Grantville gazette vol.., p.29
Grantville Gazette - Volume XVI, page 29
part #16 of Grantville Gazette Series
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."
