FAQ's

Topics  

nibs
names on handles
numbers stamped on saw blade
letters stamped under handle
finish used on handles
applewood handles
medallions
transitional saws?
oddly-shaped saws
restoring a rusty saw
crosscut saws
butcher saws
Civil War items
1840's saws
post-1955 saws
Australian or Canadian saws
saw vises
replacement handles
Warrented Superior saws
1940 Special model
saws with features not listed in catalogs
appraisals
why some saw handles have wheat carving

Q. What is the purpose of the bump on the end of the saw blade?

nib

A. It's called a nib, and discussions about its purpose, or lack thereof, have taken on the qualities of theological debate. One side says the nib had no practical purpose after 1693 A.D., but it may have before that date. Another side says nibs have always been ornamental and nothing else. A third group says the nib had an absolute purpose when it was invented, but, beginning in the 18th century, no one remembered what that purpose was, and further, we cannot agree what that purpose was either, but here is my theory.... The reason for the nib debate is the same as that for arguments among biblical scholars: there were no security cameras to document the events as they took place, and all records were generated long after the principal actors were dead.

Disston and Sons published an explanation in their Lumberman Handbook stating:

The "Nib" near the end of a hand saw has no practical use whatever, it merely serves to break the straight line of the back of blade [sic] and is an ornamentation only.
Carpenters have used the nib to hold a string that ties a blade guard over the teeth (probably a "found" use for the nib, not its reason for being). Some have started a cut by notching the wood with the nib (saw teeth do a better job of that). Speculators have speculated that saw makers tested hardness of the steel on the nib. Some have said early handsaws had an auxiliary handle near the toe to guide the flexible saws and prevent them from bending. The nib is said by them to be a vestigial handle which had become ornamental. At last count there were 117 recorded reasons, uses, or causes for the saw nib. I have heard nearly all and am not particularly committed to any of them. Please do not email your pet theory about saw nibs unless it is really funny.

Q. very old 1920? marked $ 2.50 under the name - any idea what it could sell for today? thanks for your response.

A. No response. (I don't appraise tools.)

Q. Why is there an 8 stamped on the blade on the same side as the etching, toward the toothed edge, about halfway between the teeth and the handle, about an inch in. nib

A. The stamped number 8 is the number of tooth points per inch. The most popular crosscut handsaw was 8 ppi. 5.5 ppi was the most popular rip saw. The number of points per inch could range from four to twelve.

Q. Why is the big brass screw on the saw called a medallion?

A. When new collectors started using the internet to communicate about saws in the 1990's, most had never seen the patents that refer to that feature as a label screw. The name "medallion" caught hold, and it's become ingrained. For nearly 100 years, saw makers did not call it a medallion in writing, but didn't have much reason to mention them in advertising or catalogs either. The word "medallion" had some use before the age of the internet, however. It first appears in the 1932 Disston catalog, on the page featuring replacement screws. On a related note, the fasteners on saws made before 1876 -- split screws, as they have been called -- are referred to as spanner screws by the industries that use them. Split/spanner screws and label screw/medallion are valid names for their respective parts.

Q.What type of finish did Disston use on the handles?

A.The old saws I've tested for finish were all shellac. Disston never said in advertising what they used, but alcohol breaks it down. Starting in 1928 they used nitro-cellulose lacquer.

pointed toe

Q.All of the descriptions of D-23 saws refer to them having a point of one and three-quarters of an inch or more. My late great grandfather's D-23 does not have a blunt point. Instead, the saw narrows down to less than a third of an inch at the point.

A.Assuming your great grandfather was the original owner of the saw, he probably used it to earn a living. Your saw used to be almost two inches deep at the toe. All that steel was filed away as the saw was sharpened regularly. It was normal practice for busy carpenters to have their saws sharpened weekly. In the early 20th century, some large crews had a man whose job was to sharpen the saws on-site.

docked toe

Q.Have you ever seen this model Disston saw? You don't show one with this shape.

A.You have a standard carpenter's handsaw that has been shortened, most likely because the blade was kinked or broken. The damage was lopped off and this is what remains. Disston etches or name brand stamps were normally located centered along the length of the saw plate. If your saw has an etch near the toe end of the blade, it's been docked like a Doberman's tail.

 

 

  dolphin saw

Q. Is this a special kind of curved ship point saw? I can't find another like it online. Is it rare?

A. The misshapen D-8 saw was filed improperly by its owner. That shape would not be effective for sawing. Complete saw filing includes jointing the teeth before sharpening by running a mill file down the length of the toothline to make the teeth all the same height. This took a lot of effort to make it look like a porpoise.

 

wildly misshapen saw plate

Q. What model is my saw? It doesn't look like others on your site. Is it rare?

A. It looks like a D-20 from just before the First World War. Not rare, but it's been re-shaped along the saw back, near the toe, probably to remove damage. It's been filed so many times that the toothline is higher than bottom of the handle. If the saw were still being used at the same rate, eventually it would look like a keyhole saw or a toothpick. Clearly this saw was valued by the owner, and it got maximum use.

Q. Wondering if you could please give me any information on a saw I found in Auckland New Zealand with Toronto Canada etched on the blade.

A. Disston had a factory in Toronto from 1910 until at least the 1950's. This allowed Disston to sell in the British Commonwealth without paying tariffs. The saws were the same models as the Philadelphia saws, though the handles may have been sourced with Canadian wood. Disston also had a factory in Australia which opened in Sydney in 1926, probably closing in the 1960's.

Canadian Disston etch Canadian medallion

Q. Did Disston & Son's make a one-man crosscut saw for cutting logs? My saw's blade is 42 inches long, and it has a handle shaped like an oven mitt. Etched on the blade is:


GREAT AMERICAN 1879
TAKING OUT THIS SAW DAY IN DAY OUT
WE CHALLENGE THE WORLD TO PRODUCE ITS EQUAL
CAST STEEL WARRANTED
[and the Disston symbol]

A. Your saw is a crosscut saw for felling small trees or bucking logs for firewood. They made probably a dozen models from 3' to 5' in length. They made them as well as two-man saws. They sold from the earliest days of the company until the 1950's. Tooth styles varied depending on what was going to be cut. Great American is the name of the tooth pattern. There were over a dozen different tooth patterns for crosscut saws before the advent of gasoline chainsaws.

Q. I have a Disston and Sons D-27 saw. You don't feature it on your website. The handle is rather odd, having neither top nor bottom horns, and completely lacking any ornamentation whatsoever.

A. The D-27 is a pruning saw, designed to cut tree branches. The reason it's not on the website is simply because the "Institute" concentrates on handsaws and backsaws for carpentry and woodworking. Tree saws are a subject of study that would be well-served with its own website, and it's not my area of specialty. D-27 Pruning Saw

Q.Can you include information on some of the other Disston handsaws - like the 554?

A. I'm guessing the 554 is the one-man crosscut saw featured in the 1932 catalog. I chose to focus the Institute website on carpenter's and woodworker's handsaws and back saws because that was my area of experience. I've been saying for over 15 years that long saws should have a website of their own, set up by someone who knows more about them than I do, but it's never happened. I've come to know more about them by answering emails from people who ask about their crosscut saws, but I wouldn't be a very good host for a website because I own only two long saws -- a Keystone one-man saw and a two-man of unknown manufacture. They are so bulky, I wouldn't want to own a pile of them.

Q. I have a saw that looks like a really large hacksaw, labeled Disston and Sons, USA. Overall length is 29 inches. Saw blade length is 24 inches and the blade is 1 inch wide.

butcher's saw A. The meat saw was manufactured by Disston from the 1850's until 1955. The earliest ones are labeled H&C Disston. Charles Disston was Henry's brother. A butchering saw is a commonly-found tool. They regularly get labeled Civil War-era surgeon's amputation saws on Ebay. Real surgical saws are not common, and they usually had a back like a dovetail saw, often with a dowel-shaped handle. Butchers' saws were not intended or supplied for surgery on a human. The sale of an old item is often helped with a good story. Not every tiara was worn by a queen, most guns never killed anyone, and that saddle probably was not made for a unicorn.

rare civil war vet saw nutz Q.What do you think of this?
Description (revised)
HERE ARE 2 BRASS MEDALLION; 1 PHOENIX BRASS MEDALLION AND 1 H. DISSTON AND SONS PHILADA JUSTICE SCALES BRASS MEDALLION; BOTH WERE FOUND ON A CIVIL WAR SITE. THESE MEDALLIONS ARE PROBABLY FROM SAWS THAT WERE USED BY SOLDIERS' AFTER THE CIVIL WAR THANKS FOR LOOKING! immage 600-c1

A. Any ebay auction for a Disston saw item with "Civil War" in the description is bound to be misleading.

Q. My saw has an etch with the words "Nineteen-Forty Special". The blade is 26" and overall the saw is 29 1/2". The handle has 5 bolts including the medallion, and there are 8 ppi. I did not see anything about this saw on your website and was wondering if you could tell me anything about it.

1940 Special etch

A. The 1940 Special is here. There is not much to explain, the etch says it all. The handle has a dark orange lacquer finish, so I can say only that the handle is an unidentified hardwood, most likely beech. As you will see if you scroll up to read the article on that page, the company put the saw out to coincide with a planned celebration to mark the centennial of the company, but a strike put a damper on the whole affair.

Q. How rare are Disston saws from 1840's and 1850's? Would you say one comes to sell often or every few years or a decade?

A. Most saws identified in Ebay auction listings as 1840's manufacture were actually made in the 1850's. In 1849 Henry Disston built a factory that initially employed 50-65 men, depending on which source you read. Before that he was running a two-man shop with one employee he had trained. Anything made before 1850 is rare, with less than one example per month showing up on Ebay, by my estimate. When a one-off example of something Disston was trying out shows up on Ebay, that saw might fetch $5000, provided bidders believe what they are seeing. A No. 7 saw from that time may go for several hundred, depending on condition. Some of those are the No. 7's that have the "flying eagle" medallion.

Saws made 1850-1860 are not common, but hardly a week goes by that at least three or four complete examples are not available on Ebay. Production figures are sketchy, but the Lumberman's Handbook that Disston published in 1907 says production was "but a few saws" in 1840, "dozens per day" in 1850, and "hundreds of dozens per week" in 1860. You could take that to mean by 1860 production was 50 or 100 times what it was when Disston was working with only one apprentice in the 1840's.

It's not a surprise that 50:1 is probably the ratio of 1850's saws to 1840's saws on Ebay.

Q. I have not seen this item before. It is an unusual vise, clearly marked Henry Disston and Sons.

No 1 vise No. 2 vise A. You have what is called a saw vise. It was a common tool, used to hold saws for sharpening. The C-clamp attaches the vise to a table or bench top. The No. 2 pivots forward and back, and the No. 1 does that as well as swing left or right on a ball joint. Both are about 9 or 9 1/2 inches wide.
   Other manufacturers made these as well, some being a foot wide. The wider the vise, the fewer times you need to move the saw as you progress with the tooth filing. As antiques they generally sell for less than the cost of shipping them, although a few dealers try to get top dollar for them. The one I use is a Wentworth pattern with an 1870 patent date. That cost me $10. I have another no-name that is similar to the Disston No. 2 in design, for which I paid a couple of dollars. I think it's steel instead of cast iron, and it's painted with enamel, probably of much later manufacture. Most cast iron tools were jappanned.

applewood Q. Why was applewood used for the saw handles?

A. The reason American saw makers used applewood is that it is much denser and attractive than American beech. Beech was used, but it is not as fine-grained as European beech, so it may not have appealed to English saw makers when they came to the United States, including the Johnson brothers who trained Henry Disston. Apple produced nicer handles than American beech. Traditionally, beech was used for tool handles, bent wood applications, and as a secondary wood in furniture. Today we use American beech mostly to make shipping pallets, flavor Budweiser beer, and smoke meat.

Apple trees we are familiar with today are drawf varieties, not the big, native trees that were grown in earlier times. Applewood was plentiful in Pennsylvania, New York, and New England, where the saw makers were located. Blanks for handles only needed to be about a foot long and an inch thick. This would get you two handles if laid out the right way. Farmers with trees to cut could supply plenty of them to the factory. This was the most logical source for apple. This photo from a 1917 Disston Crucible periodical article shows some of the applewood that was used at the Disston factory. The logs are at least two feet in diameter, and were brought in by railcar. For some reason Disston stopped using apple around 1945. It must have been a supply issue related to changing methods in apple farming.

Follow this link to read more about the harvesting of applewood that was used in saw handles.

Q. Do you know of a place that sells replacement handles for my saw?

A. No one sells new Disston handles. Parts for saws come from other saws, like one that's badly rusted but with a good handle, for example. Watch flea markets, auctions, or ebay to see if something comes up.

Q. I am just getting into the collecting of Disston saws. My concern is what is a safe way to clean the rusted and stained saws I have. I don't want to endanger any of the original Disston logo/label on a saw, what is safe to use. Also, what is the best way to clean the Disston emblem on the handle?

A. The important thing to do is use a sanding block if there is rust to be removed. Holding an abrasive in your hand, whether sandpaper, steel wool, a rag with rubbing compound, or whatever you choose, will erode the steel unevenly and you are likely to wear away the etch.
  Heavy dark rust I remove with 320-grit wet/dry sandpaper, followed by 600-grit. Light rust, just 600. Go very slowly and gently over the etch. If the handle is off the blade, I use water. If not, I'll use mineral oil (messy). If there is just a haze of rust from sitting in storage, I use 0000 steel wool and Johnson or Butcher's wax. Let it dry and rub out with a cloth.
  If the rust is deeper than the etch, the etch will disappear with the rust. You can't help it when it gets to that point.
  If your saw was made before 1890, be careful with the saw nuts. It's probably best not to try to remove them. The shaft of a screw on these early saws is thinner than on later saws, so the brass is easy to strip or snap, and the nuts won't go back on. You may want to be cautious, leave the handle on the saw, and clean the blade where it shows.
  Go easy with the Brasso. If a saw is over 100 years old, it shouldn't look new, and the brass does not need to be bright and shiny like a commemorative proof. I understand the tool not being dirty, but if you've ever seen an over-eager antique dealer's restoration of a tool, you'll know what too-clean looks like. The item no longer has any character or appearance of its age.
  There are many online videos showing people getting rust off a saw. You can watch them and decide whether my rather conservative approach suits you or not.

Q. Is it likely Disston did not change their designs and saw details all at once, but (like Stanley bench planes) would use up "old" parts and gradually introduce new parts into production resulting in "transition" saws? For example, I have a Disston backsaw with what appears to be a post 1918 small V-notch handle but the medallion is the 1896-1917 model. Of course it's possible someone changed the medallion or handle, but everything looks original.

A. Disston absolutely phased in parts while using up existing stocks. The clearest example of that is the many saws that exist with one son etches and two son medallions. The dates given to medallions or "label screws" are not exact, but their appearance on certain saws that come or go from a dated catalog (or that reflect changes in the name of the company) narrowed the dates fairly reliably. The only time sweeping changes to the design of all handsaws in the line happened at once was Aug. 1, 1928, when all models got a D-number, nibs were discontinued, and all saws either looked generally like a D-8 or a D-23. Interestingly, despite the thoroughly-planned design changes in 1928, the medallion design remained the same as it had since 1917, and didn't change for about another 12 years, with the PHILA abbreviation.

Q. What does the "X" stamped on the blade under the handle of a No. 12 handsaw mean?

A. There has been interest among collectors in the meaning of the initials stamped on the blades under the handle. The only reason to stamp the blade during production was for the purpose of identifying some information about the steel during the early stages of making the saw, when there would be nothing else on the blade to give that information. Disston wouldn't want to roll high-grade steel into a saw plate and then finish the saw with a No. 7 handle and etch, and sell it at the No. 7's lower price. The stamps prevented that from happening. The practice started in the early days of Disston's manufacturing.
   What does X mean? It is short for EXtra Refined London Spring Steel. All the No. 12 saws I've seen disassembled have that stamp. Similarly, CS on a No. 7 handsaw is cast steel.
   I've seen plenty of saws with the stamp HD under the handle. It doesn't mean Henry Disston made it himself, obviously. HD stamps are on Disston-brand saws. Other brands that were made in the factory, but not etched "Disston," don't have the HD stamp. The stamps would identify the grade of a batch of steel or act as a brand identification, the same way stamps have that role in steel production today. It told the saw makers something they needed to know during the manufacturing process.
   Honestly, I've never spent a lot of time studying those stamps because I can identify the age, grade of steel, and model number by looking at the rest of the saw.

DIS Q. I have a Henry Disston D-8 For Beauty, Finish, and Utility, this Saw cannot be Excelled. It's better than the one on your webpage. I can send you a photo if interested.

A. It's a graphic, not an accurate rendering of my saw.

Warranted Superior Q. Was "Warranted Superior" a Disston brand?

A. Many saw makers going back to early 19th century England made medallions with the Warranted Superior (WS) label. It pre-dates Henry Disston (1819-1878) by at least a generation, possibly more. Use of the phrase is not limited to saws. A quick online search shows it was used in advertising for manufactured goods such as shoes and Remington pistols. Warranted and guaranteed have the same meaning, which is the maker's word that his product is superior. The claim is only as good as the word of the maker, if you think about it.
   Most English WS medallions have a crown and most American ones have an eagle. Later Disston-made WS medallions have the words "Warranted Superior," a circle of dots, stars at the three and nine o'clock positions, and appear with or without an eagle. Some feature a keystone instead of the eagle. The illustration of replacement medallions in the Disston 1906 catalog shows an eagle, the 1911 catalog has a keystone, and illustrations in the 1914, 1918, and 1923 catalogs feature a blank space in the center of the medallion. None are stamped with the name "Disston." Later medallions on some of the Keystone-brand saws (1935-1954) have eagles. An example of this is shown, left.
   Most of the larger American manufacturers made saws with both branded medallions and WS versions. The purpose would have been to differentiate between the products on which they put their name and lower-priced tools on which they chose not to put their brand name. The irony is that, in America, the Warranted Superior label often was put on the companies' inferior products. Many top-grade English saws have WS medallions while others have brand-name medallions.
   When you find an American WS saw, there may be a slightly less than 50% chance that it was made by Disston. Disston had a very large portion of the market, but it was not a monopoly. Atkins, Bishop, Jennings, Woodrough & McParlin, and Simonds (1900-1926) were a few of the large saw manufacturers that made saws with some form of a WS medallion with an eagle. Atkins' secondary line was actually labeled "Phoenix Warranted."

1955-1990 medallion




Q. I have a Disston saw with a medallion not shown on your website. It has a pattern of circles around the keystone. When was it made?

A. Ford You have an example of a Disston saw made after the family sold their corporation to HK Porter in 1955. The quality of the saws spiraled into a low state as the company tried to cut costs and the market for handsaws dried up quickly. Why aren't these saws featured on the Disstonian Institute website? Imagine the enthusiam a collector and researcher of Model A Fords would have for a 1978 Ford Fairmont.

Q. I have a 26" D-8 saw that is 12 points per inch and is marked with a 12 on the blade. The medallion shows that the saw was made between 1917 and 1942. You don't list any 12 point saws in that length. What gives?

A. Most of the "catalogs" quoted on the saw pages are actually product guides for retail customers, entitled "The Disston Saw, Tool, and File Manual." These were updated annually from about 1919 until 1955. Prior to that, there was a publication called "The Saw: How to Use It; How to Keep It in Order," which served the same purpose, to guide retail buyers in the purchase and use of Disston products. That publication goes back to the 1880's.
  Another source for the information is dealer catalogs, which were much more specific in their information, but, unfortuanately, are not as easy to find.
  More to the point, the retail buyer's guides don't list every saw that was made. They give a general idea of what was sold, but sometimes the saw range grows bigger one year and gets smaller the next. So the information derived from the guides may have some omissions or inaccuracies.
   Also custom orders were possible. If a customer wanted a 12 point crosscut, a 4 point rip saw, or some other saw that was not in stock, he (or she) could ask the hardware dealer to special-order it.

Uppert

 

 

  Q. My Disston saw is unusual in that it has a brass plate on the bottom, of the handle and is stamped "Uppert" in the wood. You don't feature it on your website. Is it a special model? Patent

A. The brass is a repair to the handle after it was broken. As for the name, Mr. Uppert didn't want anyone to mistake his saw for their own so he carved his name in the handle. Disston didn't stamp handles except for a brief time in the late 1870's and early 1880's when they put patent dates on the handles of some saws. In the case of the handle on the left, HAAS was the owner, and from what I hear, you didn't want to get caught using his tools.

Q. In your FAQ section you show a photo of a saw handle w/ the name "Haas" carved in it. My mother's maiden name was Haas. Do you have any other details about that saw & it's owner that you could share with me?

A. I'm sorry, but I don't have any information on where the saw came from or where it is now. The photo was forwarded to me by an individual who was selling the saw on ebay several years ago.

Q. My saw has the number "9584" stamped on the reverse side of the handle. Would that mean that it was the 9584th one produced?

A. Disston saws weren't given serial numbers. That was stamped by the owner at some point to identify his saw on a job site or otherwise discourage someone else from taking it. Maybe 9584 was a telephone number. About half of the old saws I've seen were somehow marked by the owner. After WWII some guys started putting their Social Security or drivers' license numbers on tools. I wouldn't recommend doing that now.

Q. Why is your website so hard to read on my phone?

A. It's old-school bare-bones HTML, from the days when everyone used a desktop or laptop, and I laid out pages to look like a magazine.

wheat carving

The best question ever asked of the Institute:

Q. I'm an old hardware guy, literally. I grew up in a hardware store that my father owned for nearly 25 years. He sold it in the early seventies. My earlier years with Disston goes back to [talking with salesmen], and that is a long time ago.

Reason for my email is really simple. There are still a few of the old Disston sales people that have memories of more than catalogs. Hence the reason for the "wheat handle" design question. Obviously rosewood, apple, maple or even bakelite have their signatures on quality, the wheat represents teeth, pitch, which is never discussed. All these collectors really have no idea there is, or was, a meaning for that design. I know the medallion and etching in the blade is important but thought you would like to go back to work and find the key. [Edited of personal details and names.]

A. Your email inspired some time of thought. Several years ago I read an online comment on a tool collectors' website, making a claim similar to yours about the symbolism of the wheat carving. It sat with me because, as in your email, the author didn't elaborate or provide any printed source of his information. Despite that, I wanted to know if there is something to that claim, and if so, how deep did the symbolism go?

Was it simply a folk art chip carving motif that was easy to reproduce? Disston's No. 12 saw, first sold in 1865 appears to be the first commercially-produced handsaw with a carved handle. Could it be only an embellishment to make the saw more attractive without any thought given to symbolism? Sure it could.

Was the symbolism the rebuilding of cities to bring back the livelihood and strength of the restored nation at the close of the Civil War? Maybe.

Was it religious symbolism with reference to the Lord's Prayer?

Or maybe it's a visual comparison of saw teeth to grains of wheat on the stalk. The resemblance is remarkable, and it makes perfect sense to point it out if you are a tool salesman. The image of the rows of wheat kernels I saw when looking on Google the other night has me convinced what you wrote to me is true: wheat looks like saw teeth. I'll go one further: The wheat carving points out to us that saw teeth are as regulated and basic to man's progress in a civilization as the grains of wheat that go into our daily bread.

The question now is the same one I had when I read the claim about the wheat carving several years ago. Why is there no published reference to the meaning of the carving? Disston put all sorts of references in advertising to their company's early history, their innovation, and their place in the advancement of technology. Disston even published a book in 1916 called The Saw in History, the first page of which gives examples from nature that may have inspired the first saws made by man. It lists the snout of a sawfish, the jawbones of other fish and serpents, and the tail of a wasp as candidates. No mention of wheat, which means it was not in the mind of the writer hired by Disston to assemble into a book the fifteen pages of research someone in the company had done, combined with fifty pages of saws from their then-current merchandise line.

Was "wheat equals saw teeth" the intended message Disston had for the buyer in 1865, or did the craftsman who carved the first embellished Disston handle use a design he knew would be practical for mass production by a team of workers? The latter would mean the symbolism was pointed out later by a clever salesman. If it were the former, then someone in the room had the creative inspiration of a poet, because this symbolism had never been used on the handle of a saw, nor had it been used in literature. I've looked, but there's no reference to wheat and saws anywhere, and it's worthy of Shakespeare.

Where did you learn the wheat carving is a symbol for saw teeth? There is nothing out there. The topic got my attention when I first read it years ago, but your email prompted me to look more, and the answer is elusive.

(The reader who sent this question didn't actually ask a question, instead he suggested I go back to work and "find the key." I responded with the above reply, but he didn't write back, and I never found out where he had heard about the wheat symbolism. I assume it was from the salesmen he named in his email.)

Like the nib topic, the significance of wheat carving could lead collectors to take sides. Unlike the nib, the carving actually has an aesthetic quality and improves the appearance of the saw. Its beauty is an end in itself, and the carving doesn't necessarily have a symbolic message. There's no reason, however, we can't consider the analogy between wheat kernels and saw teeth.

 


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