ALTHOUGH the optics industry has sophisticated machines for grinding glass into lenses and mirrors, many amateur makers of optical instruments prefer grinding by hand. The term for the task is free abrasive grinding. This hand technique involves rubbing a hard object in a random motion over a fine abrasive grit on the object being ground. One usually begins with a grit of fairly large size and then shifts to progressively smaller grit sizes until the ground object reaches the desired size, shape and smoothness.

Two seeming paradoxes are associated with grinding. One of them has been understood in essence since the time when the wave nature of light was accepted. The question is: How can grinding the surface result in a smoother surface, one that is optically good enough to be useful in an instrument such as a telescope? The answer lies in the transition to increasingly fine grit. The deviations from smoothness on the surface correspond roughly with the size of the grit. Therefore they are gradually reduced during the grinding and polishing until they are the same size as or smaller than the wavelength of light. In that condition the surface then appears smooth and optically true.

The second paradox has, I believe, only recently been understood. Indeed, more work could be done to firm up the understanding. This second question is: How are scratches on the ground surface avoided in spite of the fact that in any abrasive compound the distribution of grit sizes ranges over about two orders of magnitude, so that the compound surely contains some relatively large particles that should scratch the surface? Free abrasive grinding appears to have become so much of an art, depending a great deal on the grinder's experience and sense of touch, that few people seem to have investigated why more scratches are not made.

Recently Edward J. Saccocio of Columbus, Ohio, developed a model that seems to resolve this second paradox, at least in part. The success of free abrasive grinding appears to depend on the shape of the edge of the object moved over the grit. Normally the lapping tool on top is a metal or a glass that is as hard as or harder than the material being ground. Between the two lies a slurry of the grit. Saccocio found that the leading edge of the tool determines the size of the particles that can get between the tool and the ground object.

If the edge is sharp, oversize particles will enter the space between the tool and the ground object less easily than if the edge is rounded. The height of the space is largely determined by the average size of the grit. Scratching appears to result when a particle that is much larger than average enters the space, becomes stuck on one of the surfaces and then gouges a scratch in the other surface. Hence a tool with a sharp leading edge should produce fewer scratches on the average than one with a dulled and rounded leading edge, which will more readily allow oversize particles to get under the tool.

To test these ideas about the causes and prevention ofscratches Saccocio performed several simple experiments. I have repeated them, as you can: moreover, you can use them as a base for more experiments to track down the causes of scratches. The material chosen to be ground was a molybdenum disk (brass would be more convenient for you), the harder material was glass and the abrasive grit was aluminum oxide in three nominal grit sizes: 30, 15 and three microns. The specimen of molybdenum was a short cylinder 15 millimeters in diameter; it was worked over a large plate of glass in an inversion of the normal grinding arrangement. The grinding compounds are available from the Edmund Scientific Company (7778 Edscorp Building, Barrington, N.J. 08007), from Buehler Ltd. (2120 Greenwood Street, Evanston, III. 60204) and from certain hobby shops.

A grit was spread on a portion of the glass plate to provide a grinding medium for the molybdenum disk. Saccocio mixed the aluminum oxide with water to form a slurry, which is the usual practice in free abrasive grinding, but I left my grit dry. The molybdenum surface was first made smooth and scratch-free by grinding it with each of the three grit sizes in descending order. I moved the cylinder around in the grit randomly, applying pressure as evenly as I could. One of the difficulties in the experiments, something that requires experience, is determining what pressure is appropriate. Too light a pressure prolongs the grinding process; a pressure that is too heavy results in scratches.

I had to replenish the grit frequently to avoid scratches. Perhaps this was partly because pieces of metal that had been abraded from the disk contaminated it. In addition the amount of grit under the disk seemed to diminish.

Why do scratches occur? Presumably with too much pressure the abrasive particles can no longer roll or tumble smoothly between the moving surfaces while removing small amounts of material, and the larger particles in the grit catch in one surface and gouge the other. Saccocio believes this catching occurs when the two surfaces are at an angle to each other, which happens when the pressure is applied unevenly or when the grinding has already worn the surfaces into concave and convex shapes. I could sense when a scratch was being made because the disk gave a slight jerk and the grinding sound changed noticeably. With an appropriate amount of pressure the abrasive particles grind away the molybdenum surface either molecule by molecule or at least by craterlike sections that are too small to be seen; moreover, the abrasion is confined to the surface.

Following Saccocio's lead, I checked the idea that oversize particles cause scratching. I put some 30-micron grit into grits of the two smaller sizes. I first ground the disk over a region of the uncontaminated smaller grit and then, without lifting the disk. moved it into the contaminated region. With about equal amounts of the two grit sizes in the contamination, mixed as uniformly as I could mix them, scratching seemed no more frequent than normal. As I repeated the experiment with smaller amounts of the 30-micron grit in the same amount of smaller grit, however, scratching seemed to be more likely.

In each of the trials I had to maintain about the same amount of pressure on the disk. Some variation in scratch frequency surely resulted from my inability to do this precisely. Still, it appears that if larger particles are present in small amounts, they are more likely to cause scratching. Apparently in such cases the spacing between the disk and the glass is largely determined by the smaller grit. If the larger particles enter the space, they must force the disk up. Since the disk would then be supported in fewer places, the contact points of those larger particles must sustain more pressure. With more pressure on a few spots the larger particles are more likely to catch and gouge the surface.

I next tried to rub the disk in one direction only and then only once or twice before blowing off the grit to examine the molybdenum surface. In that way I could tell where the scratches began and stopped. Some of the scratches started at the leading edge of the disk; others began at random places inside the perimeter. Some of them appeared to gin in a rather wide track that later narrowed. This narrowing could be due to the fracturing of the gouging particle. Other tracks seemed, at least when I inspected them with a simple magnifying lens, to remain about the same width. All the tracks were significantly wider than the particles. One can imagine that the point of a gouging particle catches in a moving surface and that in the course of its subsequent motion it pulls and distorts a fairly wide area of the surface before the distortion is severe enough for the surface to rip. It is possible that some tracks could be narrow at the beginning and could grow wider if the gouging particle digs into the moving surface progressively more, although I could not find any such tracks.

The fact that some scratches begin at the edge and others begin on the inside is probably due to chance. The gouging particles are not round (they would not be likely to gouge if they were) and they have sharp points. It is a matter of chance when one of these particles happens to tumble into an orientation where one side catches and the other side gouges. A degree of chance must also have been introduced by the random motion and pressure I applied to the disk. Occasionally I must have borne down more on one side of the disk and increased the likelihood of scratches on that side.

To test the effect of the leading edge on the frequency of scratching Saccocio performed several experiments with a molybdenum disk encased (except for the surface to be ground) in a hard plastic or epoxy material. The leading edge was the plastic ring surrounding the perimeter of the molybdenum surface. The ring had a slope of from three to five degrees, arranged so that the outside of the ring was farther from the glass than the inside, which was adjacent to the molybdenum surface. Saccocio did his grinding with uncontaminated slurries, and he found that with the sloped leading edge the molybdenum surface was scratched more often than when another (unencased) molybdenum disk having a sharp leading edge was rubbed in the same slurry. Once again, applying the same pressure on both specimens is difficult, and failure to do so can lead to spurious results. Nevertheless, Saccocio believed the difference in the scratch frequencies was due somewhat to the shape of the leading edge. The sloped leading edge gave more opportunity for the oversize particles responsible for scratching to get into the space between the disk and the glass plate.

I repeated this experiment with some 30-micron particles contaminating one and then the other of the smaller grits and found the same general results. I also tried the experiments with an unencased molybdenum disk, purposely sloping one edge, keeping another edge sharp and rubbing the disk through the grit in a single direction, first with the sharp edge leading and then, after inspection, with the sloped edge leading. Although the results varied, they were generally consistent with Saccocio's.

I also noticed a curious scratching pattern that appeared occasionally when the sloped edge was leading. Scratches were mostly to the sides of the sloped edge rather than directly behind it. If this pattern is indeed characteristic (more trials will be required to show whether it is), it might be because the disk pivots over a central ridge of oversize particles running from the sloped edge and across a diameter to the rear. More of the oversize particles will enter by way of the sloped edge than by way of the sharper sides, and this selection tends to raise the center of the disk. Thereafter I shall have to push inadvertently and randomly more on one side than on the other, causing the disk to pivot around the central ridge. Because the sides have fewer oversize particles than the central ridge does, the increase in pressure on one side will result in more gouging there than in the central ridge.

Much more could be done on these experiments. You could get more data with the molybdenum-and-glass system, and you could try other abrasive compounds (both wet and dry) and other grinding materials such as glass (on glass?, aluminum, copper, brass and lead. The data would be easier to interpret if you could standardize the pressure applied to the specimen. You might try placing a known weight on the disk and then rubbing the disk through the slurry by pushing horizontally on the disk and the weight. For a given grit size, how does the scratch frequency depend on the applied weight? Since the scratching is random, you will need lots of data properly interpreted statistically to answer the question.

When I first put my molybdenum disk on the grit, the full range of particle sizes in the grit was under the disk. Does the full range of sizes remain after you have ground for a while or does the grinding somehow eliminate the larger particles while a sharp leading edge prevents new ones from entering the space under the specimen? Why did I have to replenish the grit in order to avoid scratches? When I ground with the 15-micron grit for a while, the glass plate became opaque, and it was covered with a fine dust that seemed to decrease the frequency of scratching. Does this result arise because the disk is then so close to the glass that oversize particles have even more trouble getting under it?

The fireplace is an ancient and common source of heat for the home. The output of the fireplace is mainly limited to one of the three possible types of heat transfer: convection, conduction and radiation. Little of the heat comes into the room by convection because the heated air is lost up the chimney. Hardly any heat enters by conduction for want of solid objects between the fire and the room. Most of the heat enters by radiation, largely in the infrared region. Most of this radiated heat comes from the hot coals in the fire rather than from the visible flames, which is why the fire is hot only after enough wood has burned to create the coals.

THE fireplace is considered to be an inefficient source of heat because only a relatively small fraction of all the energy released by the fire ends up in the room. Even some of that energy is often wasted because it has become fashionable to place a glass screen in front of the fireplace to prevent sparks from flying into the room. The glass is rarely designed to transmit infrared radiation.

Until the conservation of energy became a matter of widespread interest little was done about improving the efficiency of the fireplace. Lawrence Cranberg, a physicist of Austin, Tex., began investigating the stacking of logs in the fireplace. He concluded that the conventional stacking (three or so in a triangular cross section) was a poor design because much of the heat radiated by the fire appeared to be sent upward and therefore lost to the brickwork above the fire or to the chimney. Cranberg also noticed that the coals, which are responsible for most of the radiated heat, are not exposed well to the room but are instead hidden under the unburned wood. Thus in order to heat the room enough one is tempted to burn the logs at such a rate that flames leap upward into the chimney and the logs are consumed fairly quickly.

With this poor radiation pattern in mind Cranberg designed a new fireplace grate that holds the logs in a slotlike arrangement. His thought was that if the fire were contained in a slot of logs, the exposed area of coals would be greatly increased and the radiated heat could be beamed into the room (instead of the chimney) by the slot. Since the radiated heat would be produced more efficiently, the fuel would burn slower, with less open flame and better exposure of the coals to the room. The slot would even be partly self-controlling to provide a uniform horizontal distribution of radiation, because if the slot widened at some point, more heat would be radiated out of the slot from that point and the local temperature of the area would drop somewhat. Eventually the rest of the slot would widen to the same extent. Cranberg's grate, which is now patented, is available from the Texas Fireframe Company (P.O. Box 3435, Austin, Tex. 78764) in five sizes.

I arranged an experiment to measure the radiation patterns from the conventional grate and stacking pattern and from Cranberg's slot design (Texas Fireframe Model U-25, priced at $39.95 plus 10 percent for shipping in the U.S.). Lacking an infrared detector, I decided to measure the radiated heat with a simple arrangement of flasks containing water and thermometers. Directly in front of a fireplace I placed four flasks at various heights from the floor and in a vertical line. They were 250-milliliter Erlenmeyer flasks containing 200 milliliters of water. I put a Celsius thermometer in each flask, and then (to avoid losses from evaporation) I closed the top of each flask by stuffing the opening with plastic food wrap. Some of the infrared radiation emitted by a fire would be absorbed by the water in the flasks and would warm it. I could monitor the warming with the thermometers and thus have a rough idea of the vertical radiation pattern from a particular fire.

One of the problems with this method is that the warming of the water lags behind any rise in the intensity of the radiation from the fire. I was less concerned with how the radiation pattern varied with time, however, than with how it varied vertically. I therefore made the assumption that the general shape of the vertical distribution of radiation into the room could be roughly determined by monitoring the changing temperature of the water in the flasks.

I tried to choose logs of the same type and sizes for both fires. The sizes were determined by the recommendations in a publication Cranberg sent me: there should be one large log about six inches in diameter in the back of the slot, one or two logs of medium size on the top and two smaller logs on the bottom. Although my wood was all the same type, I did not know or find out what kind it was. Moreover, my effort to keep the sizes of the logs the same for both fires was at best an approximation, since logs are far from being standardized objects like machine parts. Still, I think my results were not critically dependent on the type or sizes of the logs. The amount of heat radiated into the room by a fire laid to Cranberg's design, however, can be greatly increased by using a bigger rear log so that the slot is wider.

Because I wanted to measure the radiation pattern I was determined not to monitor the air temperature in the room. The air temperature would vary vertically because warmer air rises. The air temperature would also depend on the size of the room and on its contents and so would be of little general value. Hence I determined the change in the temperature of each flask about every five or 10 minutes after I had lighted a fire. A slight cool breeze was blowing through the room from a door partly open to the outside throughout the experiments, which helped to keep the room temperature constant. I lighted both fires on the same evening to avoid possible variations in the experiment because of changes in the outside air temperature and hence the draft rate through the chimney. Some variation probably occurred anyway because the outside air became cooler.

I began with the conventional arrangement, monitoring the water temperatures for about an hour. Typical temperature changes are plotted in the illustration on page 142. Note that the radiation pattern peaked in intensity in the flask that was 84 centimeters from the floor, was almost zero in the top flask at a height of 101 centimeters and was below the peak value in the lower two flasks. Apparently the heat was radiated strongly upward but not much horizontally. Evidently the top flask received little radiation, partly because the overhang from the fireplace shielded it from the fire and partly because it presented a smaller cross-sectional area to the fireplace than the other flasks did. The overall radiation pattern from the conventional stacking of logs would seem to be directed upward. As Cranberg suspected, much of the radiation was being lost to the brick in the overhang and to the chimney.

I then replaced the conventional grate with the slot design, installed fresh logs in the slot arrangement and lighted the fire. I tried to keep the logs lying tightly against one another to avoid slits or holes in the slot arrangement. The patented grating is helpful in this respect because the arms holding the upper logs are adjustable in height, so that the upper logs can be positioned snugly against the rear log. The adjustable arms are also useful because the rate of combustion can be controlled by varying the height of the slot. The burning was slower with this arrangement, and flames appeared only on the small lower logs but were uniform across the length of the slot and required no rotation or stirring of the logs. The upper logs were partly charred on the surfaces facing the slot, and the one pressed against the rear log was glowing with red coals. The rear log was largely red coals inside the slot. Presumably this was a good design because little of the wood was being consumed in the relatively useless open flames. The coals necessary for good heat radiation were there instead.

The radiation pattern was again monitored for about an hour. This time the vertical profile appeared to peak at about floor level. As Cranberg had calculated, the pattern was largely determined by the slot directing the radiation into the room. Less radiation was directed upward to the higher flasks. Thus the overall pattern implies that little of the radiated heat was lost upward to the overhang or the chimney and that nearly all of it must have been coming out into the room.

The radiation pattern from the slot design is easily determined by hand. I moved my hand upward in front of the fire at floor level and then held it directly over the top logs. The heat was very noticeable in the first position and much less so in the second.

Cranberg's conception of the radiation pattern from his log holder is correct. You might want to experiment with the adjustment of the arms, the height of the slot and the length of the logs. You could also measure the radiation pattern and intensity against time for the two types of log stacking. Does the conventional pattern always produce radiation slower than the new design? How does the rate of production from the slot fire depend on the size of the rear log and thus on the height of the slot? (To do this experiment with reliable results you will have to standardize the logs and whatever technique you use to start the fire. Cranberg recommends starting with newspaper if the wood is seasoned and with kindling if it is green.)

You could replace the wood logs with the pressed-paper logs that are available commercially. (Similar logs of waxed paper are designed to burn by themselves.) Can you find an advantageous method of stacking the logs other than in Cranberg's arrangement? While you are at it you could also test the transmission properties of a glass or metal screen placed in front of the fire. The radiation pattern should not change much (although the screen will distort it to a certain extent), but you should find your water flasks warming somewhat more slowly.

Last December I described Haidinger's brushes (the hourglass figure you can see when you look into linearly polarized light) and various experiments you can do with the figure and a homemade quarter-wave plate. Part of the explanation for that series of experiments depended on the birefringence of your cornea, which I attributed to a preferred orientation of the collagen fibrils in the cornea. I have been corrected by Frederick A. Bettelheim of Adelphi University. According to research by him and by others, only 25 percent of the cornea's birefringence is due to such a preferred orientation of the fibrils; the other 75 percent results from the fact that these long, thin fibrils do not have the same index of refraction as the material in which they are embedded. The fibrils do lie parallel in a layer, but their orientation from layer to layer through the thickness of the cornea is almost random. Although the fibrils are birefringent and would contribute a much larger net birefringence to your vision if they were parallel throughout the thickness of the cornea, the random orientation from layer to layer diminishes that contribution.

Bibliography

BASIC MECHANISM IN FREE ABRASIVE GRINDING. Edward J. Saccocio in Applied Optics, Vol.-14, No. 11, pages A224-A227; November, 1975.

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