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Thread: Complex Harmonics in swords

  1. #1
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    Complex Harmonics in swords

    In the Harmonic Balance- Introduction... post on this forum Angus Trim mentioned Demi-Nodes, and we promised to discus them in the future. The future is now, so to speak- here's an illustration:
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    Pardon me, but if I may ask...

    As I am wrapping my mind around your post above sir, I had a question arise in my mind...

    How might this concept of demi-nodes translate to, say, Japanese styled swords, where (as I undertand it) the weight of the tang itself is used as a pommel would be in other methods of manufacture?

    Or to restate... how does this idea work in swords without pommels? Yeah, that's better. Go with that, please!

    Lew
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    Good question- there are definately swords that appear to exhibit complex harmonics that have no pommel- notably my modern tactical swords like the Bladeart Departure and some others. I have noot observed this phenom in Katanas- most repros that I see don't even exhibit 'simple' harmonics (excepting Gus Trim's... well Duh...) I am currently hashing out a hypothesis as to how this can occur. Sorry for the delayed response- BLADE Show and all...
    Tinkerswords.com Fine knives, swords and daggers in the style of the European Middle Ages and Viking Era

    "Then, one night as my car was going backwards through a cornfield an ninety miles per hour, I had an epiphany..."

    Luke 22:36 Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.

  4. #4
    I'm sorry, but I have a small problem reading your graphs (especially the one on the left). You assume standing waves of cos form being formed in the sword ? what are your boundary coniditons ? It seems natural to use for boundary conditions - fixed point at the point of impact and fixed points at rivets that hold the tang ? Or is it habaki ? b.c. would seem to be the determining factor where the nodes will be located (btw is there are a reason why you choose these waves - the nodes, unless you describe the lowest spatial frequency mode will be in different positions for different modes ?).

    Do you mean on the second picture that in addition to a standing wave in the blade there is a mode excited in the tang
    (a Bessel or another cos mode in between of two rivets that hold the tang ?). So by additional demi-nodes you mean that oscillations in the blade pump the oscillations in the tang ?

    If this is correct, than not only the effectiveness of such pumping will depend on the location of rivets that hold the tang, but may be it would be a good idea to actually build an overdamped oscillator, that _very well_ tuned to the oscillations in the blade, but damps them rather than transfering them to the hand ? I think they do it with modern hammers.

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    boundary conditions

    Actually this discussion appears to be talking about the fundamental vibrational frequencies of the weapon itself. This means that the point of impact will be immaterial as it is simply a brief moment in time (otherwise you don't get blade ringing and the discussion is moot) and the impact itself is treated as nothing more than an energy input. The point of grip could be treated as a boundary condition but as the quality of this boundary is contingient upon the grip of the individual user at the time of resonance it is better to simply attempt to locate the point of grip at a node of the fundamental resonating frequency of the weapon and thus make the exact damping nature of the grip immaterial.

    So the boundary conditions are the boundaries where the sword ends, as well as any significant location where the fundamental frequency will change. It's like trying to model a tuning fork, but with a frequency lower than can be heard audibly. Rivets and junctions between blade, pomell and handle will indeed be boundary conditions however one needs to be carefull about treating them as absolute transition points. For example if you locate the rivets binding your tang to your grip at an anti-node of the complex structure you have to take into account that resonating will likely induce added stress on the contacts, leading to friction and a damping effect. As well as the eventual failure of the junction itself. I.E. if you attach it at the wrong point then it will eventually shake itself to pieces!

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    Qualifications

    On the off chance that some of you will read my recent posts here and wonder "Just who does this guy think he is?" "Has he ever made a sword?" "What makes him think he's qualified to spit out this technobabble?" or other similar questions I thought I would take a short minute to introduce myself.

    No I have never made a sword, and in fact I am fairly new to the study of longswords and other more historic types of swords.

    What I do have however, is a Ph.D. in Physics and a bit of practice at studying thermal noise, fundamental frequencies and harmonic resonances. If your curious enough to give it a look, my dissertation is here http://web1.pas.rochester.edu/~melis...ssertation.pdf and chapter 4 has the most discussion on this particular subject. Here's another link to a web page that I haven't updated in aeons http://www.pas.rochester.edu/~butler/

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    Originally posted by Michael Tinker Pearce
    Good question- there are definately swords that appear to exhibit complex harmonics that have no pommel- notably my modern tactical swords like the Bladeart Departure and some others. I have noot observed this phenom in Katanas- most repros that I see don't even exhibit 'simple' harmonics (excepting Gus Trim's... well Duh...) I am currently hashing out a hypothesis as to how this can occur. Sorry for the delayed response- BLADE Show and all...
    A couple of ideas on why a Katana might not appear to exhibit even simple harmonics. Note that these do assume that there is still a resonant frequency for the weapon or series of them depending upon the complexities of the handle. I think any claim countering this assumption would be sufficiently extraordinary as to require extraordinary proof before it can seriously be considered.

    1) Possibly the fundamental frequency is sufficiently low that the energy required to excite it to a visible level is difficult to achieve in normal testing circumstances.
    I personally would put this one at a very low probability.

    2) Those weapons tested without any observable resonance are constructed in such a way that there are multiple damping sources which will damp out the excitation prior to your ability to observe it. I think this is much more likely myself as any slop in the fitting of the tang to the handle falls into this category. If I might further expound upon my personal opinion I would say that this is an indication of a very poorly made weapon. Any excitation which is damped out in this manor must tranfer the energy of the vibration into heat. This will lead to micro heating and cooling of the materials involved with any usage and thus undo stress upon those materials, which will lead to premature wear and failure.

    If you're sufficiently curious I would recommend a couple of ways to investigate although I doubt either signal would be easy to pick out of the background noise.
    1) Mount the sword on a rigid mount (like an anvil). Place a microphone very near the blade and have it hooked up to an oscilloscope with trigger level set to capture the wave of interest and keep in on the screen long enough to evaluate the frequency. Then hit the sword with a rubber mallet. Repeat as needed using different mount locations to find the fundamental frequency of the weapon.

    2) Use an IR sensitive video camera to record the whole process and observe any locations which show an increase in infrared radiation (i.e. heat).

    Good luck!

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    Damping questions...

    I am constructing a broadsword which will wind up weighing around 45 pounds when complete...

    Yes, it's a monster, no it's not practical... please take it's size with a grain of salt. Or a bag. Whatever...

    The client wants this sword primarily for DragonCon and NekoCon and the like.

    My question is such: 45 pounds is not something to play with. If he decides to hit something solid, say a tree, it is likely he will not hit at the CP, but more likely will induce a large deformation in the blade which will travel as a wave to his hand, be potentially amplified by reflection and constructive interference and shatter his wrists.

    I intend to construct a guard for this beast using stainless steel sheet which I will braze into a box, capped with a half inch slab of mild steel that I intend to weld to the ricasso. I intend to fill this box with RTV silicone, as per tennis racquet vibration dampening devices that you snap into the strings...

    In terms of measuring vibration, however, you can clamp the sword and use a simple piezoelectric microphone/speaker element to detect a distinct AC signal. It's not going to pick up alot of room noise since the sword signal will swamp the snot out of it. Try it - put your voltmeter on AC, in the 100 mV -1V range, and look for spots with high or low voltage.

    you don't want to hold the piezo with your fingers - too soft a mount, use some vise grips or something else heavy, but don't clamp hard - you'll swamp the vibration with the DC squeeze of the pliers.

    One thing to think of is to simply glue the piezo down with something like elmer's or the like - it'll hold fast, but you can smack it off with a mallet or clean it up with some acetone later - then you can hook theinput up to a voltmeter that will let you measure the frequency... divide by the speed of sound in steel (should be high) and you'll get your wavelength. Yay. Scanning along the length would simply let you find the nodes with a relatively high degree of certainty. Another consideration is that the clamping method for the sword will create a step transition in wave-speed, and can shift the location of your nodes around in the blade, therefore a loose mount might be better, with the sword hanging from the tang/handle, or held in the hand with fluffy gloves.

    Rion
    Last edited by RionMotley; 10-31-2006 at 02:22 PM. Reason: Frequency counter comment...
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    Do you realize how BIG a 45lb sword will be? Not practical is an understatement.
    "Do not suffer yourselves to be wheedled out of your liberty by any pretences of politeness, delicacy or decency.
    These, as they are often used, are but three names for hypocrisy, chicanery, and cowardice.” John Adams, 1789

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    I feel way over my head even reading this thread, but it has made me ponder something. This may have little or no effect, but would the forging process of say a true nihonto/katana, being clay forged to achieve a different hardness on both the ha and mune have any effect? And if not, how about the curvature caused by this style of forging? Or, are these just irrelevant factors to the discussion at hand?

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    Skip,
    A properly treated and mounted sword isnt going to viberate all over the place.
    But for the 45lb sword discussion, yes, your question is out of place.
    Marc is talking about a SuperSized "SLO". And that has no place in this particular forum. IMHO. There is the FAntasy forum for such nonsense.
    "Do not suffer yourselves to be wheedled out of your liberty by any pretences of politeness, delicacy or decency.
    These, as they are often used, are but three names for hypocrisy, chicanery, and cowardice.” John Adams, 1789

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    Quote Originally Posted by Bill Butler View Post
    A couple of ideas on why a Katana might not appear to exhibit even simple harmonics. Note that these do assume that there is still a resonant frequency for the weapon or series of them depending upon the complexities of the handle. I think any claim countering this assumption would be sufficiently extraordinary as to require extraordinary proof before it can seriously be considered.

    1) Possibly the fundamental frequency is sufficiently low that the energy required to excite it to a visible level is difficult to achieve in normal testing circumstances.
    I personally would put this one at a very low probability.

    2) Those weapons tested without any observable resonance are constructed in such a way that there are multiple damping sources which will damp out the excitation prior to your ability to observe it. I think this is much more likely myself as any slop in the fitting of the tang to the handle falls into this category. If I might further expound upon my personal opinion I would say that this is an indication of a very poorly made weapon. Any excitation which is damped out in this manor must tranfer the energy of the vibration into heat. This will lead to micro heating and cooling of the materials involved with any usage and thus undo stress upon those materials, which will lead to premature wear and failure.

    If you're sufficiently curious I would recommend a couple of ways to investigate although I doubt either signal would be easy to pick out of the background noise.
    1) Mount the sword on a rigid mount (like an anvil). Place a microphone very near the blade and have it hooked up to an oscilloscope with trigger level set to capture the wave of interest and keep in on the screen long enough to evaluate the frequency. Then hit the sword with a rubber mallet. Repeat as needed using different mount locations to find the fundamental frequency of the weapon.

    2) Use an IR sensitive video camera to record the whole process and observe any locations which show an increase in infrared radiation (i.e. heat).

    Good luck!
    I guess I was thinking more along this post and not the 45lb'er. I would be interested to see such testing performed on say a nihonto vs. a a European styled blade. I am in no way a PHD, but it just seems with the change of variables caused by forging in this way (nihonto) there would be either benefits or drawbacks.

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    In fact the difference in construction methods seems to make no practical difference, though if you make fine enough measurments who knows? What actually matters with Katanas is simpler- and more complex. Most modern Katanas are of uniform thickness for their entire length. Most period katanas have a blade and tang that both exhibit distal taper in thickness that renders them thinner towards their tips. This dramatically affects the balance, handling and finished weight of the sword. And the Harmonics! The modern swords that aren't harmonically balanced are almost always the flat, untapered ones. So the first, most obvious answer to why some modern swords aren't Harmonically Balanced is simple- they aren't good swords. They are sharpened bars of metal that approximate the profile of a sword but not the details and correct geometry. On that note it needs to be said that not all antiques from Japan are good swords either- remember that then, as now, swords ran the gamut when it comes to quality- although a much higher percentage of the genuine item were 'good' than is true today, at least based
    on surviving examples. Another factor that complicates things with surviving Japanese swords that were used extensively- the sword that we see todat has been repolished, reworked and remounted often many times. The sword that we see today is not always an accurate reflection of the sword as it was when new. If any of the above operations were performed badly a sword that may originally have been 'good' may no longer be so.

    As for the 45 pound sword- I've deleted my original response as it was excessively bitchy- I'm quitting smoking today(10-01-06), sorry!

    Seriously- a 45 lb sword shaped object isn't a sword because no human being could weild it effectively, period and sorry! Nevertheless if you have undertaken this project you owe your best effort so I salute you for asking. I can't really give you an answer because a properly proportioned sword that weighs this much would be an inch thick at the base and nine feet long.

    I'm afraid that discussing the 45 lb sword doesn't belong here, but damned if I know where it does. Email or PM me and I'll see if I can help off-board, and don't be surprised if the questions are 'pruned' out of this thread by admin.
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    Michael,..

    ...I would neither be surprised or offended of my questions/comments were to be deleted/edited from this thread. This thread is clearly intended for those who are educated on the matter.
    I do understand your comments regarding "production" katana's. I have several and your points are 100% correct in regards to taper. I also have a select few katana's that are marginally more accurate in their construction and they do indeed taper at both the end of the blade and the tang.
    I guess my hope, seeings how I am a person who likes katanas more than other styles of swords, was that harmonics are a factor that was taken into consideration during the forging of "true" katanas. And this would lead to a superior weapon. I hold the smiths of these blades in very high regard, as the craft is centuries old, and great efforts are obvious in the amount of exacting detail to their craft.
    Anyways, I will continue to read, but post little here in the hopes I will learn. Sorry if my comments/questions are not to par with the content/context of this thread.
    And on a final note.... Good luck with your endeavor to quit smoking. I to am a smoker and understand full well the difficulty in quiting this nasty habit. Good for you and good luck.

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    Skip-

    I wasn't referring to your post at all but rather to the 45lb sword question! No worries, dude! I was just saying that the construction of Japanese swords, IE of different materials being forge-welded together does not seem to affect harmonics in any easily observable fashion. Also- many, many Katana exhibit good Node Location (Harmonic Balance,) But I haven't personally handled one that exhibits Complex Harmonic Balance. There are a LOT of kats that meet my definition of being a 'good' sword- but most of those are either antiques or cost considerably more than $300. OK, now I'm starting to ramble...

    On the issue at hand, I've noticed that responses on this thread are periodically 'pruned' and assume that admin or another moderator has been doing this every so often. It's very likely that in the near future this thread will be locked and the responses split off into another thread or threads.
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    I'm going to set up the piezoelectric vibration measurement device that I described, and probbably post some photos over the weekend... I have some radio shack piezo elements, and actually found some elements at www.sciplus.com for about three dollars per dozen. We'll see how it comes out... wish I had an O-scope though, but A/C volts with peak detection should work ok on my fluke DMM.

    Catch you guys soon, hopefully with some decent results. I think i'll just do the test on my stainless craptana.

    Rawr.

    Rion
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    Nodes of vibration in swords

    Interesting discussion!

    I wrote an article that was published in KNIVES '96 (DBI Books, edited by Ken Warner, ISBN 0873491742) that was entitled THE FUNCTIONAL CHARACTERISTICS OF SWORDS. Vibratory nodes exist in ANY blade, even small knives, curved or straight, dull or sharp, carbon or stainless. I like to use the referent of a baseball bat. If you've swatted a few balls then you know about the "sweet spot"... that perfect spot on any bat that sends the ball further and just feels great because there's no "jarring" vibration in the hand. Swords have that too. The loction of the nodes is scarcely affected by hand position. It is a factor of the design and construction of the blade. The ideal sword will have one of the nodes in the forward part of the handle where the controlling hand grips it. The second node will be somewhere out on the blade forward of the guard. The blade node defines the "sweet spot" which is the point on the blade where maximal energy can be transferred to the cut.

    It's not necessary to get involved with piezoelectric measurements, unless you're just an instrumentation junkie. Hold any sword in your hand with the point straight up and the hand in using position. Strike the butt end of the handle sharply with the heel of the other hand. If the handle is too short for that, strike the flat of the blade just forward of the guard. You should be able to see and feel the vibration in the blade. Move the hand until the felt vibration is minimized. That is the correct position of the controlling hand. The other node is the sweet spot. There are several ways of determining where the nodes will be in a finished sword. A heavy pommel is one way, but basic design parameters are a much more elegant way.

    In case you're wondering, yes I have made swords... some sixty of them... along with a couple thousand other blades. I have a webpage at http://www.shirepost.com/Cutlery.html that shows some photos and a list of my blades by serial number.

    Be well!
    Tom Maringer

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    Definitely an instrumentation junkie, and I have a few dozen piezo transducers lying around from a project I worked on a year ago, so I might as well put them to use.

    I am, however, a bit delayed on this project since my mom's service dog passed away wednesday as a result of multiple malignant lymphomas. I've had my hands full managing his care for the past couple of weeks.

    Once I get everything else caught up, probbably after exams in 2 weeks, I'll post some photos and such when I get it all worked out.
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    Please, can someone SIMPLY explain what are harmonics in a blade, is it good or bad to have them, and what they do to a blade? Thanks.
    Last edited by Sam Salvati; 11-28-2006 at 01:47 PM. Reason: gorsh
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    Blade Harmonics

    Quote Originally Posted by Sam Salvati View Post
    Please, can someone SIMPLY explain what are harmonics in a blade, is it good or bad to have them, and what they do to a blade? Thanks.
    Sam, take another look at the drawing that Michael Pearce attached in the very first post of this thread. The idea is that a blade is an oscillator that can vibrate in the primary mode with two nodes... in exactly the same way that a xylophone key vibrates. All blades have harmonics... it is neither good nor bad to have them... it's just a fact. The character of the harmonics... the period of the wave (determined by the stiffness of the blade and the distribution of mass along the blade) and the location of the two primary nodes (determined by an even more complex interplay of factors) will determine how effective the sword is in varous types of use. By "effective" I refer to the efficiency with which muscular energy can be transmitted to the target via the sword's edge, and how effectively that energy is used to cleave the target.

    Anytime you hit something with a sword some of the energy will go into oscillating the blade. But if the target is struck precisely on one node, and the hand is gripping precisely on the other... there is no opportunity for that energy to be absorbed in oscillation and it is ALL transferred to the target.

    If you know three things about a sword... the weight, the balance point, and the nodal points... you can know a LOT about it.
    Tom Maringer

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    Observing the stationary nodes in the direction perpendicular to the cutting direction can be done with the naked eye, but are we seeing the right thing?
    The nodes for vibration parallel to the cutting direction are too small to see but can be felt with a tapping test (with the hand or with instrumentation). With different blade profiles in each dimenstion (distal taper and profile taper can be completely different) one would not expect them to be the same, yet in complex shapes, energy can move from one node to another. Which node is the important one. Since blades are much more stiff in the cutting direction, and harmonics seem to be more critical when the geometry of the strike is slightly off, it might be the nodes in the transverse direction after all. Any thoughts?

    Mike
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  22. #22
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    Quote Originally Posted by Michael Stora View Post
    Observing the stationary nodes in the direction perpendicular to the cutting direction can be done with the naked eye, but are we seeing the right thing?
    The nodes for vibration parallel to the cutting direction are too small to see but can be felt with a tapping test (with the hand or with instrumentation). With different blade profiles in each dimenstion (distal taper and profile taper can be completely different) one would not expect them to be the same, yet in complex shapes, energy can move from one node to another. Which node is the important one. Since blades are much more stiff in the cutting direction, and harmonics seem to be more critical when the geometry of the strike is slightly off, it might be the nodes in the transverse direction after all. Any thoughts?

    Mike
    Hi Mike

    Its been my observation that in a properly balanced sword, the nodes are in the same position.........
    For Good or Ill......

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    Perpendicular nodes?

    Interesting question! I agree with Angus that the nodes APPEAR to be in the same place. I base this thought on experiments with a couple of dozen different swords. I would test by sight and feel for the transverse node... mark the node on the blade with a maker... then work the sword against a wooden target. When the the strike was right at the mark, there was no vibration in the sword, when off the mark, the vibration was noticeable. My assumption was that minor misalignment of the blade with the target would transfer some energy into the perpendicular plane... the transfer being greatest when off the node. But as Michael notes, the effective "thickness" and therefore the stiffness of the blade in the plane of the blade itself is very much greater, and it's theoretically possible that the nodes in that plane do NOT correspond perfectly with the nodes in the weaker plane. In my experience it's not noticeable, the nodes APPEAR to coincide, possibly because they are fairly close together and a target is not encountered at a discrete point but along some finite length of blade. If both nodes are closely associated it may make no practical difference. How far apart those perpendicular nodes may be is an interesting question though... are we talking centimeters or millimeters here? Perhaps the piezo-instrumentation that's been discussed can answer this question!
    Tom Maringer

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    For the two sets of nodes to coincide the blade's stiffness distributions would have to be very close on these two orthogonal planes. Not impossible but highly unlikely by chance, considering the time of developement for swords I would imagine that if the coincidence is desirable it has evolved in designs.

    Two standard ways to solve this, modal analyzer and FEM model, the latter is hampered by the problem of boundary condition definition. In a way standard structural enigineering but highly non-trivial nontheless.

    TLM

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    First, welcome Tom! Very good to see you here.

    For the gentlaman asking about basic harmonics as applied to swords look here if you have further questions- http://forums.swordforum.com/showthread.php?t=42946

    We can really make this as simple or complicated as we like. Empirical data suggests that the nodes are either located identically in both planes or are so close as makes no difference. I don't worry about it much- real-world performance is the bench-mark and the sword acts as if they are the same- good enough for me!

    That having been said torque-transfer is worth thinking about. The sword experiences resistance on the axis of the edge when cutting but is so rigid that this has little chance of expressing itself to a notable degree on a 'perfect' strike. If the strikes angle is slightly off however the resistance isn't entirely along the axis of the edge, which will cause the edge to twist slightly. This will tend to express itself as if the torque was being transmitted from the edge axis into the lateral axis where it's expression is more obvious. In other words the blade flexes side-to-side. An illustration of this is if an impenetrable, immovable object is struck hard with a swords edge (you should NEVER do this BTW!) and you hit with perfect alignment directly on the cop the sword will bounce off the target- and begin vibrating side-to-side! This is because it is easier for the blade to 'collapse' to the side, which defeats the rigidity of the edge axis and the torque of this is transfered from the edge axis to the lateral axis- thus the lateral vibration.
    Tinkerswords.com Fine knives, swords and daggers in the style of the European Middle Ages and Viking Era

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    Luke 22:36 Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.

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