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Quote this post and reply to it Post#1 @ 12-28-02 , 03:36 AM


. There are infinite ways to cut an oval. Here I will show various ones with slopes adapted to suit diamond. Non-cutters may find it interesting; cutters may find it useful. Those who cut colored-stones can change the facet slopes using the slide rule provided in my recent thread "Changing Facet Slopes" at http://www.diamondring.com/forums/s...ead.php?t=23989
. This will lead to the "Perfect Oval Brilliant", which was submitted to Lapidary Journal in 1975, and which will illustrate the use of the special slide rules I promised a month ago for changing girdle length:width proportions without trial-and-error, such as stretching a round design into an oval one.
. For reference to the gem-cutting terms, see my recent thread "Girdle Scallops" at http://www.diamondring.com/forums/s...ead.php?t=23362 which had close-up photos of my faceting machine. I repeat one of those photos here for reference.
. I plan an illustrated gem-cutting sequence for the future, as I did in Raytech literature and some magazines of the late 70's. Some may recognize the illustrating style.

. If you use the same indexes and slopes to cut an oval, that you used to cut a round, you get an ugly-looking thing (illustration later). And now to the specific examples ...

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Oval with Std.Indexes & Const.Main Slope
Quote this post and reply to it Post#2 @ 12-28-02 , 04:18 AM


. Here is the simplest solution, which uses the same indexes as a round, = 32 equal spaces, and provides the same slope on all main facets. I show index degrees and 2 decimal places to keep the non-cutter purists happy, but index notches for the real cutters (who must also do their best to control 1 decimal place). I show 4:3 oval ratio as the extreme - I would not cut a longer oval = too much distortion.
. I have used Tolkowsky proportions = 40.75 mains at pavilion, 34.5 mains at crown, and 54% table width. I chose pavilion breaks 3/4 deep (75%) and crown breaks 2/3 high (= 2:1 kites; note that star radial % is useless definition on un-round stones).
. To maintain this uniform height/depth of break facets it is necessary to use a different slope for each break facet and star in a quadrant. I label the facets 'a-b-c-d-e' with breaks 'ab-bc-cd-de' between them. An oval has double symmetry, so the facets in one quadrant are repeated in the other three by mirror-image. There are no stars 'b' and 'd' on this pavilion (later - 'zircon' cut).
. Note that the end mains 'a' on the pavilion are almost non-existent. They add nothing to the beauty of the stone and trouble for the cutter (too sensitive to over-cutting), so I show the option of cutting with slightly deeper breaks 'ab' and 'bc'. This is like cutting a marquise = no end mains.
. Note that the table is very long - more than 54%, that the diagonal stars 'c' are distorted, and that the end stars 'b' are 'scrunched'.
. The broad side mains 'e' give a strong cross-reflection that gives a big 'bang-bang' on-off effect, like the 'old-miner', as the stone is tilted; I like that - a lot.
. Because the mains are all the same, we do not see the 'bow-tie' effect of many ovals and most marquise cuts. This, however, requires a ridge pavilion, rather than a point; it is worth it for the effect - less scintillation in the center but a big bang instead - with scintillation by the smaller facets at the ends.
. The bad thing is the girdle scallops, which range from 1.23% total depth at the ends to 3.49% at the sides. I make all these pics with 2.7% girdle between main points = 1.0% at the thin places on a round (see "Girdle Scallops" thread). If you look closely, you will see that they cross each other in this illustration, which is not real - they would actually form short straight knife-edges at these 'overlaps'.

Last edited by beryl : 12-28-02 at 04:57 AM.
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Oval with Special Indexes & Const. Main Slope
Quote this post and reply to it Post#3 @ 12-28-02 , 07:24 PM


. Here is a better solution than the previous one. It still uses constant main slopes but special indexes which are derived by 'stretching' a round brilliant in one direction; this is done by the first of the shape-change slide rules (to be discussed later).
. It looks a lot like the previous one. The table is the same length and the pavilion has a ridge but there is less distortion of the facets = less bunching-up of scintillation at the ends. It still has the big 'bang-bang' on-off reflection across the waist that I like so much.
. The breaks and stars have much less variation than in the other; they are almost the same as for a round stone, so the optics should be similar.
. The stars don't quite meet - there is a flat spot about 2 thousandths of an inch long at the top of mains 'c' (on a 1-ct stone). This is theoretical and not as bad as mis-matches on most stones. It is easily corrected by a little 'tweaking'.
. The total depth of girdle scallops varies only from 1.8 to 2.3%, which is much better than the first design. Oddly, the thinner part of the girdle is at the ends here, whereas it was at the sides before.
. It looks like this would be an excellent cut for diamand, where the crown and pavilion main facet slopes are so critical for best optics.
. But you have to use special indexes. You can do it by adjustment if your machine has a 'cheater', but its easier to have special index wheels made, which is no problem for a profitable cutting shop. I made my own with a plain disc and a knife-edge file, using the teeth of a standard wheel for reference (the 2-decimal place data I give here are absurd; my hand-filed wheel works fine).

Last edited by beryl : 12-28-02 at 07:33 PM.
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Girdle Stretch Index Converter
Quote this post and reply to it Post#4 @ 12-29-02 , 10:52 AM


. Here's how I got the index angles of the previous example:
. The formula for index angles of a stretched design is ...
... tan (new) = tan (old) x stretch ratio
In the preceding example, the index angle for main facet 'c' would have been 45 on the round stone. For a 4:3 oval therefore ...
... tan (new) = tan (45) x 1.333
... = (1) x 1.333 = 1.333 = tan (53.13)
... new index = 53.13 ... which you will see in that example.
. Some folks don't know how to do trigonometry, or are afraid to. For that purpose I made the following slide-rule back in '75, fancied-up here. This was on the opposite side of a companion slide-rule for changing facet slopes of the stretched design with the new indexes.
. The example I show in this Fig.4b is for a 5:4 stretch, so the answers are different from the present 4:3 example.
. Note that, with this you can also change from one ratio to another. That is, if you had workable data for a 6:5 cushion-cut and wanted to change it to a 4:3 cushion-cut, you could do it by lining-up 1.333 (4:3) with 1.2 (6:5) at the ratio scales (bottom) and reading the corresponding index changes on the upper scale (based on 96-tooth index wheel).
. I can post a clean copy if anybody wants it to cut out to make their own slide-rule. Print it on light card stock or glue this to card stock and put a pin, screw, or grommet in the middle so you can turn the inner scale on the outer one.

Last edited by beryl : 12-29-02 at 10:58 AM.
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The "Perfect Oval Brilliant"
Quote this post and reply to it Post#5 @ 12-29-02 , 09:22 PM


. The illustration below shows true stretching of a round brilliant into an oval. Everything grows 4:3 in one direction only. The pavilion stays as a point and the table retains its proportions = 54% lengthwise as well as crosswise. Note the red radial lines show the same relationship to the facets as in the round gem.
. There is no bunching of facets at the ands, and all of the scallops are the same depth as the round brilliant = 1.7% total!
. The facets toward the ends get longer but not higher or deeper, so their slopes decrease. This is not necessarily good. Years ago I called this the 'perfect oval brilliant' because of its geometric perfection. I cut a few and they were beautiful as colored stones, but in cutting colored stones one looks for pretty patterns rather than quantity of light return and fire.
. I think this would not be a good idea for diamond - note how much the main facet slopes 'a', 'b', and 'c' differ. The crown vs. pavilion combination of these slopes is very important in diamond, whose principal feature is light return. We all now know that you can vary the combination and maintain good appearance if the crown increases about 5 as the pavilion decreases 1. Here they both decrease together, so you will get significant variation in light return.
. I think the previous design, "Special Indexes with Constant Main Slopes" is the best design for diamond because it keeps the same main slopes and the breaks are nearly constant and similar to the round gem.

Last edited by beryl : 12-29-02 at 09:24 PM.
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Quote this post and reply to it Post#6 @ 12-29-02 , 09:44 PM


as an oval lover i am facinated, dumbstruck , but facinated. as a'wishywashy" as i have been about diamonds, i sure do always come back to the oval, i only wish i could find one that performs like a round on the white light scope. (oh yea and one that is reasonably priced)


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Re: The "Perfect Oval Brilliant"
Quote this post and reply to it Post#7 @ 12-29-02 , 10:44 PM


Quote:
Originally posted by beryl
I cut a few and they were beautiful as colored stones, but in cutting colored stones one looks for pretty patterns rather than quantity of light return and fire.

Did you mean you're looking for pretty patterns externally or reflected?

The reason I ask is that when we saw the Scott collection exhibit at the Bowers museum in Santa Ana a month or two ago, one of the stones that impressed me the most was a very large oval garnet, where sections of the pavilion facets appeared to open and close like flower petals as your view moved across the stone, both side to side as well as up and down.

Folks here get so worked up over static patterns and refracted light in diamonds, but I wanted to think this was the most precise display of cutting I've seen because of this very symmetrical but very dynamic effect.

With an "expensive" starting material like nice sapphire or ruby, it seems to me that as with diamond, weight retention is the primary goal, and this very important part of my enjoyment of the finished stone is not considered at all.

BTW Bruce, the posts are great...over my head, but I pick up a thing or two and it helps with my education .

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Quote this post and reply to it Post#8 @ 12-30-02 , 02:37 AM


teacups:
. I can't recall ever seeing an oval diamond.
. I don't know how one would perform on a FireScope or IdealScope, but I wouldn't use one, anyway, to decide if I liked it. My guess is that the 2nd one I showed - "Special Indexes & Constant Main Slopes" - would be best but that it would show a number of leakage paths because the ray reflections are not as well controlled as in a round.
. What do you mean by 'white light scope'?
. Cutters often try to bring ovals (and marquise) to a pointed pavilion. In so doing, there is a great difference between the slope of end mains 'a' and side mains 'e'. They try to correct this by cutting a deeper stone to reduce the slope of the end mains, with the result that they get too-steep side mains and the resultant 'bow-tie' dark area across the 'waist' caused by head reflection.

dogbert:
. Good to hear from a colored-stone lover in here. Is there a better forum? I see many good comments by you; thanks for this one. Thanks for the praise, also.
. I mean 'pretty patterns reflected internally'; I, too, like to roll a stone and watch the movie from within - totally different from just wearing it.
. What kind of garnet? Rhodolite or malia? Most garnet is too color-intense to show pretty internal reflection patterns, and hessonite masks them because of its 'roiled' interior. Can you get me any information about the cutting details of this stone?
. I think the large pink sapphire pendant I cut for my wife was a 'perfect oval zircon-cut' = the 'pob' with 8 extra facets at the pavilion (coming later in this thread if time permits); I will have to find it and see. It was magnificent - about 18x13mm. At that time I had a consignment of large boules of Linde synthetic material; I wonder if any of that is available today.

Last edited by beryl : 12-30-02 at 02:41 AM.
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Slide-Rule for Stretched Slopes - Ends
Quote this post and reply to it Post#9 @ 12-30-02 , 10:07 AM


. Here is the other slide-rule for stretching girdles. It is actually two in one. When I made them I put this on the opposite side from the previous one which was used above to determine the new indexes.
. Step 2 is getting the new slopes of end mains 'a', which exceed the scope of the other scales (Step 3). On the 'ratio' scale at lower left, turn the new ratio (1.25 = 5:4 in this example) to the 'old' one (1.00 = round) then go to the 'facet-slope' scale (top half of slide-rule) and find the new slope opposite the old one (34.5) at 'b'. In this 5:4 oval example it is 28.8; in the 4:3 oval of this thread, it would be 27.3 as listed on the gem diagram. This is for the crown; for the pavilion, the 40.75 slope becomes 34.6 for the 5:4 oval and 32.9 for the 4:3 oval.
. This can also be done by the following formula:
... tan (new) = tan (old) / R ... where R is the ratio.

. All of this, of course, can be done instantly and brainlessly via computer program but this does not require a computer or a calculator. It was significant in 1975, when I had only a slide rule and not even a calculator. A bit of obsolete history.

Last edited by beryl : 12-30-02 at 10:18 AM.
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Re: The "Perfect Oval Brilliant"
Quote this post and reply to it Post#10 @ 12-30-02 , 10:46 AM


Re: The "Perfect Oval Brilliant"

Bruce,
We use same parameterization of oval in our programs . But some cutters say what it is not good.

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Slide-Rule for Stretched Slopes - Other
Quote this post and reply to it Post#11 @ 12-30-02 , 11:11 AM


.
. Side mains 'e' do not change at all when the design is stretched.

. Step 3 is to determine the new slopes for the other facets = diagonal main 'c', stars 'b' & 'c', and breaks. This is done with the same slide-rule, as shown below in Fig.5b.
. Having determined the corresponding indexes from the first 'shape change' slide-rule in Fig.4b, align them on the scales on lower right of this slide-rule, then read the corresponding slopes on the upper scales.
. In the 5:4 oval example of these slide-rules, for diagonal main 'c', tooth #12 of the 96-tooth index wheel became 13.7 in Fig.4b (Step 1). Now setting these opposite each other, as at 'a', we see that the 34.5 slope on the round brilliant crown becomes 31.9, as at 'b', on the 5:4 oval; the 40.75 pavilion slope would become 37.9.
. For the 4:3 oval the index corresponding to 12 is 14.7. Aligning these as at 'a', the corresponding slopes, as at 'b', would be 31.3, 34.5, respectively, for the crown and pavilion of 34.5, 40.75, as listed in the previous 4:3 ratio illustration of 'perfect oval brilliant'.
. For each facet - 'b', 'c', 'd', and breaks - you must re-align corresponding indexes as at 'a' and read the corresponding slopes as at 'b'; you can't do more than one facet location (label) with each setting.

. Again, this could all be done nicely today with a computer. I know someone will point that out.

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'Perfect Oval Brilliant' not Suited to Diamond
Quote this post and reply to it Post#12 @ 12-30-02 , 11:36 AM


Sergey:
- and they are correct, for the reasons I cited above. But it makes a beautiful colored stone, where the beauty is in the color and pretty reflection patterns, rather than in the dazzling light return and fire which is the only beauty advantage of a colorless diamond.
. Colored-stones are far more interesting and fun; I much prefer them to diamonds for interest. In addition, the cutter has the problems of alignment and gem shape vs. crystal shape because of dichroism, as in corundum (sapphire , ruby), beryl (emerald, aquamarine, morganite, heliodor), tourmaline, iolite, etc. In some stones, notably topaz and spodumene (kunzite, hiddenite, triphane), easy cleavage adds to orientation problems.
. In the case of spodumene, both dichroism and cleavage problems combine to create a setting nighhtmare - the cleavage is perpendicular to the table = across the girdle edge. I know one jeweler who set a kunzite in rubber and bezel (collet) to avoid splitting it when setting with prongs. I have never successfully cut a spodumene and I would not want to try to set one. Worst of all - after all that - the kunzite fades if you display it in a sunny window!
. Garnets and CZ have terrible thermal conductivity and will crack by expansion if you are not careful while cutting them. This also happens if you put them to a buffing wheel, as many jewelers can sadly relate. Emerald will explode when heated because of the water in its inclusions, as non-gemologist jewelers can attest by sad experience.
. Some colored-stones,like diamond, have a grain which requires directional polishing; I have seen this on tourmaline. Some form a 'Beilby-layer' of harder non-crystalline form which is a nightmare - you must remove it and start over; this is most common in corundum.
. You must cut colored-stones to enjoy the full spectrum of gemology and cem-cutting; mathematics becomes academic compared to the practical problems and esthetic factors of their beauty. I have suggested this to Yuri before; it is also a fun hobby.
. Then you must make and repair jewelry with them to encounter these other problems. You must be a good gemologist to be a good jeweler. As a manufacturer, I am sure Garry knows that.
. My older son and I have even tasted another 'facet' of gemology. We live near the 3rd-best pegmatite area of the USA and spent many days picking the dumps of the old mica and beryl mines for various-colored beryls. In 1979 we found and uncovered the Reynolds mine - only a few miles from here - which yielded the finest aquamarine in the world in the 1800's (according to Bauer). That son became a fine gemologist and jeweler as a result of this activity, but now travels the world to buy fine stones much cheaper than I will cut them. As you know, Anton Vasiliev, a professional colored-stone cutter, also enjoys this hobby and sends interesting photos from high places occasionally.

Last edited by beryl : 12-30-02 at 12:15 PM.
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Re: Re: The "Perfect Oval Brilliant"
Quote this post and reply to it Post#13 @ 12-30-02 , 03:34 PM


Quote:
Originally posted by Serg
Re: The "Perfect Oval Brilliant"

We use same parameterization of oval in our programs . But some cutters say what it is not good.

. I interpreted this as meaning it was optically bad, which is the theme in which I replied.
. If it means that the facets did not meet properly, then I assume they did not have the right index information or did not know how to use it. I cut several stones with these data and the special index wheel I made, and it worked-out perfectly. Note that the angle from the center of the gem to the center of the facet (blue) is not the same as the index angle (red) - see illustration below.
. The stone in the faceter photos I put in DT recently is one of these (has been on the dop for 20 years!)
. I have had experiences with cutters who thought they understood but did not. For example, the beautiful pale blue sapphire I cut from studies with GemRay: we sent some poorly-cut stones to an 'expert' cutter in Bangkok to be recut to my recipe. They came back 'vanilla'; he had no idea what the numbers meant.

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Stretching the Cut Vertically
Quote this post and reply to it Post#14 @ 12-30-02 , 06:07 PM


.
. In the illustration below, I have taken the previous 'Perfect Oval Brilliant' and stretched it vertically* to achieve the original main slopes (34.5 crown, 40.75 pavilion) at the diagonal mains 'c' instead of at the side mains 'e'.
. This increases the slope of the end facets - which is good - but also increases the slope of the pavilion side mains to about 45 - the classic 'nailhead' by Cowing's terminology (a perfect retro-reflector as on the back of a car or bicycle). This stone would have a terrible 'bow tie' = dark shadow of viewer's head reflection across the waist of the stone.
This is a very bad idea for diamond but doesn't look as bad on a colored-stone.

* This was done using the simple slide-rule shown in "Changing Facet Slopes" 11-26-02 at http://www.diamondring.com/forums/s...ead.php?t=23989

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Quote this post and reply to it Post#15 @ 12-31-02 , 12:23 AM


Quote:
Originally posted by beryl
dogbert:
. Good to hear from a colored-stone lover in here. Is there a better forum? I see many good comments by you; thanks for this one. Thanks for the praise, also.
. I mean 'pretty patterns reflected internally'; I, too, like to roll a stone and watch the movie from within - totally different from just wearing it.
. What kind of garnet? Rhodolite or malia? Most garnet is too color-intense to show pretty internal reflection patterns, and hessonite masks them because of its 'roiled' interior. Can you get me any information about the cutting details of this stone?[/B]
Thanks . I'm not aware of any other forum, but I'm a colored stone newbie. I don't remember what kind of garnet this was...I just looked in the exhibit guidebook and it didn't give any details. The color was a pinkish red with more subtle orange overtones, medium tone. I'll see later if I can't get a decent digital photo from the book. Now that you mention it, most of the garnet I see in the jewelry stores is too dark to see much inside...definitely not the case with this.

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Quote this post and reply to it Post#16 @ 12-31-02 , 01:48 AM


Dogbert:
. Probably a rhodolite or a malia; both can be pale pink.
. Garnet is a continuum of bi-metal silicates, having a 2-valent and a 3-valent metal but which ones, and how much of each, varies a lot, and so garnet comes in every color but blue. Each of the various names cover a range of combinations, and there can be variations of color in each. There are almandite, andradite, pyrope, spessartite, hessonite, grossular, uvarovite, etc. Tsavorite is a pretty green variety of grossular. Rhodolite is a half-breed.
. There were some pretty pinks called 'Scottish' garnets but I know not what they were. I wrote "Pink Pinky Ring" in Rock & Gem about a pink gold ring I made with one.
. 'Malia' is Swahili for 'whore' because it also does not fit any of the classifications. It was discovered in Africa in the late '70's; I see the trade has since mis-named it 'malaya' garnet but it has no connection to Malaya (roll over in your grave, Fred Pough).
. Garnets grow in solid rock under heat and pressure, coming out of solid solution in their host (like rutile in star sapphire). As a result they are generally strained and prone to crack. A woman born under capricorn asked me to carve her a goat out of garnet; I declined, unless she would let me use ruby instead, which is much easier to work with, even though it is harder.
. The study of gemology leads to mineralogy, then to crystallography and then geology. It is a delightful trip.

Last edited by beryl : 12-31-02 at 01:54 AM.
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"Perfect Oval Zircon Cut"
Quote this post and reply to it Post#17 @ 12-31-02 , 03:26 AM


.
. As promised, here is the 'zircon cut' stretched mathematically in one direction. The crown is the same as the brilliant but there are now 'star' facets 'b' and 'd' on the pavilion.

. Not a good idea for diamond, but a beautiful cut for colored-stones, where pretty patterns are more important than the amount of light return.

Last edited by beryl : 12-31-02 at 03:27 AM.
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A Nice Touch
Quote this post and reply to it Post#18 @ 12-31-02 , 08:41 PM


.
. So far, the 4:3 oval design shown here that is best-suited to diamond appears to be the one of Dec 28 - "Special Indexes & Constant Main Slopes". Here's a simple modification of that design for those who don't like the chisel ridge at the pavilion - just 4 extra facets cut at indexes for star facet 'd' round the ridge and add a little 'action' at gem center.


. Happy New Year all! Its already New Year for Garry, Sergey, Yuri, Vladimir, Anton, and Iiro. I'll be making Z's when the change occurs here.

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Index Angles for Various Ratios
Quote this post and reply to it Post#19 @ 01-01-03 , 06:24 PM


. The dominant factor in all of the above was the need for special indexes to cut ovals.
. Here I tabulate the indexes for an 8-point brilliant for eight common ratios seen in oval settings (e.g. 4:3 = 8x6mm). The chart of this reply does angles, which mean something to a theorist or a shop making you a new index wheel, but nothing to a cutter.
. Note a few slight differences in the last decimal place: the angles I posted earlier are from my old records or measured from the pic's I just made with AutoCAD (4:3). My notes on this are dated 3/25/74, at which time I had only a slide rule. The data below are from a little PC program I wrote today to check. No problem - you can't make them or set them that accurately anyway. That's one beauty of slide rules - you can't get a lot of 'significant figures'. Don't worry about the 2nd decimal place in any of these data.

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Index Teeth for Various Ratios
Quote this post and reply to it Post#20 @ 01-01-03 , 06:42 PM


. And here are the data in terms of teeth on a 96-tooth index wheel. I could make a 'cheater' that would read to the 2nd decimal place, but a slight looseness or deflection in my machine, or use of a different part of the lap, would obviate this precision. So don't worry about the last digit - it just gives some folks a nice fuzzy feeling.
. Actually, I only made one wheel (5:4, I think) and used it for a range of ratios up to 18:13, and I made it with a file, so this is not as critical as it may seem.
. I would rarely cut an oval brilliant longer than 4:3, but I showed some longer ratios in these tables - be my guest.
. By the way, you could make a wheel with only one quadrant of notches, with two registration holes 180 apart and flip it over as well. Have fun!

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How to Make the Slide Rules
Quote this post and reply to it Post#21 @ 01-05-03 , 12:52 PM


. A cutter has written to ask how to make the slide-rules shown here (and in "Changing Facet Slopes"). Easy: just make two copies of illustration, glue them to card stock (such as poster-board), cut one to the borderline of the two scales, and assemble them to rotate, as illustrated below.
. You will want better-quality illustrations than I was able to transmit to DT. For that I can send you the AutoCAD-2000 .dwg files by e-mail, or some printed copies (5-inch diameter scale-dividing circle) by snail-mail (send SASE for 8x11 flat copy).
. For the Shape Change slide-rules I put the complete picture of each on opposite sides of the same card, then the inner scale of each on opposite sides = double-sided slide-rule. You get the new indexes on one side (Step 1) and the new slopes on the other (Steps 2 & 3). Or you can make two single slide-rules, as illustrated below, if you prefer.
. Perhaps slide-rules are not as common today as in my day; that was the best we had = our pocket computer. I even took a course on graphical computation, in which we learned to make slide rules, nomographs, and other good things (including how to generate approximate formulas for experimental data). I hope these things have not become lost sciences.
. A beauty of graphical computation is that it prevents you from getting a lot of digits beyond reality - as you will get from a calculator or non-limited computer printout. With the slide-rule you had to THINK about the answer because it did not tell you where the decimal point was; thinking has become a forgotten factor in calculation.
. The math of these is very simple and could be programmed on a programmable calculator, such as TI-59, which was available circa 1980. Perhaps there is something similar and smaller today. I will provide the formulas to anyone who wants them.

Last edited by beryl : 01-05-03 at 01:34 PM.
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'Perfect Oval Brilliant' Slopes
Quote this post and reply to it Post#22 @ 01-09-03 , 09:43 AM


. Here are the tabulated tangent ratios for stretching 8-point round brilliants into 'Perfect Oval Brilliants' with 8 common oval ratios.
. Multiply the tangent of the facet slope on the round stone by these numbers to get the tangents of the corresponding facet slopes on the oval.
Facets 'a','c','e' are calculated from the mains; facets 'b','d' from the stars; facets 'ab','bc','cd','de' from the breaks.
. The results for a 4:3 oval with specific proportions were already provided earlier in this thread; this will give you other ratios and proportions.
. This does not apply to cuts other than the 8-point round brilliant. If you are stretching other cuts, such as square, etc. you must use the slide-rules for Shape Change.
. In all cases, if you do not like the results, you can change slopes by aligning one with its chosen new value using the the Slope Change slide-rule (other thread).

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