ROGER HAYWARD, whose drawings for this department unfortunately can be made only in black and white, has been for many years a student of color, both as an amateur painter and as a successful architect in Los Angeles. Here are his interesting conclusions on the subject.

"People," he says, "are unreasonable about color. At least, most of them do little reasoning about it. I used to think that only artists were privileged to express opinions about color and I resented scientists meddling in it. After sitting in conferences with artists for more than 30 years, however, and listening to them defend their individual preferences with passion while disagreeing violently among themselves, I now think the artists are the dumbest of the lot. Most of them think the only thing that matters is their blessed emotions, a sentiment open to doubt.

"Physicists who know about light have unwittingly implied that they also know about color, but the two are not exactly the same thing. The stimulus for color is light, all right, but color is a sensation in the brain and can be termed strictly a psychological effect. A red light in an otherwise dark room will cease to appear colored after a few minutes. A piece of gray paper may appear brown or green or red, depending on the background. A piece of red paper may appear red or black or white, depending on the color of the light source. Again, although blue is a popular color, a blue beefsteak would be nauseating. Bright yellowish green is wonderful in primroses but ghastly as a complexion.

"However expert a physicist may become in the field of colorimetry, the color sensations experienced by the human brain must remain outside his field. They are a mixture of (1) the color of the surface as measured in white light; (2) the color of the light source; (3) the color of the background; (4) the colors which the observer has been viewing in the previous few minutes; (5) the color the observer expects the object to be; and (6) the color that the observer's friends and relatives believe appropriate for the object in question.

"Artists, though far from scientific, are in some measure objective in their view of color. They usually think of color as such as part of a color scheme. They take the position that people's likes or dislikes of individual colors, such as pink, have no meaning. Some of the significance of a color depends on its relation to other colors, just as a word has part of its meaning implied by the context."

Thus color, like music and economics, appears to partake both of science and art. A mathematical basis underlies musical harmony. Is this also true of color? Is it possible to find a quantitative basis for the expression of color harmony and to explore color values by means of logical processes? Some scientists have thought so, and Hayward became convinced that painstaking experiment and research might turn up some mathematical rules for predicting color combinations that would be generally accepted as harmonious and pleasing-at least in the narrow field of color decoration. He decided to find out. Now, after several years of work, he not only has a working theory of color harmony but a full-scale avocation. His experiments are fascinating, and anyone can easily repeat them. Moreover, they enable an amateur of limited artistic endowment to turn out pleasing color designs on the first try.

The tool that Hayward uses in his investigations is the so-called "color top," first employed in color research by the physicist James Clerk Maxwell. "The color top," says Hayward, "is the simplest device with which a quantitative study of color can be made. It is merely a spindle, capable of rotating 30 or more revolutions a second, on which adjustable colored sectors can be mounted. As it spins, the colors are seen as a mixture, and the hue you see will depend on the proportions of exposure of the individual colors.

"An unused fan motor is ideal as the basis for construction of the top [see drawing below left ]. Prepare some disks of colored cardboard and punch a hole in the center for the spindle and make a single radial cut in each disk. Now when you mount the disks on the spindle you can interleave them so as to expose as little or as much of each color as you wish. A slightly larger disk, placed behind the colored disks and calibrated in hundredths of a circle, will enable you to read directly the percentage of the circle occupied by sectors of each color.

"For coloring the disks it is desirable to use show-card colors, such as Prang's Tempera, so that you can always be sure you have the same colors. It is unwise to do any mixing of paints, because of the difficulty of duplicating any color exactly.

"Suppose you start the experiment with three disks of the primary colors-Prang's red, green and ultramarine blue. If you adjust the disks to expose approximately 34 per cent red, 46 per cent green and 20 per cent blue, when you spin the wheel you will get a shade of gray. Now put on the spindle a pair of smaller disks, one black and one white [as shown in drawing]. By carefully adjusting the relative amounts of black and white exposed, as well as the mixture of primary colors, you can obtain the same shade of gray with both combinations when the wheel spins.

"The mixture of red, green and blue needed to match the black-and-white gray depends on the light source: it is different in daylight from that in artificial light. The difference is a measure of the colors of the two light sources. Individual observers also differ in the way they make the match-very markedly if they are color blind or partly so.

"With different proportions of primary colors you get different colors when the wheel is spun. Now if you cover part of the disk with black sectors, the addition of black to the mixture will make the color darker, but the hue will be the same.

"One can now start reasoning about color. Since the original set of colors makes gray, any two parts of the wheel must be complements. Actually two complementary colors, when mixed, make white, but we get gray in this case because there is some black in the mixture. If we turn the black sector step by step so that it exposes various parts of our color wheel, we can see the whole range of complements. We can display all the complements simultaneously by making a color wheel in two parts, the central area having the color sequence in one position and the outer ring displacing the same sequence by 90 degrees [detail at right in middle row of drawing]. When a black mask which leaves only opposite quadrants exposed is placed over the disk, the central color will always be the complement of the outer part. Other masks can be cut to show various combinations of complements and near-complements.

"I have experimented with a number of such combinations to find complements. For example, let the outer section of the wheel be 34 per cent red and 16 per cent green; the inner section, 30 per cent green and 20 per cent blue. The sum of the two sections is 34 per cent red plus 46 per cent green plus 20 per cent blue, which equals 100, or gray. Now the red and green combination in the outer section gives a reddish orange, while the green and blue combination in the inner section gives a blue green. The experiment shows that these two colors, adding up to gray, are complements. Similarly I have found that an apple green composed of 4 per cent red and 46 per cent green is the complement of a reddish purple made of 30 per cent red and 20 per cent blue. A brownish yellow made of 23 per cent red and 27 per cent green complements a purplish gray made of 11 per cent red, 19 per cent green and 20 per cent blue. Note that in this last a mixture of red and green produces a dark yellow. Yellow is not a true primary, despite the contrary teaching of many schools. A mixture of red and green can be matched with a mixture of yellow, black and white (the white being added to dilute the yellow, because Prang's red and green are not as bright as one could wish).

"From the results of color-wheel experiments extending over several years, it seems to me that a possible numerical theory of color harmony can be stated in the following terms: The general formula is that the sum of the components of each color, when multiplied by the fraction of the area of the design which that color is to occupy, should be equal to gray (100). In the simplest case, that of a two-color pattern with each color occupying half the space (e.g., a checkerboard), the sets of color complements given above would yield harmonious combinations.

"Now suppose we have a two-color pattern in which one color is to occupy twice the area of the other. First we select one of the two colors, according to personal taste, and decide that this color will occupy one third of the area. Let us say we select bright green. What color should we choose for the other two thirds to make a harmonious and pleasing pattern? We multiply by three each of the components of gray (34 red, 46 green and 20 blue). This gives us 102 red, 138 11 green and 60 blue, equaling three times gray. Now we subtract the color-wheel value of our green (100) from the value of three-times-gray and divide the result by two. Thus we get 102 minus zero divided by two, or 51; 138 minus 100 divided by two, or 19; 60 minus zero divided by two, or 30. This gives us the components of the color that will harmonize with bright green in our pattern; the color will be composed of 51 per cent red, 19 per cent green and 30 per cent blue. This color is plum.

"One of the traditional rules of color harmony is that the smaller areas should have the brighter color. Observe that in this example the theoretical working out of a harmonious complement for bright green did indeed yield a duller color. It is interesting to make experiments with other combinations as a further test of the theory.

"The theory can be applied to combinations of several colors in any given area proportions.

"Suppose, for instance, we want to use four colors in the proportions of 1:2:2:4. Say we select red as the first color, to occupy one tenth of the area, and yellow as the second, occupying two tenths of the area. The third color will occupy three tenths and the fourth, four tenths. The combination as a whole must equal 10 times gray, that is, the primary colors must add up to the proportions 340 red, 460 green and 200 blue. The red component will give us 100 red (100 times 1); the yellow component, 100 red and 100 green (50 red times 2 and 50 green times 2). To obtain the required totals for 10 times gray we need 140 more red, 0,60 more green and 200 blue. The requirements are satisfied if we use a light blue as the third color, occupying three tenths of the area (180 green and 120 blue), and a light plum as the fourth color for four tenths of the area (140 red, 180 green and 80 blue)."

Hayward recognizes the obvious limitations of his theory. As he points out, it applies only to simple patterns and treats all colors as emotionally equivalent. "Another defect," he writes, "is that it assumes all colors to have approximately the same value whether light or dark. Black may have to be included as a color. Physically black is merely the absence of light, but psychologically it appears to have almost the same properties as any other color. Within these limitations, however, the theory yields quantitative answers to questions in the field of color harmony, however strange it may seem to be working out such schemes with numbers."

THE fact that a third book of the Amateur Telescope Making series is just off the press may be interesting news for amateur astronomers. The new book's title is Amateur Telescope Making: Book Three. "ATM-3," as it will be known to the amateur, is not a revision of Amateur Telescope Making (Book One) or of Amateur Telescope Making-Advanced (Book Two) . It is a generally new work, of 644 pages with 820 illustrations, setting forth new optical projects for the amateur who has made telescopes and learned the feel of optical work. The preface explains:

"The amateur telescope making pursuit began with the simple aim of making telescopes, but in next to no time the nimble-minded people to whom it appealed were running all over the field of precision optics in search of other instruments they could build, while some delved into physical optics to understand its theory, and all to some extent did both. The old demarcation between amateur and professional optics receded, became blurred or vanished. Neither can that demarcation be found in the present volume, which is for all who are interested in optics, though essentially for amateurs. Some of its authors are amateurs, some are professionals who began as amateurs and have remained so in their spirit of enthusiasm, and a few are professionals who never were amateurs but nevertheless have fun with optics.

"Some of the chapters describe projects and procedures, others techniques, others tests, others professional methods adaptable to amateur use; still others the design of telescope lenses by professional methods, including ray tracing, made lucid by sympathetic writers who have striven not to 'keep 'em mystified.' There are chapters on the selection of lenses, plates and films for astronomical photography, and on the construction of lens systems for the same purpose. Others are on the construction of spectrographs, a spherometer, a precise photoelectric photometer for variable-star work, a monochromator for solar observation, and on the mechanical understanding, complete overhaul and accurate adjustment of binoculars. A chapter explains the design considerations for eyepieces, describes 91 eyepiece types and includes the specifications for 39 eyepieces. Another is on the understanding of diffraction Others are on the Barlow lens, optical fiat making, Schmidt camera making and making elementary camera lenses, lens production on a small professional scale, coating of lenses and aluminizing of telescope mirrors, building and using an optical testing bench, preparing scratchless optical abrasives, a null test and an ultraprecise test for mirrors, and a procedure for designing a Maksutov Herschelian telescope. An innovation is a brief, intimate biography of each contributor, from which the reader may discover human interest that should increase his enjoyment of the book."

James G. Baker, who made a three-inch telescope lens from a glass bathroom shelf when in high school and is today a noted optical designer, gives complete data on making two optical systems for astronomical photography. The first is a detachable correcting lens which converts a photographically narrow-field paraboloidal telescope into a wide-field photographic telescope that gives full Schmidt performance-anastigmatic- and will photograph stars clear out to the 1Sth magnitude. The second is a three-inch (six-inch if desired) Cooke triplet lens of high quality and light gathering power. Data for two designs are given, one for blue-violet (photographic), the other photo-visual. Detailed plans for the lens mounts are included.

Earle B. Brown of the Farrand Optical Company, who began as an amateur, writes understandingly of amateurs' problems in building and using high-vacuum equipment for aluminizing mirrors and coating lenses. To his fellow "T.N.s" (telescope nuts-the amateurs' own name for themselves) he writes: "Not the least of the appeal of high vacuum to the T.N. is its natural perversity Compared to a high-vacuum system, the most recalcitrant optical surface is a paragon of meek submissiveness. This sort of thing makes raving maniacs of most people, but T.N.s are of the peculiar breed of cat that thrives on frustrations." Fully to describe all the techniques of vacuum practice would call for an entire shelf of literature, to which Brown gives references in an ample bibliography. Following the policy of the ATM series, the names and addresses of the sources of all the materials needed are included.

During the entire life of the amateur optical hobby there has existed virtually no practical literature on spectrograph construction. Therefore 80 pages of ATM-3 are devoted to that subject. In one chapter the physicist C. Fred Clarke describes in minute detail, with scale drawings, the construction of a laboratory spectrograph with a small replica grating of 106 centimeters focal length mounted on an old 54-inch lathe bed. In another, Strathmore R. B. Cooke and Robert A. Wilson describe in equal detail the design and construction of a larger laboratory spectrograph using a small grating of five-foot focal length. Such instruments, if bought ready-made, would cost several thousand dollars. If well constructed, they are capable of professional chemical analysis. Several smaller spectrographs are described in the spectrograph section of the book.

R. E. English, a professional maker of optical flats who began as an amateur, describes his method of making flats having an accuracy of one five-millionth of an inch.

Patrick A. Driscoll once coined the descriptive term "amateur-professionalamateur" for the amateur who has become a professional but nevertheless remains an amateur in the original sense of the word (lover). In a detailed chapter the amateur-professional-amateur optical workers Fred Ferson and Peter Lenart, Jr., fully describe lens production on a limited scale in a professional plant. Their contribution has three special values to the amateur. The methods are applicable to small production runs in the hobby shop; the description satisfies amateur curiosity about professional methods, and, best of all, it contains numerous details and insights having direct applicability to the one-piece work that amateurs do.

Irvine C. Gardner's instructions permit the worker to build a special spherometer for precise measurement of the curvature of small short-focus lenses such as eyepiece lenses.

The "G-sum" method of designing achromatic objective lenses is described by Alan E. Gee of the Frankford Arsenal. His algebraic method is a little more difficult than those of Ellison and Haviland, but it gives full control over spherical aberration and sometimes over coma. It more nearly approaches the exactness of ray tracing.

Practical literature on binoculars up to now has been virtually non-existent. In World War II, C. Dallas Hanna, a California Academy of Sciences paleontologist with a flair for the mechanics of precision instruments, headed a group of amateurs who were making roof prisms until they were discovered by the U.S. Navy and asked to recondition its optical instruments They reconditioned 6,000 Navy binoculars. In ATM-3 Hanna records all that he learned, not alone on the overhaul and exact adjustment of binoculars but on their basic principles. Hanna explains those basics clearly. He also gives instructions for building, around a telescope mirror, an autocollimator for testing the prisms used in binoculars, as well as other prisms

Lives there an amateur telescope maker who has never been baffled or driven to desperation by mysterious scratches that appear on his optical surfaces while he works them? Hanna discovered a major cause of the scratches. Agglomeration of the fine abrasive grains strongly held together produces large grains called "cobblestones." Many discouraged workers have tried separation of grain sizes by washing, but as Hanna states, segregation is not that easy. A dispersing agent, or deflocculent, is necessary. He and the amateurs who kept his wartime workers supplied with optical surfaces developed a technique for breaking the powerful attractive forces that clump the grains. This requires only two jars, a chemical and a siphon. He writes: "We use our abrasive alongside roughing mills and never take any precautions such as taking a bath before fine grinding, yet it has been a long time since any of us has had scratches on glass."

While excellent Barlow lenses are on the market, an amateur may be prouder of his Barlow if he designs and builds it himself. In his chapter on the Barlow lens C. R. Hartshorn tells how.

The photoelectric photometer is becoming a must for scientific variable-star observing, and it has other uses. Gerald E. Kron of Lick Observatory (another amateur-professional-amateur) minutely gives data for building two amplifiers for use with them-one for battery current, the other for lighting current. He also provides a lead to a source of inexpensive instructions for building the photometer.

In a chapter on lenses for astronomical photography and another on plates and films Henry E. Paul distills his extensive experience with both, saving the reader from making the standard expensive mistakes and enabling him to become expert relatively early.

Amateurs have made relatively few Schmidt cameras, largely because of the scarcity and inaccessibility of practical instructions. They have clamored for such instructions for years. Paul's Schmidt chapter should give the Schmidt a new birth. He demonstrates the optimum focal ratio for Schmidts and describes the construction. He includes a test for the deep sphere which will be new to most, and tells a new method of figuring correcting plates. He lists the best half-dozen of hundreds of existing articles on the Schmidt. These articles are reprinted in the book. An editor's note explains: "Theoretically the articles cited in the preceding selected bibliography are available to everybody. You just drop in at a large public library and read them to your heart's content. Actually, this would be so difficult for most of the owners of this book that the articles might almost as well not exist. Even if you knew of a library that had them all, you'd probably have to travel some distance and snatch at the articles and you couldn't take them home with you. What you want is something that's yours, at home, where you can refer to it whenever you feel like it." The reprinted articles include two by British authors on figuring correcting plates and on the construction of a whole Schmidt, and the classic Mount Wilson Optical Shop piece on 18 unconventional types of Schmidts and on the design of correcting plates. The Schmidt section also has an intimate biography of Bernhard Schmidt himself-the eccentric bachelor with only one hand who always worked in a claw-hammer cutaway coat and striped trousers, chain-smoked cigars and cared more for schnapps than for money. A translation of Schmidt's own classic paper is included in the reprints.

A description of every detail of the construction of Henry E. Paul's most recent quartz polarizing monochromator for solar prominence observation, written by him immediately after he had finished it, while the job was still "warm," is included in this volume. It is followed by Edison Pettit's classic paper, which he has revised and expanded, on the interference polarizing monochromator.

Irwin H. Schroader describes a test which not only detects but actually measures errors as small as one five-millionth of an inch on a telescope mirror. Those who argue that this is finer precision than is needed overlook two facts: first, that one of the mainsprings that drive the telescope maker is the enjoyment derived from the highest possible mechanical precision; and second, that extreme precision is significant in resolving fine detail on the planets and moon; the higher the precision, the better the resolution. The tests described by Schroader are at their best on short-focus mirrors.

No telescope maker can become an advanced amateur until he has learned what diffraction is. Horace H. Selby describes it in a chapter titled "Interference of Light." He explains diffraction in elementary terms and interprets the various edge appearances of a mirror and their causes by means of a diagnostic table. In another chapter Selby shows drawings of the 91 types of eyepieces and gives specifications for constructing 39 of them. In a third he describes a homemade optical bench with which you can mount lenses of all kinds, even complete telescopes, in proper and variable relationship to one another for analysis, demonstration and testing. Bench methods are rapid, direct and fundamental, and put an end to guesswork.

Thousands of telescope makers have clamored for years for instructions for making their own camera lenses. The amateur-professional-amateur James W. Shean of the Bausch & Lomb Optical Company has supplied instructions and data for making a number of these lenses. The ultimate effect of his chapter should be the enlargement of the amateur optical hobby by a substantial new wing.

A chapter by Charles L. Woodside describes a method by which an objective lens may be computed from glasses having unknown constants.

Franklin B. Wright gives a procedure for designing and building a superb Herschelian telescope having a Maksutov lens.

The last word in optical exactness is ray tracing by trigonometric methods. Most amateurs have believed it beyond their ken-mainly, perhaps, because no book treating it sympathetically has existed. In a detailed chapter James H. Wyld robs "ray trace" of its mathematical mystery, leads the tyro by the hand and shows that the bogey is largely a myth. The requisites for ray tracing are patience, persistence, accuracy, a knowledge of common algebra and a little trigonometry-far less than is given in high-school courses. Wyld writes: "The amateur telescope builder who takes a real pride in exact workmanship, and who wishes to keep his theoretical design studies on the same high plane as his practical work with glass, pitch and rouge, will find a great mental satisfaction in carrying out his designing by exact ray-trace methods; he will furthermore develop an invaluable insight into the whole subject of theoretical optics which no amount of book study can supply.

The last chapter of ATM-3 contains the editor's informal biographies and snapshots of the contributors. Throughout the book are innumerable side observations which should illuminate many puzzles that bedevil optical workers.

SIX methods of dividing a circle into degrees for setting circles on telescopes are described in Amateur Telescope Making-Advanced. T. R. Macfarlane of Regina, Saskatchewan, now adds a seventh. His method is based on the tables of chords of arcs used by some engineers, architects and mechanics. Each angle is represented by a decimal fraction. To lay off an angle you multiply the fraction by the radius of the circle, which gives you the chord. For example, .5345 corresponds to 31 degrees, and to inscribe a 31-degree angle on a circle eight inches in diameter, you multiply .5345 by the radius, four. The product, 2.138, is the number of inches in the chord for the arc of this angle [see drawing at left, above]. Roger Hayward points out that if no table of chords is available the answers may still be derived from a table of sines. The chord is equal to twice the sine of half the angle [drawing at right, above].

Since the arithmetical work needed for converting decimal fractions of an inch is laborious, it is easier to use a metric scale, laid off in decimal fractions. Macfarlane describes the procedure as follows [see drawing below].

"Drill a small hole neatly in a sheet of metal. With this as a center cut a circle of size desired.

"Provide two flat strips of metal a bit over a meter in length and a one-meter steel rule.

"Scratch a clean straight line on each of the strips, near one edge, as shown in the third drawing.

"Carefully measure one meter along these lines, mark the points and drill holes in both strips.

"Cut away the sides of the strips back to the scratched lines to give access to the radius of the circle.

"Bolt the strips to the circle, mark the starting point with one strip, swing the other until the meter rule has the correct length of chord for the desired angle. As an example, 60 degrees calls for a chord of exactly one meter, 90 degrees for 1.414 meter.

"As a preliminary practice run, to test your precision before inscribing any lines, cut the zero scratch, mark the 60-degree line with a fine pencil point, start at this point for a new 60-degree point and continue around the circle to see how nearly you close after the six measurements with their random and systematic errors. If you come out precisely enough to satisfy your requirement, reset at the zero point and make needle scratches to be cut as coarse as needed for legibility."

Hayward, a fine mechanic, points out that the precision of the method is limited by the precision with which the bolt holes are positioned (drills always wander a little from a centerpunch mark) and by the precision with which the bolt fits the holes.

Bibliography

COLOR: IN THEORY AND PRACTICE. H.D. Murray. Chapman and Hall, 1952

AMATEUR TELESCOPE MAKING. Edited by Albert G. Ingalls. Scientific American, Inc., 1952

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