clubs.

So far as light pollution goes, Mannington is in Bortle Class 4, “Rural/Suburban transition.” ( http://www.novac.com/lp/wv.php ) But Morgantown and Fairmont are worse, and they have amateur astronomers.

Rick Boatright did an informal survey of his “middle-to-upper-middle class” neighborhood in 2000: “In the four blocks nearest my house, (16 house/street segments) there are 104 homes. In those 104 homes, there are ZERO reflecting telescopes, two sub-three-inch refractors, and 11 pairs of binoculars.”

Still, it is now canon that at least one up-timer is an amateur astronomer of sorts: high school graduate Johnnie Farrell. See Peter Hobson’s “Lessons in Astronomy” (Grantville Gazette, Volume 11).

At the end of 1634: The Galileo Affair, the new Cardinal-Protector Mazzare wangles the appointment of Father Christopher Scheiner (1573–1650) to Grantville. Mazzare tells the Pope, ” . . . we have books on astronomy in Grantville, and are creating a great university nearby at Jena—but we have no astronomers. And he is a superb one.”

Refracting Telescopes and Their Problems

Credit for the invention of the telescope is usually given to Hans Lipperhey (Lippershey?), who filed a patent application on Oct. 2, 1608 (Panek 25). This touched off a priority dispute, with Jacob Adriaenszoon and Saccharias Janssen. The States General solomonically decided that none of them deserved a patent, on the theory that a device which was simultaneously invented by several parties was probably obvious.

The Lipperhey spyglass combined a weak biconvex lens away from the eye (later termed, the objective lens) and a strong biconcave lens near the eye (the eyepiece). In 1609, Galileo created his own spyglass; it used a planoconvex objective (“plano” indicating one side flat) and a planoconcave eyepiece. By March 1610, he had published his first set of observations, in The Starry Messenger.

The two basic refractor designs are the Galilean and the Keplerian (the latter described in Kepler’s Dioptrice, 1611). Both use a planoconvex or biconvex objective lens. The Galilean uses a negative (planoconcave or biconcave) eyepiece, and the Keplerian a positive (planoconvex or biconvex) one.

The Galilean creates an upright image, whereas the Keplerian image is inverted. The Galilean telescope is also more compact; the distance between the lenses is the difference between the focal lengths of the objective and the eyepiece, whereas for the Keplerian design it is their sum.

On the other hand, for a given magnification, the field of view (FOV) of the Keplerian telescope is much broader. The FOV for the 20x Galilean design was perhaps fifteen arc minutes (half the diameter of the full moon). Huygens’ 1656 Keplerian refractor, 23 feet long, 100x, had a seventeen arc minute FOV. (Van Helden).

Also, in a Keplerian design, you can mount a micrometer at the focal plane, so you can measure the angular size of the object observed. (Pope GvK). The micrometer was first added by William Gascoigne (1620?–44) in 1638 (Bell 12).

Kepler was not an observer, and it appears that the first astronomers to use his design were Scheiner, and Francesco Fontana (1585-1656). In Scheiner’s Rosa Ursina (1630), he noted that he had been using the new type for several years. Fontana, in Novae coelestium terrestrium rerum observationes (1646), claimed that he had put two convex lens into a tube back in 1608 (and thus to have priority not only over Scheiner, but also Kepler).

At the time of the Ring of Fire, most astronomers still had Galilean refractors. According to Van Helden, these typically had an planoconvex objective lens, with a focal length of 30–40 inches, and an aperture (stopped down) of 0.5–1 inch. Combined with an eyepiece of focal length 2 inches, that gave a magnification of 15–20x. As to the actual optical quality, he says, “The glass was full of little bubbles and had a greenish tinge (caused by the iron content of the glass); the shape of the lenses was reasonably good near their centers but poor near the periphery (hence the restricted aperture); the polish was rather poor.”

However, Pope says that although Galileo’s glass “suffered from many cosmetic defects,” at the apertures he chose, his lenses “should have performed essentially as well as any modern lens of similar design.”

The Keplerian design was dominant by the mid-seventeenth century. The Capuchin friar Antonius Maria Schyrlaeus de Rheita (1597–1660) added (1645) a reverting eyepiece to the Keplerian refractor, and also experimented with binocular telescopes.

The first telescopes were called refracting telescopes because convex lenses focus light by refracting (bending) it. The simplest convex surface to impart to a lens is a spherical surface. Unfortunately, if the lens has a spherical cross-section, then paraxial rays (rays parallel to the axis of the lens) passing through the lens near its center will not meet at the same point as those passing through the periphery of the lens. This problem is called spherical aberration, and results in a fuzzier image.

The problem of spherical aberration was recognized and mathematically analyzed by Rene Descartes, who published his analysis in 1637 (I don’t know how much he had already figured by, say, 1634.) Spherical aberration increases as the square of the aperture (Thompson 5), which of course discouraged attempts to increase light-gathering power by increasing the aperture.

Descartes also pointed out how to overcome the problem with lenses having a non-spherical surface. But attempts to grind such surfaces in the seventeenth century were unsuccessful (Bell 12).

There was a second problem which could not be solved solely by use of an aspherical surface. A simple lens will refract light of different wavelengths (colors) to different degrees (this is called dispersion), so each color has its own focus distance. Focus on an object, and it will have a reddish or bluish halo. This problem is called chromatic aberration. Isaac Newton discussed it in his Optics, and commented, “’tis a wonder that telescopes represent objects so distinct as they do” (417).

The spherical aberration could be reduced by using a high f-ratio (ratio of the objective focal length to the aperture). Perhaps more importantly, the relative chromatic aberration (the chromatic blur relative to the size of the image) could also be reduced by that strategy (Bell 11).

In consequence, the focal length of the objective, and hence the length of the telescope, was greatly increased. The Huyghens brothers used a twelve footer in 1655. The tubes of these long-focus scopes were made of wood, which was stronger than the paper or leather used by the Galileo, and lighter than iron.

By the early 1670s, Johannes Hevelius had built a 150-foot telescope. This was called an “aerial telescope” because it was suspended in the air. Pity the Renaissance astronomer who was observing on a gusty night! It didn’t have a tube, strictly speaking; an illustration reveals that it was a long spar, with the objective attached at one end, and the eyepiece at the other, and wooden diaphragms at intervals in-between (Bell Fig. 11).

Newton comments that “very long tubes are cumbersome, and scarce to be readily managed, and by reason of their length are very apt to bend, and shake by bending, so as to cause a continual trembling in the objects.”(421). While I am sure the 140-footer was a great tourist attraction, the productive work was done on somewhat more modest contraptions, 25-35 feet long and with apertures of 2-3 inches (Bell 18).

The first major improvement in refracting telescopes came in the eighteenth century, with the invention of the achromatic lens (originally by Hall in 1733, but rediscovered by John Dolland in 1758). This combined a positive biconvex crown glass and a negative concave-convex flint glass lens in such a way that their focal lengths were inversely proportional to their dispersions. Flint glass exhibited much greater dispersion than crown glass.

The purpose, of course, was to minimize chromatic aberration. Specifically, the design caused two wavelengths (e.g., red and blue) to focus at the same place. There will still be chromatic aberration at the wavelengths not specifically corrected for, but the degree of aberration would be less than for a traditional lens. The overall chromatic blur is reduced by about a factor of 40 (Smith, Modern Optical Engineering, 399).

The “Achromatic Telescope” is described in “Telescope,” 1911 Encyclopedia. Unfortunately, the essayist was more concerned with the merits of Dolland’s claim to be the first true inventor than with communicating the practical details of how to construct an achromatic lens. The practical mathematics are in another encyclopedia article, “Aberration in Optical Systems,” and see also “Light,” “Dispersion (Optics).”

An achromatic lens may be a triplet; the encyclopedia mentions that Peter Dollond sandwiched a concave flint lens was sandwiched between two convex crown glass lenses.

In 1632, flint glass (a lead-rich glass of high refractive index) was unknown. Formulae for flint glass are in the encyclopedias, see Cooper, In Vitro Veritas (Grantville Gazette, Volume 5), but it will take time to bring flint glass on the market.

To make an achromat, you have to be able to accurately determine the refractive index of a glass. Willebrord Snell (1591–1626) was the first scientist to measure the refractive index with sufficient precision to deduce the law of refraction (Snell’s law, unless you’re French, in which case you call it Descartes’ law.) So this was “leading edge science” when Grantville arrived in Thuringia.

The achromatic lens is a type of doublet lens, that is, one which consists of two simple (singlet) lenses which are attached to each other. Even a cemented doublet potentially yields a big increase in quality from a singlet, since its three independently specifiable surfaces allow one to achieve a particular focal length and at the same time correct for chromatic and spherical aberration (Levenson 14). Cemented doublets are limited in size to perhaps three inches by the differential thermal expansion of the two glasses.

In an air-spaced doublet, a fixture holds the two simple lens in close proximity, with an airspace in between. There are four surfaces which can be specified, so the design can more readily correct for coma, too (Levenson 19). On the other hand, there are more air-glass surfaces and alignment is more difficult (Smith, Modern Lens Design, 115).

There are two ways of making an apochromatic lens, that is, one which eliminates chromatic aberration at three different wavelengths (e.g., red, green and blue). (Levenson 21-23). One is to use a triplet with appropriately configured surfaces.

The other is to make a doublet in which one of the lenses is made of a very low dispersion material, such as fluorite crystal or certain rare earth glasses. The low dispersion glass is not going to be available until well after RoF. And nowadays, such apochromatic lenses cost about twenty times as much as a “mere” achromatic lens (antiquetelescopes.org).

Reflecting Telescopes

The first reflecting telescope was built by Niccolo Zucchi (1586–1670),a professor of mathematics at the Jesuit College of Rome, in 1616. He used it to observe the belts of Jupiter in 1630. His book Optica philosophia experimentalis et ratione a fundamentis constituta (1652–56) may have influenced the later, better known reflector designs of Gregory and Newton. Zucchi’s telescope used a bronze concave mirror instead of a lens. He viewed the mirror image through a lens, possibly handheld. Some authorities say that he had to put his head in front of the mirror in order to make observations—which would have been something of a nuisance. Others say that the mirror was tilted to avoid obstruction by the observer. With a tilted mirror, the light would be reflected obliquely, and the observer could stand to one side of the telescope tube.(Wilson, 2).

In 1630, French astronomer Marin Mersenne (1588–1648) proposed using a second, concave mirror to reflect the light down through a hole in the center of the larger primary mirror. (He may also have suggested that these mirrors be paraboloid in shape.) Unfortunately, René Descartes persuaded him not to proceed, apparently because of the difficulty of securing high quality concave mirrors of sufficient size. But Mersenne explained his design in his l’Harmonie Universelle (1636). (Rybski; Hong)

A similar design was proposed by James Gregory (1638–1675), a Scottish mathematician, in his treatise Optica Promota (1663). The telescope was to have used both a concave parabolic and a concave ellipsoidal mirror(ZOOM). The image formed would have been right-side-up, so the Gregorian telescope could have been used in the daytime to observe terrestrial sights, not just at night to see the heavens.

One of the disadvantages of the Gregorian reflector design was that it featured an eyehole in the primary mirror, which reduced its light-gathering power. Another was that an ellipsoidal surface is hard to grind. Worse, “if an optical system contains two sequential reflectors, regardless of their shapes, the combined effect is to magnify any geometrical imperfections in either surface.”(Zebrowski 113) Gregory commissioned craftsmen to build a working telescope according to his plans, but without success(White, 169).

The credit for actual realization of the reflecting telescope goes to one of the intellectual giants of world history. Sir Isaac Newton (1642–1727), declaring that “the improvement of telescopes of given lengths by refractions is desperate,” adopted a radically different approach, employing reflection, and “using instead of an object-glass a concave metal.”

His speculum had a diameter of about 2 inches, and a thickness of one-third of an inch, and it was ground to the shape of a sphere with a diameter of about 25 inches. While not mentioned in Newton’s Optics, it may safely be assumed that he placed it in the bottom of a tube and caught the reflected rays on a 45° secondary mirror, which in turn redirected the light to a planoconvex eyepiece.

The first Newtonian reflector was only about six inches long and magnified about 35 times. Newton says that the primary mirror was made of copper(420–21), but more likely it was speculum metal, which was then an alloy of six parts copper, two parts tin, and one part arsenic(CYBRATIONS).

Unlike Gregory, Newton did not place his trust in craftsmen to reduce his design to practice. “I asked him where he had it made,” recalled John Conduitt, “he said he made it himself, & when I asked him where he got his tools he said he made them himself & laughing added ‘if I had stayed for other people to make my tools & things for me, I would have never made anything of it . . . ‘”(White, 168).

With his new scope, Newton saw “Jupiter distinctly round and his satellites, and Venus horned.”(Id.) Newton displayed it at a meeting of the Royal Society of London in December, 1671, and shortly thereafter he was voted in as a Fellow(White 169–71, RICE).

The great advantage of reflectors (telescopes with mirrors) over refractors (telescopes with lenses) is that they do not refract light. When light is reflected, all wavelengths are redirected at the same angle, so chromatic aberration does not occur.

The original Newtonian design had a spherical primary mirror. Like a spherical lens, a spherical mirror cannot focus parallel rays of light down to a single focal point; it suffers from spherical aberration.

In 1723, John Hadley (1682–1744) replaced Newton’s spherical primary mirror with a parabolic one, thereby avoiding this problem. There is no doubt that Newton was aware of the advantages of a paraboloid shape over a spherical one. In analyzing refractor (lens-based) telescopes, he declared, “the imperfection of telescopes is vulgarly attributed to the spherical figures of the glasses, and, therefore, mathematicians have propounded to figure them by the conical sections” (Newton, 412);those, of course, would include the parabola. But Newton calculated (erroneously) that the contribution of spherical aberration to the scattering of the rays was only 1/5449th that of chromatic aberration. Having solved the latter problem by replacing lenses with mirrors, Newton was no doubt of the opinion that the additional sharpness achievable with a paraboloid mirror was insufficient to justify the effort necessary to grind a mirror to that shape.

Hadley’s greater contribution was that he devised a reliable method of monitoring the approach to a parabolic cross-section. First, he ground the mirror to a spherical shape. Then he ground the mirror more deeply in the center than at the periphery. Without his assay method, this would have been entirely hit-or-miss. But he “placed a tiny illuminated pinhole at the mirror’s center of curvature and examined the reflected cone of light in the vicinity of the image. From the appearance of this cone, Hadley could infer the state of the mirror’s surface and was thus able to pass, by successive polishings, from a spherical to a paraboloidal figure.”(TRIPOD) Like Hadley’s telescope, modern Newtonian reflectors use a parabolic primary mirror.

Problems in mirror grinding and in maintaining an untarnished surface discouraged the early adoption of reflector telescopes.

Other Telescope Designs

In the Newtonian reflector, an on-axis planar mirror moves the focal point of the primary mirror (spherical or parabolic in shape) outside the main telescope tube. The eyepiece tube is perpendicular to the main tube. In the older Gregorian design, it was parallel to the main tube, and aligned with it. Of course, while Newton avoided the need for an eyehole in the primary mirror, his secondary mirror would of course prevent some of the incoming light from reaching his primary mirror in the first place.

Herschel tried eliminating the secondary mirror altogether. That made it a “front view” telescope (like Zocchi’s), and Herschel tilted the mirror so he could see the image without blocking the view. A “Herschelian” reflector, of 48-inch aperture and 40-foot focal length, was used by its “inventor” to discover Enceladus and Mimus. (Bell 33)

Herschel had eliminated the light loss due to the secondary mirror, which was rather high with speculum metal. Unfortunately, it wasn’t easy for the observer to see into a large Herschelian reflector if the target were near the zenith—forty-foot ladders being somewhat rickety.

Also, the tilt created an astigmatic distortion, albeit one alleviated by the high f-ratio (Doherty 16).

Hence, we turn the clock back to the early seventeenth century to look at an alternative design. Laurent Cassegrain (1629–93), a Catholic priest, wrote a paper on the megaphone, published in the Proceedings of the Paris Academy of Sciences for 25 April 1672. An accompanying note described his telescope design. A Cassegrain telescope is a wide-angle reflecting telescope with a concave mirror that receives light and focuses an image. A second, convex mirror reflects the light through a gap in the primary mirror, allowing the eyepiece or camera to be mounted at the back end of the tube.

While not pointed out by Cassegrain, the combination of a concave mirror and a convex one tends to limit the adverse effects of geometric imperfections in either surface. Despite this advantage, the Cassegrain reflector sank into obscurity for almost three hundred years, under the weight of Newton’s scathing criticism of it(Zebrowski, 114).

Catadioptric Telescopes

If the primary mirror of the Cassegrain reflector were spherical, it would suffer from spherical aberration. A correcting plate (a lens) was added (in front of the primary mirror) in 1930 by the Estonian astronomer and lens-maker Bernard Schmidt (1879–1935), creating the Schmidt-Cassegrain telescope(ZOOM). Since it uses both a mirror and a lens, it is called a catadioptric design. The Schmidt correction lens was flat on the front side, and had a complex curve on the rear side.

    A. Bouwers of Amsterdam, Holland, in February of 1941 and Dmitry Maksutov of Moscow, Russia, in October of 1941 independently invented an alternative correction lens which was curved on both surfaces. It is called a meniscus corrector shell, and the overall telescope design which incorporates it is called a Maksutov-Cassegrain reflector. In 1957, John Gregory realized that the secondary mirror could be dispensed with if a small central portion of the rear surface of the meniscus corrector shell were silvered to make it reflective. The result was the “Mak” reflector.(Weasner).

    In what is now called the “classical” Cassegrain design, the primary mirror is parabolic and the secondary mirror is hyperbolic. This avoids spherical aberration without the need for a corrective lens. It is unclear whether Cassegrain himself conceived of the hyperbolic secondary mirror; or whether it was a later development. Accurately grinding both parabolic and hyperbolic mirrors would have been extraordinarily difficult in the late seventeenth century.

    Mirrors for Telescopes

    The mirrors for reflecting telescopes were usually made of speculum metal, a mixture of copper and tin. The metal at best reflected only about 60% of the light (Swadha; Thompson 13),and less as it tarnished.

    Newton recognized both the problem, and a possible solution: “because metal is more difficult to polish than glass, and is afterwards very apt to be spoiled by tarnishing, and reflects not so much light as glass quick-silvered over does, I would propound to use instead of the metal a glass ground concave on the foreside, and as much convex on the backside, and quick-silvered over on the convex side.” In other words, he had conceived of a back-silvered glass concave primary mirror.

    However, nothing came of this suggestion until the German chemist Baron Justus von Liebig devised (1835) the method of depositing a film of silver on a glass surface. This technological advance made large reflectors practical. The preparation of speculum mirrors was an esoteric art, while many nineteenth-century workers knew how to grind and polish glass.

    Also, while glass was fragile, it was still easier to handle than speculum metal, which one writer has called “wilfully perverse.” Speculum metal was also more than three times the density of plate glass (Texereau 25).

    The story of the 1870 Melbourne Cassegrainian reflector is instructive. The Australians decided not to use the newfangled silvered glass mirror. They ordered a 48″ (1.2 meter) speculum mirror from Dublin. It was only with the third attempt at casting that success was achieved. The mirror was shipped with a protective coating of shellac. When the Australians removed the shellac, they damaged the reflective surface. Rather than shipping the mirrors back to Ireland, the Australians decided to polish it themselves, with unhappy results. G. Ritchie wrote, “I consider the failure of the Melbourne reflector to be one of the greatest calamities in the history of instrumental astronomy.”(Learner, 107–9).

    Finally, while silvered mirrors, like speculum metal, will tarnish, the silver of a silvered glass mirror could be dissolved away and replaced with a fresh coating, leaving the mirror shape unaffected. (GEOCITIES)

    The first silvered glass reflecting telescope, just 4 inches in aperture (smaller than the one I owned as a high school student), was built by Steinheil in 1856. Foucault made a 13-inch silvered glass mirror in 1857. Soon thereafter, a reflector with a 48-inch silvered glass mirror was installed at the Paris Observatory, but its performance was mediocre.

    Big Glass

    The problem with reflectors was that they were much more sensitive than refractors to temperature effects, to the flexion of the telescope tube, and to misalignment of the optics. Nonetheless, for large telescopes, they had substantial advantages.

    As lenses were increased in size, they had to be made thicker, which increased their absorption of light. This was particularly a problem for astrophotography, as the film was most sensitive to violet and ultraviolet light, and flint glass strongly absorbed these radiations. The large lenses also had to be supported at the edges, and hence liable to warping. In contrast, silvered mirrors strongly reflected violet and ultraviolet light, and large mirrors could be supported all the way across the rear of the mirror “blank,” rather than just at its edges (Learner, 110).

    Toward the end of the 1930s, silvering was superseded by aluminizing. While aluminum is not quite as reflective as silver, it is much more durable. To recoat a mirror, it must be lifted out of its frame. The Mount Wilson mirror weighed four tons; obviously, the less it had to be played with, the better.

    Another advantage of aluminum is that when it is oxidized, the resulting aluminum oxide coating is transparent, whereas silver oxide is black (think “tarnish”).

    Another important development in the history of telescope making was the invention of PYREX® glass. This glass was much less sensitive to temperature changes than plate glass. The first use of PYREX® glass in a large telescope was in the 76-inch reflector for the Canadian David Dunlap Observatory (Learner, 118).

    Eyepieces

    The purpose of the eyepiece (ocular) is to enlarge what is seen at the focal plane. The magnification obtained is the ratio of the focal length of the objective (mirror or lens) to the focal length of the eyepiece.

    Unfortunately, the greater the enlargement, the smaller the field of view. Which is why big scopes often have guide scopes piggybacked on top of them. Raising magnification also makes the image dimmer.

    The original Galilean eyepiece was a singlet. Since light can come into the eyepiece at steep angles, the designer most worry, not only about spherical and chromatic aberration, but also coma, astigmatism, and other distortions. The use of multiple elements (see table) allows the correction of one or more distortions. A compound ocular was first constructed (Augsburg, 1649) by Johann Wiesel(Dijksterhuis 60); the better known Huyghens eyepiece was made in the 1660s.

    Eyepiece

    Collector

    Field Lens

    Eye Lens

    Huyghens, Ramsden

    Singlet

    Singlet

    Kellner

    Singlet

    Doublet

    Erfle

    Doublet

    Doublet

    Doublet

    Orthoscopic

    Triplet

    Singlet

    Plossl

    Doublet

    Doublet

    Cooke

    Triplet

    Doublet

    (Levenson, 48-52).

    The 1911 “Telescope” article has figures showing the Kellner and Cooke eyepieces, and the Huyghen and Ramsden eyepieces are depicted in the “Microscope” essay. The Erfle, Orthoscopic and Plossl designs may be more difficult to recreate.

    Mounting the Scope

    The purpose of the mount is to support the telescope, with minimum vibration, yet permit it to be readily pointed at a target and to track the target’s movements. And, of course, if the telescope is not in an observatory, the mount has to be light enough so the telescope is still portable. These goals are not easily reconciled.

    The intricacies of predicting where a celestial object will be at a particular time, and the various coordinate systems in which its location can be expressed, are covered in my article, “Soundings and Sextants” (and I am very glad I don’t have to explain them a second time).

    Here, I will concentrate on the issue of how to mount the scope so you can point it in a particular direction. Telescope mounts are diagrammed and discussed in the 1911 “Telescope” article, and of course pictures of telescopes in various books on astronomy will inadvertently reveal additional variations on the theme.

    General purpose telescope mounts, in order to point anywhere in the sky, must be freely rotatable on two axes, and for scientific use you have to be able to set the angle on each axis. The two basic mounts correspond to the two basic coordinate systems.

    An altitude azimuth (“alt-az”) mount has vertical and horizontal axes. The vertical axis allows the user to set the altitude and the horizontal axis, the azimuth. An alt-az mount is similar to a gun mount on a battleship. One form of alt-az mount is shown in Hevelius, Selenographia (1647).

    One common implementation of an “alt-az” mount is a “rocker box”; the vertical axis is provided by a yoke, and the yoke is pivotably mounted on a horizontal base. Another is found on some camera tripods; one end of a C-shaped arm is attached to the base, which rotates on top of the tripod, and the other end provides a pivot for the telescope. This is only suitable for small telescopes.

    In an equatorial mount, the base, instead of being horizontal, is tilted so it is parallel to the earth’s equatorial plane. The advantage of this is that the apparent motion of the stars is the result of the rotation of the earth and, with an equatorial mount, one just needs turn the telescope on the one axis (which points toward the north or south pole), in order to keep a star in view. That in turn means that the telescope can be kept pointing at the star by hooking it up to a simple clock-regulated motor drive. In contrast, with an alt-az mount, the telescope must be adjusted on both axes to keep a star in view.

    The two axes of the equatorial mount are the right ascension and declination axes, which are the tilted counterparts of the altitude and azimuth axes of the alt-az mount. The RA axis points toward the pole so turning the telescope about that axis tracks the star.

    The first equatorial mount is believed to have been constructed by Scheiner (!) in 1638, for a helioscope (King 42).

    There are many different ways of implementing the equatorial mount (Smith).

    My home telescope of decades past used the German equatorial mount, which features a lopsided-T. The crossbar serves as the declination axis. The midpoint of the telescope tube is pivotably mounted to the short end, and a counterweight is slid onto the long end.

    The central staff of the T is the RA (polar) axis. On a large observatory scope, it will probably be held on a fixed, slanted pier, customized so that the slant causes the RA axis to point toward the pole. On a portable amateur scope, it will be pivot-mounted on a tubular base, the base lockably hinged to a pedestal (so the angle can be changed if the telescope is moved to a location with a significantly different latitude), and the pedestal mounted on a tripod.

    There are two problems with a German equatorial mount: the polar axis is subject to a lot of stress (since the tube hangs on one end) and the telescope sometimes has to be swapped from one side of the pier to the other (“meridian reversal”).

    Next we have the English cross axis. Instead of a T, we have something like a plus sign. Imagine that one bar of the “plus” is short and horizontal; that is the declination axis and the telescope tube and the counterweight are attached to opposing ends. The other bar (the RA axis) is long and threads through the declination axis; one end touches the ground and the other (the high end) is attached to two legs. Thus, the RA axis and its legs form a lopsided tripod, with the polar end of the RA axis high off the ground (high enough so the telescope can be rotated all the way around the declination axis).

    In the English yoke, the declination axis is modified; instead of the telescope tube being attached to one end, it is mounted “inside” the center of the axis, in a rectangular yoke. At the midpoint of the long sides of the yoke there are opposed pivot points to which the tube is attached; these form the declination axis. The short ends of the yoke are attached to opposing pivot points, the ends of a large L-shaped base, to form the RA axis. This is the design which was used to mount the Hooker Telescope on Mount Wilson. It is stable but can’t be used to see stars close to the pole because the tube would crash into the yoke (which is shorter than the tube) if you tried.

    The “horseshoe” mount (Savard) is a modification of the English yoke. The higher of the short ends of the yoke is replaced by a C-shaped piece (the “horseshoe”) which cradles the telescope tube when it points toward the pole. In essence, we have modified the piece of the yoke which the tube would otherwise crash into. The “horseshoe” itself is supported by the high end of the L-shaped base.

    The English Fork combines the polar axis of the German mount with half a yoke mount (that’s the “fork”). It doesn’t require a counterweight. It may be thought of as the equatorial analogue of a rocker-box; the base axis of the fork sits on a wedge (pier) instead of lying horizontally.

    There are still more mount designs . . . but it is clear from the foregoing that the astronomers of the new time line have plenty of choices.

    The cost of building a telescope with an equatorial mount increases as roughly the 2.7th power of the diameter of the mirror (AST110).

    In general, the equatorial mount is heavier and more expensive, and the modern trend in the old time line was to return to the alt-az mount. Computers can be used to drive movement, simultaneously, on both axes. Of course, in the decade following the RoF, and outside the vicinity of Grantville, computers are going to be hard to come by.

    ****

    There are special mounts which afford more limited movement (but are cheaper and more stable than the general purpose mounts).

    A transit telescope, like a telescope with an alt-az mount, can be adjusted vertically, but it cannot turn horizontally. It always points somewhere on the half circle corresponding to the upper half of the local meridian (i.e., north or south). It is used to create star catalogues; when a star crosses the local meridian its altitude (declination) is measured and the time (right ascension) is noted. The transit telescope can also be used to accurately determine the time, based on when a star of known right ascension crosses the meridian.

    A poor cousin of the transit telescope, a “meridian circle,” was used by Tycho Brahe. It was a quadrant; the altitude was measured as with a transit telescope, but the star was sighted with the naked eye.

    A zenith telescope is even simpler than a transit telescope; it points directly overhead. Such telescopes, which are cheap to construct even when large in diameter, were traditionally used in latitude and time measurements. There are now some very large zenith telescopes which use, as their mirror, liquid mercury. When spun, it naturally assumes a paraboloid surface.

    Drives and “Gotos”

    The equatorial mount made it possible to automate the process of tracking stars by using a weight-driven clockwork mechanism to turn the telescope at just the right speed about the polar axis.

    At some point in the twentieth century, the clockwork drive was replaced by an electric motor.

    Advances in electronics made it possible to “drive” a telescope with an “alt-az” mount, rotating it more or less simultaneously on both axes.

    The next step was the “goto” telescope, which could not only track a star, but could also “jump” to one. Canon says that there is a “goto” telescope in Grantville. When the “goto” is turned on, it may ask the observer to enter the longitude and latitude, or try to locate itself from a GPS signal (the latter won’t work after RoF, of course). The “goto” also needs the time and date. (Obviously, it is not going to accept a date of “1632.”)

    What date and time do you enter? Ideally, you enter a date in the twentieth century which is within the “goto” date range but is an integer number of sidereal days separated from the actual date of observation in 163x. (The sidereal day is the time interval between two successive crossings of the same celestial meridian by a star. Or, less precisely, the time for the star to return to the same apparent “place in the sky.”) This will require a bit of calculating but once you have identified one correspondence you can just count days forward from there.

    When the “goto” is turned on, the user has to calibrate the system by pointing the scope at one or more bright “alignment” stars in the unit’s database. This will allow the unit to correct for errors in the mounting of the scope, or in the observing parameters.

    The unit’s database, of course, is going to be expecting the stars to be in the positions in the celestial sphere which they occupied around the year 2000. As opposed to 163x. The positions are going to be something like five degrees off.

    Obviously, the “goto” isn’t designed to correct for time travel-impelled precession, which is the revolution of the North Celestial Pole around the North Ecliptic Pole. However, it will think that the astronomer has failed to point the RA axis of the scope toward the NCP and correct for this “polar misalignment.” Thus, it will unknowingly try to correct for precession. What I am not sure of is whether there is a limit on how much polar misalignment is correctible. At some point the “goto” may just “shrug electrons” and refuse to do anything.

    Telescope Performance

    The astronomical telescope is a device for gathering light so that the observer can see dim objects which are far away. It takes almost all of the light which falls on a relatively large diameter lens or mirror (the objective) and delivers it to your eye (pupil diameter about one-quarter inch). The light gathering power is proportional to the effective area of the objective, and thus to the square of the aperture (the effective diameter). The aperture is sometimes less than the nominal diameter; stopping down (blocking the periphery of) the objective can counteract certain optical imperfections. Galileo’s telescopes were stopped down.

    Since telescope mirrors are not perfectly reflective, and telescope lens are not perfectly transparent, there is some light loss at every optical surface. Crown glass reflects away four percent of the light at each surface; each simple lens is two surfaces and thus a net light loss of eight percent. A silver mirror loses about the same amount of light to absorption.

    Sharpness is a function of the resolving power of the telescope, the clarity of the atmosphere, and the visual acuity of the observer.

    The theoretical limit on the resolving power of the telescope is set by diffraction. Light behaves like a wave and when it passes through a small hole (the opening of the telescope), it forms “diffraction rings.” If you are trying to see small detail, adjacent bright spots form overlapping rings of light and darkness. The “Dawes limit” (suggested for observing double stars of equal brightness) on a perceptible separation is 4.56 arc seconds divided by the telescope’s aperture (the useable diameter of the front lens or the primary mirror) in inches.

    Useable magnification is something like 20x–30x per inch of aperture for seeing planetary detail, and 50x per inch for “resolving” (separating) double stars. (Nagler). Fifty times 4.56 arc seconds is 3.8 arc-minutes, and the normal naked eye can resolve 2-3 arc-minutes.

    Imperfections in the telescope can reduce sharpness and contrast. These imperfections could be a function of the design (a spherical surface will create spherical aberration, if not corrected in some way; a flimsy tripod will vibrate) or of its implementation (an inaccurately ground lens or mirror; misalignment of the optical elements; a misplaced counterweight).

    The atmosphere, of course, itself is not transparent even at the best of times, with light being scattered or absorbed by air molecules or particles. Turbulence in the atmosphere causes wobbling of the light waves, making it more difficult to see detail. The “twinkling” of a star is typically by an angle of 0.05–2 arc-seconds (Martinez 190); compare this to the Dawes Limit.

    Astronomers learned to site their telescopes at high-altitudes (less atmosphere to peer through) and to wait patiently for moments of clear seeing. At least light pollution is not going to be a big issue in the early seventeenth century. Especially outside the immediate vicinity of Grantville.

    Visual acuity is affected by innate acuity, age, eye disease, dark adaptation, diet (eat your carrots!), fatigue, and observing technique (Slotegraaf). Galileo apparently had ophthalmia when 12 or 13 (Pope). Newton was near-sighted (CoO), and Kepler’s vision was so bad that he relied on the observations of others. Hevelius, on the other hand, was said to be able to see seventh magnitude stars with the naked eye (HAO).

    Telescopes in Grantville Before RoF

    George W. Bowers, of Bowers Mansion fame, was an amateur astronomer, but it is doubtful that his telescope, let alone his astronomy books, will be considered canon.

    Johnnie Farrell shows Father Scheiner (a famous down-time astronomer) his eight-inch Schmidt-Cassegrain “reflector” (it’s really a hybrid reflector/refractor) with an equatorial mount and a “goto.”

    There might be another “real” telescope or two at the high school.

    According to the North Marion High School website, a course called “Earth and Sky” is available to eleventh and twelfth graders. I don’t know when this course was first given.

    There are, of course, other up-time telescopes in Grantville. For one thing, there are spotting scopes mounted on rifles. Julie uses a Remington Model 700 with an ART-2 scope (1632, Chap. 39). There are references to additional scopes in Van Natta, “Curio and Relic” (Grantville Gazette, Volume 1), Donahue, “Skeletons” (Ring of Fire), and Flint and Zeek, “Suhl Incident (1634: The Ram Rebellion).

    Typically, whitetail deer hunters use rifle scopes with magnifications of 3x–9x, and objective diameters of 40–44 mm. The lenses may be coated to reduce reflection, and high-end riflescopes may use achromatic objectives.

    Julie is either using a Leatherwood M600 version (3–9 x 40 mm) or an M1200 (6–9 x 50 mm).

    You may find a military rifle sold with a scope that offers a high magnification (up to 40x) and a large objective lens (up to 75 mm). They aren’t very useful for hunting or warfare, in view of their weight and field of view, but they may come in handy for astronomers. (Optics Planet).

    Birders may also have spotting scopes, although binoculars are more common. In 2000, a typical birding scope had a zoom eyepiece with a magnification of 20x–60x, and an objective diameter of 70–90 mm (Birdwatching.Com).

    Then there will be the “toy scopes.” These are the ones which are sold to unsuspecting parents whenever a new comet is discovered (Kohoutek) or an old one returns (Halley’s). Anything purchased in a department store or toy store is worthless by modern standards. But perhaps not for a down-timer.

    The advertising for the toy scopes touts magnification. However, for magnification to do you any good, you need to gather enough light. One rule of thumb is that the maximum useful magnification is 50x per inch of aperture (the useable diameter of the objective), and the toy scopes usually violate this rule. The lenses are likely to be spherical singlets (subject to aberration), and they may be made of plastic, not glass. The material may be inhomogeneous, or high in dispersion. The surfaces may be poorly figured (curved surfaces not really spherical), they may be “wedged” (front and rear surfaces not parallel), and they may even display ripples. They may be heavily stopped down to hide some of the defects. Even if the lenses themselves are acceptable, they may be poorly collimated (that is, optical axes not aligned). And the mounts are likely to be flimsy.

    How would “toy scopes” compare to down-time telescopes? I suspect that they are better on average, but that the best down-time scopes are superior to the worst “toy” scopes.

    Unfortunately, I have not been able to find any head-to-head comparison of a department store scope to an authentic Galilean telescope. I did find a site (ATS) which compared a Tasco of 60 mm aperture (claimed magnification of 660x!) with an Astro-Phsyics of 155 mm aperture. The theoretical resolution of the Tasco, for yellow light, would be about 2 arc-seconds. It is obvious from the comparison that the actual resolution was quite a bit worse, but they didn’t quantify it.

    Galileo’s 21X leather-bound scope, with a 37 mm nominal diameter and a 15 mm aperture, has a theoretical resolution of 8 arc-seconds. Its actual resolution, determined by measurement, is 10-arc seconds. That implies that its optics are quite good, regardless of glass imperfections. Pope’s replica of a Galilean scope, with a 23 mm aperture, resolved 6 arc-seconds. (Pope)

    If a reader has a department store telescope, he or she can compare it to Pope’s replica by using it to read newspaper text at a distance. To equal the performance of that replica, it would need to be able to read 2 mm (8 point) newspaper type at a distance of 100 feet.

    In 1660, when the Tuscan Accademia del Cimento was directed to judge who was the better telescope maker, Eustachio Divini (1610–85) or Giuseppe Campani (1635–1715), they tested the telescopes by using them to read texts at a distance, and gave the laurels to Campani. Nonetheless, Divini’s telescope was good enough to see Saturn’s shadow on its ring (Medicean Skies).

    Perhaps the best method of comparison, absent formal resolution measurements, is to ask what one can see with these department store scopes as opposed to what the seventeenth-century astronomers saw.

    In 1655, Huygens (1629–95) discovered Titan, and clearly distinguished the ring of Saturn from the planet, using a telescope of twelve-foot focal length and small aperture. With a 23 footer of 2 1/3 inch aperture, he observed Syrtis Major on Mars. Cassini (1625–1712) found Iapetus with a seventeen footer and Rhea with a thirty-four footer; and discovered the Cassini Division (the internal gap of the ring) with a twenty footer at 90x magnification. (Bell 18).

    The impression I have, from internet browsing, is that the department store scopes will usually show the rings of Saturn, but not the Cassini Division.

    If the “toy scopes” in Grantville are better than Galileo’s instruments, they certainly aren’t much better.

    Making New Telescopes

    The Grid contains the following interesting comment: “Cathy and Matt (McNally) are beginning to act as assistants to their father (Jim McNally, the optician) in his venture with Dave Marcantonio, the owner of the smallest machine shop in town. They have created excellent telescopes which undercut the price of the artistic items from Nuernburg. They aren’t nearly as pretty, though.”

    A private communication from Laura Runkle confirms that McNally was able to grind his own lenses. “He really is based on someone who still has lens-grinding equipment in the back of the shop for strange orders. The optician is also a physics grad.”

    Of perhaps equal importance, when barflies visited Mannington in 2000, they discovered that the high school science department had the first volume of Ingall, Amateur Telescope Making (4th ed., 195x) (ATM).

    We have three kinds of optical elements to consider: glass mirrors, glass lenses, and metal mirrors. While glass mirrors weren’t available in the seventeenth century in our time line, and the other two elements were, the emphasis on ATM is on the glass mirror and hence I will consider that first.

    Making Glass Mirrors

    The most common mirror shape for a reflecting telescope is paraboloid. While a modern shaving mirror may be at least roughly paraboloid, that doesn’t mean that it is useable as a telescope mirror.

    First of all, like most mirrors in common use, it is a rear surface mirror. That means that the reflective aluminum coating is on the rear surface of the glass. Unfortunately, if a rear surface mirror is used in a telescope, you will have a ghost reflection off the front surface. Telescope mirrors have a silvered or aluminized front surface.

    Secondly, shaving mirrors are very low magnification and hence don’t have to be manufactured to the same tolerances as telescope mirrors.

    To obtain a resolution as good as Rayleigh’s theoretical diffraction-based limit, that is, a one-quarter wavelength difference at the wave front, the optical surfaces of the telescope must be accurate to within one-half wavelength of the light for a refractor and one-eight wavelength for a reflector. (Texereau 6–7). One-eighth wavelength, for yellow-green light, is three millionths of an inch (Berry 236).

    There are essentially five steps in making a glass mirror (Howard, 14–7):

    1) Rough grinding. The mirror glass blank is placed on top of a similar sized piece of glass (the “tool”), with grit in between. The grinder makes long strokes, in every direction, with the top glass, and this results in the upper piece becoming concave and the lower piece, convex. A template of some kind is used to determine when the center is deep enough to correspond to the desired focal length. If the grinding was symmetrical, the mirror blank now has a roughly spherical surface.

    2) Fine grinding. Shorter strokes and progressively finer abrasives are used to create a more smoothly spherical surface. The surface is tested to confirm sphericity.

    3) Polishing. The glass tool blank is replaced with a “pitch lap” (see below) and the abrasives with polishing agents (e.g., rouge).

    4) Figuring. Continuing to use the “pitch lap,” we “parabolize” the surface. Such figuring is impossible without a proper test method (see “Foucault tester” below) since mechanical gauges cannot discern differences on the order of millionths of an inch.

    In theory, there are three ways of altering a spherical surface into a paraboloid (Thompson, 74). The simplest involves deepening the center, tapering off to zero change at the edges. This slightly reduces the focal length of the mirror. If you remove too much (over-correct), you get a hyperboloid, and if not enough (under-correct) you are left with an ellipsoidal mirror.

    Please note that if the mirror is small enough, or its f-ratio high enough, it can be left spherical. That would be the case, for example, with a 6-inch f/12 mirror (Thompson 186; cp. Texereau 19).

    5) Metallizing. Finally, we silver or aluminize the surface. Amateur telescope making manuals have instructions for silvering, but not aluminizing. Of course, we hardly have enough aluminum for it to matter.

    Thompson (197) estimates that the first four steps should take the average amateur, working alone from book directions, about thirty to forty hours for a “starter” (six inch aperture, f/8) mirror. Howard (277) adds that the difficulty of making a mirror increases roughly as the third power of the aperture.

    Glass. Howard recommends PYREX® borosilicate glass for the mirror blank and plate glass (which is a soda lime glass) for the tool blank.

    Borosilicate glass will not be available in quantity for several years after the Ring of Fire. See Cooper, In Vitro Veritas (Grantville Gazette, Volume 5). Canon says that the USE is attempting to obtain boric acid from the Maremma of Tuscany as of 1634. See Cooper, Under the Tuscan Son (Grantville Gazette, Volume 9).

    Soda lime glass is available, but it is not produced in the form of plate glass. The largest available size is only a few feet in diameter, and the quality leaves much to be desired. This isn’t a big problem for the tool blank, but until borosilicate glass is put in production, we will be using soda lime glass for the mirror blank, too.

    Of course, there is some modern plate glass which could be scavenged. Unfortunately, it is probably too thin for use as a mirror blank. For a six inch mirror, the minimum thickness (given that the mirror must not flex too much when supported at three points) is 0.9 inches, and it increases roughly as the square of the diameter (Texereau 27).

    The standard window glass thickness is one-quarter inch. The normal range is perhaps one-eighth to one inch.

    Obviously, the requirements for glass quality are more stringent if the glass is being ground to make a lens, since then we must worry about its transparency. For the glass of a glass mirror, inhomogeneity matters mostly because, under the stress of a change of temperature, the mirror surface could be distorted.

    Abrasives. The preferred abrasives are carborundum (silicon carbide) for coarse grinding and corundum (aluminum oxide) for fine grinding (Howard). Carborundum is not available in the seventeenth century, but it will eventually be made by fusing silica sand and carbon in an electric furnace. Corundum is available from the island of Naxos, Greece, where it has been mined since ancient times. Other abrasives which are immediately available include sand and pumice dust.

    It will be important to “grade” the abrasives. This will be done by first separating them, according to particle size, by meshes of progressively greater fineness, and then measuring the settlement time of the particles.

    Star Testing. The old-fashioned way of determining whether the lens or mirror had the right shape was to use it to look at a star, both in focus and slightly inside and outside focus (Berry 215–20), and then try to remove any observed aberrations. This had numerous problems, including having to wait for the right observing conditions and inability to determine the magnitude and location of the defect (Texereau 60). Still, it was used by Hadley in 1722 (Thompson 11) and Texereau avers it has been used as long as telescopes have existed.

    Foucault Tester. This test method was devised by Leon Foucault in 1858. It is very fortunate for us that it is described in that amateur telescope making manual at the high school. One simple Foucault tester design uses a frosted light bulb, an off-the-mirror axis light slit, a scale, and, on a slide, a knife edge and a scale indicator. The light shines through the slit and is reflected off the mirror and back to the observer, who is looking “over” the kinfe edge. The knife edge can be moved so as to obstruct part of the reflected light. By studying the patterns of light and shadow on the mirror, the mirror maker can determine whether the mirror surface is spherical or paraboloidal, the radius of curvature of different parts of the mirror, and the location of bumps and hollows.

    Pitch lap. Howard says, “a pitch lap is simply a layer of pitch applied to the tool, smoothed to fit the surface of the mirror, and channeled to permit free circulation of air, water and polishing agents.” (65).

    The pitch lap, of just the right softness, is very important to properly parabolizing a mirror. Thompson (6–7) said that an attempt was made to construct a Gregorian reflector soon after its invention, “but whatever chance it may have had of performing creditably was lost by polishing the speculum on a cloth lap—putty (tin oxide) being used as the polishing agent. The unyielding lap was an insurmountable barrier to parabolizing . . . .”

    The culprit was Reive, a London optician, and Bell says that his 1664 use of the (presumably customary) cloth lap was “sufficient to guarantee failure.”

    Likewise, Howard (79) warns that paper, silk, beeswax (honeycomb foundation), and cloth have all been used to polish mirrors, but all are “relatively unyielding” and have “a tendency to produce a ‘lemon-peel’ surface on the mirror.” Texereau (46) takes a somewhat more judicious view; he agrees that the cloth lap (“widely used in making spectacle lenses and various inexpensive optics”) is unacceptable, but admits that Foucault and the Henry brothers obtained good surfaces with paper laps.

    Newton said, in Opticks (1704), that he used a pitch lap, and putty, to polish his specula (Thompson 10). These, of course, were metal mirrors, not glass.

    While ATM no doubt talks about the proper characteristics of the pitch lap, in the seventeenth century there is precious little quality control (and frequent adulteration), and the pitch will have to be tested for suitability.

    Silvering. Methods are given in ATM. Also, the basic silvering reaction is a favorite for chemistry demonstrations, and the Summerlin book is in the high school.

    Making Glass Lenses

    Our first problem is obtaining good optical glass. Bell (50) says, “the purity of the materials is of the utmost importance . . . The silica is usually introduced in the form of the purest of white sand carrying only a few hundredths of one percent of impurities . . . .” The glassmakers of the seventeenth century simply did not work at this level of purity and neither did their suppliers. The glassmakers can accept, even pursue, the tints offered by iron (green), manganese (pink), etc., but these are undesirable in a lens.

    As the components of the glass melt are mixed together, they react, which results in the formation of bubbles. It was not until 1805 that Pierre Louis Guinand discovered that replacing the wooden stirring rods with ones made of fire clay served to bring the bubbles to the surface, much improving the result. It is fortunate that this secret is divulged by EB11 “Glass.” Until the time of Guinard, the largest flint glass discs which could be cast without unacceptable flaws were 2–3 inches (Doherty 16).

    Striae (thread-like inclusions) form as the result of evaporation of glass components during melting. Like bubbles, they are left in the glass by incomplete stirring.

    Optical glass tends to be required in thicker pieces than the glass used for windows and mirrors. For the purpose of lens making, it is probably best for glass to be formulated in relatively small clay pots (perhaps half ton capacity), with heating and cooling tightly controlled.

    After cooling, the glass must be examined for flaws (bubbles, striae, chips, cracks, etc.). One trick which will probably be rediscovered is to put the block of glass into an aquarium-like receptacle and fill this with a liquid of the same refractive index as the glass. This eliminates reflection and refraction at the surface making it possible to see flaws deep inside. Typically, in the early 1900s, not more than half, and often much less than a quarter, of the glass would pass this inspection, and of course attempts were made to cut out suitable fragments.

    Candidate lens blanks can be further examined for bubbles and striae, and sometimes these can be worked out. Bell estimates that the price of lens blanks increases as the cube of the diameter.

    The starting point for creating a lens is a rough disk or spheroid of glass. In the early seventeenth century, the lenses were ground using a “primitive hand operated lathe,” and the lens surface compared with that of a metal template. One of Galileo’s lensmakers, Ippolito Francini, had a lathe with a pivoted boring bar, and a flywheel to maintain a constant rotation speed. The lathe could be used to grind the lens directly, or it could be used to make a metal lap, with which the lens was subsequently hand-ground. (Woods).

    In 1652, when Huyghens tried his hand at lens grinding, he had to ask an expert how to make the grinding mold, what sand to use, and so forth. There were no books to teach the art. However, the craftsman did not hold the art an absolute secret; Isaac Beekman learned the techniques in 1632 from Johannes Sachariassen; and Huyghens was tutored by Gutschoven. (Dijksterhuis 57).

    Finding good lenses is not going to be easy. In 1616, Giovan Francesco Sagredo complained to Galileo that “out of a lot of 300 lenses he had purchased for Galileo from Venetian glass maker Maestro Antonio only three proved suitable for use in his telescopes.” (Pope) I suspect that some of the lenses rejected by Galileo got palmed off on those whose interest in astronomy was obviously casual (the telescope as “room decor”).

    Reviewing descriptions (Medicean Skies) of mid-seventeenth century lenses, I find:

    20:-50 (20 mm aperture, -50 mm focal length) eyepiece: “a very slight green tint and some spherical bubbles”

    ?:1022mm objective: “many small bubbles and inclusions as well as a slight yellow tint”

    70:3600 objective: “slight red colouring . . . numerous small bubbles of elliptical form.”

    84:6050 objective: “red tint . . . elliptical bubbles and some inclusions”.

    40:1480 objective: “red tint . . . elliptical bubbles and some inclusions”.

    25:-64 eyepiece: “clear . . . a number of aligned elliptical bubbles”.

    26:-140 eyepiece: “good transparency . . . some elliptical bubbles”.

    27:-84 eyepiece: “slight green tint . . . elliptical bubbles.”

    111:111.6? objective: “reddish tint . . . some bubbles.”

    35:-67 eyepiece: “slight green tint . . . some small bubbles.”

    35:-94 eyepiece: “slight yellow tint . . . some bubbles and inclusions.”

    Even at the end of the nineteenth century, there were still problems with making big lenses. The 1911 “Telescope” article says, “the difficulty of procuring disks of glass (especially of flint glass) of suitable purity and homogeneity limited the dimensions of the achromatic telescope. It was in vain that the French Academy of Sciences offered prizes for perfect disks of optical flint glass. Some of the best chemists and most enterprising glass-manufacturers exerted their utmost efforts without succeeding in producing perfect disks of more than 31 in. in diameter. All the large disks were crossed by striae, or were otherwise deficient in the necessary homogeneity and purity.”

    Making Metal Mirrors

    It is not very likely that any of the up-time books on telescope making will teach this lost art. Of course, down-time metalworkers know how to proceed. Indeed, it is perhaps no accident that one of the great telescope designers, Sieur Guillaume Cassegrain, was a sculptor who worked in bronze.

    In Pirotechnica (1540), Vannuccio Biringuccio describes (388–390) how to cast and polish a metal mirror. According to Biringuccio, the ancient method was to make them of the same alloy used for bells; 75% copper and 25% tin (optionally adding 1/18th antimony or 1/24th silver). However, in his time, he says, most of the masters reversed the proportions, that is, their mirrors were 25% copper and 75% tin.

    In any event, to make a flat mirror, they melted the alloy and poured the molten metal into a mold, typically three dita (inches) thick. The metal piece is removed from the mold and fastened to a board with plaster of Paris, pitch or glue. Next, the metal is polished, using a millstone, or sand and water. Biringuccio warns the reader not to “continue to rub long in one direction.”

    Scratches made by the coarse materials are removed with very fine emery or powdered pumice, placed on a woolen cloth. Then the mirror is dusted with “Tripoli,” ochre, or “calcined tin,” and rubbed some more. Finally, the mirror is detached from the board and framed.

    The manufacture of a concave mirror is similar, but one starts with a concave mold, and the mirror is polished while still in the mold, which is turned on an axle like a potter’s wheel.1

    The 1911EB gives the preferred “speculum metal” composition, 4 parts copper to one part tin (or by weight, 252 copper: 117.8 tin). Note that this is different from the “modern” mirror composition recommended by Biringuccio. It also comments, “Shaping, polishing and figuring of specula are accomplished by methods and tools very similar to those employed in the construction of lenses. The reflecting surface is first ground to a spherical form, the parabolic figure being given in the final process by regulating the size of the pitch squares and the stroke of the polishing machine.”

    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:

    Diameter (in.)

    Focal length (in)

    Magnification

    Price (guineas = 21 shilling)

    1.1

    3

    18

    3

    1.9

    7

    40

    6

    4.5

    24

    90-300

    35

    6.3

    36

    100-400

    75

    18

    144

    300-1,200

    800

    (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

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About Iver P. Cooper

Iver P. Cooper, an intellectual property law attorney, lives in Arlington, Virginia with his wife and two children. Two cats and a chinchilla rule the household with iron paws. Iver has received legal writing awards from the American Patent Law Association, the U.S. Trademark Association, and the American Society of Composers, Authors and Publishers, and is the sole author of Biotechnology and the Law, now in its twenty-something edition. He has frequently contributed both fiction and nonfiction to The Grantville Gazette.

 

When not writing (or trying to get an “orange blob” off his chair so he can start writing), he has been known to teach swing dancing and folk dancing, or to compete in local photo club competitions. Iver adds, “I can’t get my wife to read my fiction, but she has no trouble cashing the checks.”

Iver’s story “The Chase” is in Ring of Fire II