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Presents, a Life with a Plan. My name is Karen Anastasia Placek, I am the author of this Google Blog. This is the story of my journey, a quest to understanding more than myself. The title of my first blog delivered more than a million views!! The title is its work as "The Secret of the Universe is Choice!; know decision" will be the next global slogan. Placed on T-shirts, Jackets, Sweatshirts, it really doesn't matter, 'cause a picture with my slogan is worth more than a thousand words, it's worth??.......Know Conversation!!!

Tuesday, April 14, 2026

Title: iMMEDIATE ATTENTION TO THE 2025 State of Indian Nations Address

 


I made the word Sky equate word Door for the American Indian in Cantore Arithmetic!!  

Cantore Arithmetic is able to state word Earth[see NASA] equated word door[Door[DOOR]], word door equated word window[Window[WINDOW]], word window[Window] equated word sky as word door[Door[DOOR] equated word at before word available equated.  Words, So, word Slide!!

Now word slide is not word Slide until word Verse equates word Slide.  So, I placed a part of a Post to show the word importance of the way of Slide, and, the remainder of the Post is on this Post just beneath the other Blog Posts listing words the way of slide from the Blog The Secret Of The Universe Is Choice 'The Continue’ America Set Evolution Types!!


You searched for

"SLIDE" in the KJV Bible



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Psalms 37:31chapter context similar meaning copy save
The law of his God is in his heart; none of his steps shall slide.


Psalms 26:1chapter context similar meaning copy save
(A Psalm of David.) Judge me, O LORD; for I have walked in mine integrity: I have trusted also in the LORD; therefore I shall not slide.


Deuteronomy 32:35chapter context similar meaning copy save
To me belongeth vengeance, and recompence; their foot shall slide in due time: for the day of their calamity is at hand, and the things that shall come upon them make haste.



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Wednesday, July 2, 2014

Public Informational Postings Know Contact



Ayes!!, to the frosty mourn of the Root Beer cure of that chilly slide of a spoon in stirs the pear of blamage,
the grit of the fruit bold fares as the proof that food cares set the meeting test at the dining table of the Hall,
is it fabled or the roast that is still moving on the plates of listing over cooked Veg. as the Salty Prim Pepper.

Ask the wailing members as the drop in the bucketed educational tripped on the Upper Lip stuck in framed,
a Caste in the Proper dialect for sewn the Accent to a Show of Directional Spinal Taps in the Future past,
a sordid backwards defense in an offensive play to regarding the Same in Exact to the Covering up of ACT.

Trim the sit with lots of 'It' the Rack to the Basic primal Fear of Repeating Lives in Same the Sinking feel,
around and around and around incarnate to the Thought of a Universal Cheer as the Base Idea of Binning,
to waste a single 'bout with know same mistake in a Compass of the Take I hear the Echo of Stonehenge`d!!

That Way my Lovely deer in the Light calling the Vocal in bead the Knight Asked knot the Quest Tonned,
Confucius Set Inn back at the Ancient Tribal Review of Evolving the Style in the Wall their's Aged Gate,
the gentile Read as the Thrifty deads place ist the Finish Lined in the Ribbon of the Yellow Ponds Taste!!

A Golden Scrub with Platinum craved a Vase by no Mistake a the Mold of the Crockery Trades Lauded,
lacing the string to the tightly knit theme producing the Wares in Advance of the Shared in the Tie of rots,
a body beating to the rhythm of going to the Courts of Life while in the Left Handed turns for Real it burns.

Drop Life 'It's A Pick`Up Called Sea Floats or The Porcelain Bus either pays for the Ticket to Ride,
                                                                                                        back on over to the other side,
           it's a Pirate, it's a Plank, it's a Dive, it's A Board,Know it's a Site & It's JUST CALLED Life.

Modus operandi  

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Never In The Face Of Breeds Cuddled



From Top too Bottom the Switch is in the Actual of the Trust in the Act of the Guest in the Treads of spill,
one to the detail and a couple in the joint to make the elbow bend in the ladder of the choke Joe,
in the eye of the tempt is a could or a phone to the piece of the heard cans the joke of absurds,
walking Centrally to the beating of the brass a Balling in the Keeper Take Earth tablets Coastal shakers!!

Crispy Crunch in the Indy Punch for if the Main String ever Clammed the Gritty Wood ached dirty lily Horn,
blow, blow, blow my butter stuck for if you stoke the fire Blokes the whistle Stop is said Reproached,
guess what gets cud the liquid in the Cows Blood drunken to with the batter rub swallow 7 Tum tongues,
twist the gut to an Eleven-Up bony growth for a Spur in the Leather theirs is Verb`d to vibrate The Nerve!!

Oh well how deep is the Cut to the Value of the Took as the Look is the Guy in the bitter Ending Booked,
eclectics be cool for in that fraught I speak Feather and You scream smight Righteous scribe kibble clines,
dishing list in a kindled tea the Mad Hatter bunny bops the Topper as the Mashed Tattler copper pie,
flipping coinage like the Dollar hide in Invented as the Opus Tiger in the Cylde Filler of an Opaque Slide!!

Microscopics clique in Life fill Her up with Petrol Tied to the Grands a Buggered Showed at Table Colds,
salad Caesar whips truth chains beating Cats of Nine Ing cames Dick~Less member killers timbered,
warp that bend que the Bar conquesting is a digger's scarred Three Tombs Over kid the Start It's,
swinging beneath the nimble steed Jacked jump over the Candled Ste variable of Vis and Vee Period leak.

Take, Take, Take a Countered Dog reverse the Spell Abbreviate Hell ache the Bone it is a Sod,
falling steep the Ram or Sheep no that Can't it must be Stone a Kinder Gander to the Grey Hare,
dye it back to Blondie Tack best in Show is Never Lack expulsions formalize a SAC threaten CLAPPED,
oh the Mattress of the Maat fickle Picking WAY WRONG Sot garbaged Kelp An Got a Cropper!!

Clipper Trades In The Mastered Laid 
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My photo
Presents, a Life with a Plan. My name is Karen Anastasia Placek, I am the author of this Google Blog. This is the story of my journey, a quest to understanding more than myself. The title of my first blog delivered more than a million views!! The title is its work as "The Secret of the Universe is Choice!; know decision" will be the next global slogan. Placed on T-shirts, Jackets, Sweatshirts, it really doesn't matter, 'cause a picture with my slogan is worth more than a thousand words, it's worth??.......Know Conversation!!! 
Showing posts sorted by relevance for query the way of slide. Sort by date Show all posts

Friday, January 31, 2025

This is Word peculiar[perfect[word[???#goes here#???]


peculiar

*???#goes here#???]:  Question goes to there is meant to be a number{#} so the Slide Rule Men are beginning to word forward word equating in Cantore Arithmetic as one word:  Word fester[Fester]...!! 

Question:  Is this able to square?

Question:  Has this word boxed[Boxed]?

Answer:  This is a bubble dot word thatch.

Cantore Arithmetic is able to State[state] word Dave’s Slide Rule equate word Devil.  Words[Slide rule] Pickett Microline 80 equated word PLACEK[OWNERSHIP[septic]]

*word Huge[huge[enormous[found]]]:


You searched for

"HUGE" in the KJV Bible


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2 Chronicles 16:8chapter context similar meaning copy save
Were not the Ethiopians and the Lubims a huge host, with very many chariots and horsemen? yet, because thou didst rely on the LORD, he delivered them into thine hand.

Pickett Microline 80

    A very cheap student rule made by Pickett, with A, B, C, D, CI, K, L, S and T scales. One-sided, kinda rattle-y. Traded one of several Microline 120s I got in the wake of the newspaper article for this. So, yes, this one is a bit out of chronological order, so is the yellow Microline 120 below.

Slide Rules!

Last Updated: 12/11/24
Titaner rule added to Circular Rules.


My Slide Rules

    This gallery is in the process of some updating, as many of the scans are from the 1990s, when my way of taking pictures was to put the slide rule on a flatbed scanner and hope it came out reasonably clearly. Some of the pictures will display at smaller than full size, all can be clicked on to get the full size if you're on desktop and can't just pinch-zoom. Within each section, the acquisitions are roughly in the order of acquisition, although I may have clustered a few "same manufacturer" rules more closely together.

Short Rules

Post Model 1444K

    The "Sun Hemmi" line tended to be made from laminated bamboo, which has stood up surprisingly well over the decades, even as the plastic part has yellowed. A clever bit of non-standard practice here is putting just the S, L, and T scales on the back, with a fixed cursor window to read. For the longest time I thought the center stick had to be removed and flipped around to use it, which led to a backwards L scale. 
    This was the first rule I got. I'm not sure if I found it in my grandpa's basement or at a clearance store, but I know I was about 14-15 when I got it and started to try and puzzle it out. To give some idea how bad the old scans were by comparison, this was just sliderule1.GIF back in the day. Yes, GIF used to be used for something other than animation.

Pickett Log Log Speed Rule Model N600-T

    A fine aluminum slide rule from Pickett, this one has scales A, B, C, CF (from pi to pi), CI, D, DF, DI, K, L, Ln, LL1, LL2, LL3, S, ST and T. Scanned slightly enlarged, it's six inches long and comes with a leather scabbard. The scabbard has a clever pull tab to bring the rule out far enough to grab easily. I also got the manual (my first!), which is an excellent example of a bad Thorndykian textbook...impenetrable prose followed by lots of drill exercises. I acquired this one from a friend, who had it sitting around in storage. When I showed him my N-515 (see long rules), he remembered having this one.

Pickett N400 Business Rule

    Another of Pickett's fine aluminum rules, this one has the standard A, B, C, D, CI, K and L scales on one side. On the other, however, it has several scales intended for the businessman or shopkeeper, including the C% and R% scales for calculating percentages (percent increase, percent discount). Also has the "folded" CF and DF scales that start at Ï€ instead of 1, which is also seen on the business rule down in Unusual Rules, so I guess business sorts needed to be able to deal with round stuff? Comes in the same sort of nifty scabbard as the N600 above. This one has the first owner's name scratched into the scabbard, and the fact he was in Granvill [sic] Ohio.

Guedon celluloid pocket rule

    Purchased on eBay. It's copyright to a French company (Unis), but was produced under license by Guedon in Schenectady NY and sold in Chicago. The celluloid plastic has yellowed significantly. The back is just a centimeter scale ruler, plus the original owner's name.

Long Rules

Acu-Math Model 400

    I sort of permanently "borrowed" this one from my father before heading off to graduate school. It's 12.25 inches long, and has the same scales as the Post, but with the more standard setup of S, L and T scales fixed. The back is entirely blank, and this was clearly one of the "gotta have a slide rule for class, but not majoring in STEM" deals like the Microline 80. Made of plastic. Came with a leather scabbard. When my parents moved after retirement, my dad found the instructions and sent them to me. 

Pickett Electronic Slide Rule Model N-515-T

    This aluminum slide rule does not contain electronics, it's for use in electronics, so it has special scales for finding frequencies and so forth. It has A, B, C, CI, D, L, Ln, S and T scales, plus two more scales for dealing with electrical formulae (2Ï€ and H scales). Comes in a leather-covered hard plastic scabbard. Inside the flap is the original owner's last name, Trutt, and a P-T combination glyph.
    The shot of the back of the N515T shows one of the scales used for figuring out orders of magnitude. Normally, a slide rule can't give you the order of magnitude of your answer, but this setup allowed engineers to find the magnitude of results from specific equations. You can also see a the "cheat sheet" that covers most of the back of the rule. While all slide rules are reminders of a time gone past, things like listing wavelengths in feet and frequencies in Megacycles (rather than Megahertz) further place this rule in the past.
    I got this rule from Dave Crate in exchange for listing his page on mine (since, due to the age of my page, it had good search engine penetration at the time), and it really kicked off my serious acquisition of slide rules, between my showing the rule around and the attention I got from a newspaper piece soon after. 

Aristo Nr.966

    This was my first Aristo rule, at the time I got it I hadn't heard of the trademark (or the manufacturer Dennert & Pape) before. On the front side, it has C, CF, CI, CIF, D, DF, K and L scales. On the back side are A, B, C, LL0, LL1, LL2, LL3, S and T. It comes in a slim box that is capped at one end. The cursor has to be all the way at one end for the rule to fit in the box.
    Acquired as part of the "Walker Collection," a batch of slide rules I got all at once when my appearance in the newspaper caused a woman to recall her husband's slide rule collection and decide that I might appreciate it.

Aristo Nr.970

    My second Aristo rule, this one apparently manufactured in Germany by Charvoz. It was a going-away gift from Dr. Benenson, one of my bosses during the two years I worked at Michigan State University's Lyman Briggs School, it was his first slide rule in high school/college. The front side has K, A, B, T, ST, S, C, D, DI and LL0 scales. The back side has LL01, LL02, LL03, DF, CF, CIF, L, CI, D, LL1, LL2, LL3 scales. The front side has raised "bumpers" at each end that connect the fixed parts together. When flipped over, the bumpers keep the cursor raised off the table. On the right side of each scale is the mathematical operation for that scale. "DBGM" is printed on the back of the cursor and the front right end of the center stick. Holger Petersen tells me it's short for Deutsches Bundes-Gebrauchsmuster, or "German Federal Utility Model." So, made either for government work, or to a set of government specifications.) The cursor itself is two plates of clear plastic spaced apart by aluminum top and bottom pieces. It has a Watts to Horsepower conversion on the front, and several more hairlines on the cursor whose purpose I haven't figured out yet. The left one on the A/B scale has a separation that represents a multiple of about 1.28, the right side one on the A/B scale has a separation that's a multiple of 1.34, and the one on the C/D scale a multiple of 1.13. And there's one extra hairline on the CF/DF scale on back, this a multiple of 1.145. Came in a leather scabbard with Dr. Benenson's name stamped on the inside.
    Thanks to Stefan Vorkoetter for explaining some of the mysterious gauge lines.  This site has more on them in general, and 1.28 bit above is 4/pi, with 1.13 useful for calculating the volume of a cylinder. Another of the lines lets you convert radius to area for a circle: place the main hairline on the radius on the A scale, and the other line will show the area on the D scale.

Pickett Microline 80

    A very cheap student rule made by Pickett, with A, B, C, D, CI, K, L, S and T scales. One-sided, kinda rattle-y. Traded one of several Microline 120s I got in the wake of the newspaper article for this. So, yes, this one is a bit out of chronological order, so is the yellow Microline 120 below.

Pickett Microline 120

    A fairly basic one-sided plastic rule, with A, B, C, D, CI, K, L, S and T scales. Cheaply made, the center stick doesn't always line up when flush against the ends of the rule, but it can be used for basic learning and so forth. I got a bunch of rules from a man near town in the wake of being in the newspaper, and three of this rule came as part of the deal. 120s are pretty common, I expect a lot of student bookstores stocked them. They're mostly found loose, but I kept the one which had a decent case out of the pile I started with.
    I later acquired a yellow version of this, which used to be the official "loaner" rule for Engineering Physics 2 at Kansas State University. And I use it occasionally for that purpose, to encourage students to remember their calculators....

Pickett N-902-ES

    A 2001 eBay purchase, this is a fairly simple trig rule, but it came with all the packaging and paperwork, including the warranty card. The back of the rule has a sort of cheat-sheet for operation of the rule. Page down a bit to see the classroom demonstration version I acquired in 2015, under Unusual Rules. Given the existence of the large demonstration rule version, I suspect that the N902 was another common college rule, a step or two above the Microline series and intended for those who were in majors that needed more than core math courses.

Pickett N-903-ES

    I don't remember where or when I got this rule, although odds are pretty good it was about the time I was moving to a new job, since I'd have been too busy to document stuff like this. The 903 is "Trig and Conversion" where the 902 is "Simplex Trig" and it has the "folded" scales on front. The back is similar to that of the 902, but it flips the top and bottom content, and the middle part has conversion tables.

Lawrence Engineering Service 10-B

 

    This rule came as part of a book entitled The Slide Rule And How To Use It, published by Grosset and Dunlap in 1942. It's a workbook with a small box glued to the inside front cover containing the rule pictured above. It's a very basic learning rule, with only A, B, C, D, CI and K scales on a rather cheap painted softwood. The back has a number of conversion tables and useful information (such as the weight of a cubic inch of "wrot" iron). One interesting feature is the cylindrical magnifier over the center of the cursor.
    I got this as part of the same deal that included the 120s. However, I have since seen eBay infested with these cheap rules, often advertised as "Antique Wooden Slide Rule!" Hard to get more bottom of the line than the Lawrence rules, tho.

Empire Pedigree Precision Rule

    I didn't want to open the packaging back when I got this, but in the intervening years the blister crumbled enough to let me slide the rule out and look at it more carefully. This was the sort of thing that probably got sold in office supply stores and the stationery aisle of stores like Giant (Wikipedia has several defunct department stores by that name). There is no date on the package or the instructions, nor a copyright on the rule itself. It's slightly higher quality than the Microlines, if smaller. And I discovered upon removing it from the package that it has the S, L, and T scales on the back side of the slider...and unlike the Post 1444, you're supposed to pull it out and reverse it. The cross-section of the rule is somewhat hollow, to get maximum strength from minimum plastic.

Sterling DeciTrig Log-Log


    A very nice two-sided long plastic rule, complete with mathematical notation (as on the Pickett N-515T) to explain the use of the rule. Has scales: A, B, C, CI, CF, CIF, D, DI, DF, K, L, S, ST, T, LL1, LL2, LL3, LL01, LL02, LL03. Obtained on eBay. I made it into an art installation as seen on the main page, and didn't feel like disassembling that to get a new picture of the back side, hence leaving up the ancient scan.

Dietzgen 1739-L Clear Scale

    Another very nice two-sided plastic rule. It lacks the LL01-03 scales of the Sterling, but it has two T scales (T1, T2). The green background on some scales is a nice touch, and seems to be Dietzgen's answer to the "ES" yellow scheme used by Pickett, meant for ease of reading.. The cursor has multiple hairlines, many of which I can't figure out, but two of which are clearly a way to quickly convert from kiloWatts to horsepower (1 hp = 1.055 kW). Some are probably the same Ï€ factors seen on the Aristo 970. Bought on eBay.

Post Model 1460 Versalog

    It has a cracked window and needs some cleaning, but this big Sun Hemmi bamboo rule is otherwise pretty nice. The front has LL0, LL/0 (LL00 in more standard notation, the inverse line), K, DF, T, ST, S, C, D, R1 and R2, L. The back has LL/1, LL/2, LL/3, CF, CIF, CI, C, D, LL3, LL2, LL1. Oddly, there's no A or B. R1 is the square root of C, R2 extends that scale (so 9 on C gives 3 on R1 (square root of 9) and 9.49 on R2 (square root of 90)). Bought on eBay.

Pickett Model 3

    This one doesn't do many things considering its size, but it does them very precisely. In addition to having the LL and LL0 indices on back (although it refers to them as N1 or 1/N1 instead of LL1 and LL01) and the S, T, and ST on front, it also replaces the A and K indices with square root and cube root scales, taking a single decade and splitting it into 2 lines for square root, or 3 lines for cube root. This gives it the precision of a much longer rule for doing roots (for cube roots it's effectively nine times longer than using a K register to do cube roots at the same physical size). The back has a cheat sheet for using the different sliced up indices. It also has a few other indices I'm not familiar with, like DF/M or Co. DF/M folds at about 2.3 rather than pi, and looking that up I see it's the base ten log of e to three digits, useful in converting from natural to base ten logs. The Co index seems to be an unusual case of using a rule for subtraction, as the black oval number of the Co index is one (or ten) minus the number on the D index that it accompanies. Co for "complement"? It would have to be complementary angle in gradians, though (there's 100 gradians in a right angle). 

    Copyright 1947, made of a light non-ferromagnetic metal, but it doesn't look like aluminum unless it's really grimy...aluminum doesn't corrode the way this appears to be. Magnesium, perhaps?

(Expect an update on this soon, waiting on whether the person I got it from wants to be acknowledged.)

Circular Slide Rules

Scientific Instruments Co. Model 300-B
Circular Slide Rule

 

    This was the first circular rule I obtained, bought over the phone from Boston Museum, and it quickly got stolen off my desk at work. The inner wheels on both sides rotate independently and the radial cursor has the scales printed on it in red. Has the following scales: A, B, C, D, CI, K, L, LL2, LL3, S, T1, T2, ST. Made of laminated bamboo, came with a carrying case (which was also stolen, sigh). Obviously, I can't take a better photo of it now. Every so often I check eBay to see if one is available, so far no luck. Concise Co. in Japan still sells their version as of 2019, though.

C-Thru Proportional Scale Model PS-79
Circular Slide Rule

    Has only the A and B scales, plus a window which gives the percent size and multiple of reduction between the outer and inner wheels. Made from plastic sheets. I got this at the drafting section of the student bookstore at OSU, it's one of the few types of slide rule to hang on until the calculator age, although they too fade as layout is more and more handled on a computer.  2019 picture is a little clearer, but very yellowed. While I had this on display in my office for a couple of years, it did most of its yellowing while stuffed in an envelope along with the instructions of other rules, so probably a chemical rather than a photodegradation effect. 

Keyline Concise Rule

    A multi-layer plastic laminate with a turning inner disc and a cursor molded to fit over the raised central disc. Only has A, C, CI, D and K scales, and is very compact. The back has various conversion formulae between English and Metric. Stamped with Northrop Wilcox emblems, both on the rule and on its vinyl case. Comes with a small folded up page of instructions. Acquired on eBay.

Dietzgen Midget Slide Rule

    A single, immovable and rigid celluloid-coated aluminum disc with two cursors on one side and one cursor on the other. Most of the scales are unlabeled on the front, and it also has the unusual "V versus U.S.S." scale and a scale with letters instead of numbers. I later got a photocopy of the instructions from someone selling another on eBay (these show up a lot), revealing that the V/U.S.S. scale was for screw threading/tapping systems, and the letters are the bit sizes. The instructions also revealed the manufacturer, something not actually printed on the rule itself. The reverse side has multiple sine and tangent scales, plus conversion from fractions to decimal. The case is imprinted "A&B Smith Co." The copyright dates are 1931 on the front and 1936 on the back, but the sheer number of these floating around makes it difficult to nail down the year of manufacture of any given sample.

Aero Products Research CR-4 Computer

 

(Original pictures from 2003)

(2019 pictures)

    Built for pilots as a tool to figure out things they needed to know. Very few "standard" functions, mostly specialized stuff I don't really understand even after reading the included manual. It yellowed significantly while sitting in a box for several years, probably the same chemical effect as yellowed the PS-79. Thanks to the yellowing, the new pictures aren't necessarily any clearer than the old ones (which were, at least, taken with a digital camera). Purchased on eBay.

    Stefan Vorkoetter points out that the scale just inside the B scale converts hours on B into minutes on the inner scale. Other front scales convert indicated and true airspeed (correcting for altitude, as airspeed indicators are sensitive to pressure differences). On the back are windspeed compensation calculators (as Stefan writes about here), and scales for finding vector components (TAS arrow on x, look next to the degree mark d to get x sin(d) or x cos(d) depending on whether you're looking at the black on white or white on black marks).

AN5837-1 Altitude Correction Calculator

    Another aviation rule, I got this one from American Science & Surplus. It's made by Cruver Manufacturing Co., and is a spiral rule that lets you figure out true altitude from indicated altitude by compensating for temperature. The only instructions are printed on the back, and I never quite managed to make it work in a sensible manner. But I don't really have avionics training. 

Titaner Slide Rule/Rolling Ruler

    This is a brand new circular slide rule crowdfunded on Kickstarter in 2024. It's made to be a sort of mix between jewelry pendant and "EDC" gadget. Titaner makes a bunch of little Every Day Carry gewgaws out of titanium. It came with a lanyard that's too short to use as a necklace unless you have a tiny head and can't be made short enough to use as a bracelet unless you have huge hands. It seems to mainly be sold as a rolling ruler, with the slide rule side being more of a gimmick. I suspect the one using inches might be easier to read, since it's a little bigger.

Unusual Rules

K&E Desk Rule N-4096

    This rule is 22" long, and comes in a wooden box with latches to hold it in. Once removed from the box, it has metal legs it stands on. Designed for everyday simple jobs, it only has the C, CI, CF, D and DF scales. But with a single decade spanning 20", it gives pretty good precision. Being made of wood, however, it has warped slightly with age, so the precision isn't what it used to be. It comes with an somewhat decayed instruction pamphletextolling the virtues of the slide rule for use in the average merchant's shop. Part of the Walker Collection.

155mm Howitzer Slide Rule Set

 

    Purchased on eBay, this is a set of slide rules used by artillerists to aim their big guns. Based on the materials, I'm guessing it's Vietnam vintage or thereabouts. The small rule on the right is the only "slipstick" style, and seems to be a rough approximation rule, with the cursor sticks below it used for specific loads and uses. It seems like I'd need specially made charts in order to get any use out of these rules, but if anyone can make sense of the instructions and can figure out how to use them alone, let me know. Click on either picture to show at larger size.

Slide Rule Tie Clasp

    I got this clasp on eBay missing the clip part (although I've since seen this model complete on eBay). I bought a cheap tie clasp and kitbashed the pieces together to create the thing seen above. It only has A, C and D scales, plus a cursor, and is 2" (5cm) long.

Nuclear Bomb Calculator

    Grant Pilkay sent me this book with included rule, meant to help calculate the effects of nuclear blasts. Sadly, some of the paint bound to the wrong side of one of the wheels and peeled off, so turning the wheel shows a gap. Click on the image to see at full size.

Picket N902-ES Classroom Demonstrator

    After years of trying, including some bot-sniped attempts on eBay, I finally got a demonstration rule for a price I could afford. It helped that "a price I could afford" went up recently. Pictured in my office, with the regular-sized N902-ES tucked onto the left-hand stand.

Metric Converters

    A question from Chad Smith helped me figure out a neat trick not in the instructions that can be done with any metric converter with a cursor. Say you want to convert between two units of the same sort without a direct conversion, like miles to yards. Use the converter normally to convert the thing you have to something else, hopefully something that converts to the unit you want. Place the cursor on the answer, then very carefully slide the center stick to put that number as the input for another conversion. Continue until you get what you want. This is "indirect conversion."

    Example: Using a rule with meters to yards and miles to kilometers, I want to find the yards in 3.50 miles. I place the center stick with the miles arrow on 3.50 and then line the cursor up with the number of kilometers. Kilometers to meters is just order of magnitude, so I'll multiply my final answer by 1000. Now I carefully move the stick so that the meters arrow is under the cursor, and read off 6.16 on yards (guessing on the last digit). That means 6160 yards, give or take ten yards...and 6160 is the correct answer.

Universal Circle Metric Converter

    Like the proportion wheel, this is another "hidden" slide rule. Sold by Chadwick-Miller (probably an office supply store), it uses two identical cylinder scales to do fixed multiplication tasks, converting units into metric and back to english. Rather than complicate things for the users, the log scales cover three decades explicitly, with things like .5 and 30 on it so users need not mess with order of magnitude estimates. Usually. Inches to feet requires dividing by ten. And the scales aren't lined up as well as they could be, this is just a cheap novelty item, really. The bottom scale is just a linear C/F temperature converter.

Sterling Pocket Metric Converter

    A simple metric converter like the pencil cup above. Made by a subsidary of the Borden company, it came in a plastic slipcase and had nothing on the back. In fact, the main body was molded out of fairly thin plastic, which had a broad T-shape cross-section. The back of the center piece has a temperature converter with a few notes like "Freezing" and "Fever."

Sterling 11" Metric Converter

    Same basic idea as the pocket converter, but about twice as long so that you can get more precision. It has a few more unit pairs than the pocket rule: length and area on the front, volume and weight on the back (no temperature). I got this loose (no paperwork or case) from someone who was doing some housecleaning prior to a move. :) Lots of yellowing (browning?) made obvious when I flip the center stick around. This has the same physical shape as the Empire Pedigree, so Empire probably licensed or stole the design from Sterling/Borden Chemical. (Or Empire was a subsidiary of Borden too.)

Sterling Engineers' Metric Converter

    A much more involved metric converter by the same company, it's twice as long as the basic metric converter and has tons and tons of units. Energy, flow, power, heat flow, velocity, density, pressure and so forth. Some of the units I don't even recognize (mostly flow-related), although the instruction booklet does explain them all. As indicated by the case, this is part of the Walker Collection as well.

Datalizer Temperature Converter

    This is part of the class of "barely a slide rule" things that do still show up, especially for things like recipe unit conversion. Made in 1999, it's a temperature converter that includes the Rankine scale, which is the absolute temperature scale that is in Fahrenheit-sized degrees. While sold by Scientific Instruments, the back shows Datalizer Charts to be the maker. The back also proudly proclaims this to be ISO9001 certified.

Send e-mail to dvandom@gmail.com.
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Types of Slide Rules

Some of the possible combinations of scales on a slide rule have received standardized names. In 1859, Amédée Mannheim developed a slide rule with the scale layout

A/B C/D

(this standardized notation means that the scales are A on the top of the body, B and C on the slider, and D on the bottom of the slider) with a cursor. In some senses, this could be thought of as the first modern slide rule, and Mannheim's design was the occasion for a great increase in the use and popularity of the slide rule.

Shortly after Mannheim's design of the slide rule, another design was also introduced, the "Règle des Ecoles", which had the scale layout

DF/CF C/D

in modern terms, although the scales were actually still labelled A, B, C, and D in order. This arrangement survived on the reverse of many elaborate duplex slide rules, with accompanying CIF and CI scales, to allow more efficient multiplication.

During much of the 20th century, a slide rule advertised as a Mannheim would (thankfully) have a somewhat more elaborate layout:

A/B CI C/D K
S L T

where the S, L, and T scales were on the reverse of the slide, and the S scale usually was made to coincide with the A scale. Keuffel and Esser, on the other hand, used their trademark "Polyphase" to refer to this type of rule, and used the term "Mannheim" for one without the CI and K scales, but still with the S, L, and T scales on the back of the slider.

In Europe, the term "Rietz" was often used for slide rules which had a few more scales than the original Mannheim rule; a common scale layout to which this term was applied was:

K A/B CI C/D L
S ST T

Here, the presence of the ST scale shows that the S scale works with the C and D scales through the use of the cursor. Many slide rules with this complement of scales, but in different arrangements, were made for use in Europe.The original Rietz slide rule, however, did not include an ST scale.

The term "Darmstadt" or "Système Darmstadt" refers to a simplex rule with log-log scales, having an arrangement such as:

S T A/B K CI C/D P
L LL1 LL2 LL3

and, again, there were many variations on this scale arrangement, most of them minor. Unlike the Rietz slide rule, there was a large enough difference between this and the type usually sold as a Mannheim slide rule for it to also establish a foothold in the North American market, especially during the early years when Keuffel & Esser held patents on the duplex log-log slide rule.

The Darmstadt arrangment of slide rule, however, is a relatively recent one, which originated only in 1934, long after both the Yokota slide rule from 1907 and the duplex log-log slide rule (the first example of which, the K&E 4092, apparently dates from 1909 or earlier): this surprised me when I heard it, as I would have expected that some form of simplex slide rule with only one set of log-log scales would have been in use, likely for a long time, before either the Yokota or the duplex log-log slide rules were developed.

Of course, it could well have been that such slide rules did precede the Yokota and the duplex log-log, just without being developed to a standardized type like the Darmstadt.


Both Mannheim and Darmstadt slide rules usually had, on the back, two small windows with hairlines corresponding to the two index positions on the stator. This allowed the use of the scales on the back of the slider without turning the slider over.

In the case of the Mannheim, bringing an angle on the S or T scale to the appropriate one of the hairlines would allow a number on the body of the rule to be multiplied by a sine or tangent, and then found on the slider.

In the case of the Darmstadt, taking a number to a power without reversing the slider is more complicated, but it can be done. Put the number to be raised to a power on one of the hairlines, then, on the front of the rule, place the cursor where the index of the slider is located. Although this position reflects the inverse of that number's position on the log-log scale, one still moves the power on the C scale of the slider to the cursor (and not the CI scale) in order to advance the log-log scale so that the number raised to that power will appear at one of the index hairlines on the back.

The Darmstadt slide rule, with log-log scales and trig scales, offered all the standard mathematical functions commonly found on general-purpose slide rules. However, placing the trigonometric scales on the body of the rule meant that products involving more than one trigonometric function would require writing down intermediate results; because of how the log-log scales are usually used, no benefit is derived from placing them on the slider.

Thus, the scale layout on the Yokota slide rule, a simplex or closed construction slide rule patented in 1907:

LL3 LL2 LL1 A/B K C/D LL01 LL02 LL03
S Sec T

although it lacks a CI scale, would seem to me to have been an even better basis on which to arrange a slide rule than the Darmstadt design, but although duplex designs did proceed in that direction, simplex designs generally did not.

The secant being the reciprocal of the cosine, the secant scale served as an SI or inverse sine scale, except that one would subtract the angle from 90 in one's head, so the effort is split evenly between sines and cosines.

The original Yokota slide rule differed from modern slide rules with log-log scales in aligning them so that 3.5, rather than e (2.71828), on the LL3 scale corresponded with the index. As with those Pickett log-log slide rules that use base 10, this doesn't change the length of the scale, only its position.

This slide rule was made in Europe by Dennert and Pape, the company that invented the celluloid-on-wood construction for slide rules in 1886, until 1938. It also had a centimeter scale on the top of the slide rule, and an inch scale on the bottom, like many Darmstadt and some Mannheim slide rules; but on this rule, because the scales were made to be exactly 10 inches in length instead of 25cm, the inch scale, by means of an indicator on the base of the cursor, also served as an L scale!

As the trig scales are much more commonly used than the log-log scales, having the log-log scales always visible, and the trig scales relegated to the back of the slider, probably failed as lacking immediate appeal to purchasers, and thus even Aristo never came out with a less idiosyncratic version of the Yokota design. A modernized version of the Yokota design could have had, for example, a scale layout such as this:

LL1 LL2 LL3 A/B K CI C/D LL03 LL02 LL01 L
S ST T1 T2

had it been produced.

However, the Aristo 915 and the Nestler 370 are examples of simplex slide rules with the trig scales on the slider and a single set of log-log scales (consisting only of LL2 and LL3) on the body.

Both of these were slide rules made for electrical engineering; the Aristo 915 had a dynamo/motor scale and a voltage drop scale for the resistivity of copper; the Nestler 370 had U and V scales, the V scale again based on the resistivity of copper, but being a folded D scale instead of a folded A scale, and the U scale being another folded D scale, this one folded at pi/6.

Nestler also made slide rules of the more common Electro type, such as the Nestler 137 or the Nestler 11E, which happened to have a cos theta scale which is the same as the cos theta scale on the Pickett N-16 ES. (The UTO 611 also had this scale.) Despite the fact that the laws of elecricity are the same everywhere, I was astonished to see a scale from the most esoteric of slide rules for advanced electronics reappear on a slide rule intended for work with alternating current motors. And the Aristo 815 was their version of the Electro slide rule without the log-log scales.

The Electro type of slide rule, which exists both with or without log-log scales, is another one of the types of slide rules, along with the Mannheim, Reitz, and Darmstadt, that has been provided by multiple makers. Its scale layout typically runs something like this:

D/M V A|B CI C|D K LL2 LL3
S L T

but with numerous minor variations.


I have finally come across one modern example of a more recent slide rule which follows the basic pattern of the Yokota slide rule, a closed-body slide rule with a set of multiple regular log-log scales and a similar set of multiple inverse log-log scales on the stator.

This design of slide rule was made by Faber-Castell; it was apparently one possible design of the slide-rule component of the TR1, TR2, and TR3 pocket calculators (which seem to have also been available with a less elaborate slide rule component).

The variation I'm thinking of had this scale arrangement:

LL03 LL02 LL01 K A|B BI CI C|D LL1 LL2 LL3
T ST S P C

So just before the slide rule disappeared into obscurity due to the arrival of the pocket calculator, the Yokota scale arrangement, after all those years, finally made one brief return appearance.

As for examples with only one set of log-log scales, while this occurred many times on variations of the Electro type of slide rule, I found that the Jakar 1011 slide rule from Japan had a set of four normal log-log scales without being a special-purpose slide rule, making it perhaps the next-closest approach to a Yokota.


A little-known slide rule with great historical importance is the one devised by one Gregor Rudolf Ferdinand Heinrich Cuntz.

The scales on it, in modern nomenclature, were:

L T S ST CF' CF Q3 Q2 Q1 R2 R1 | C|D CI

This slide rule was the one on which the idea of continuing the S and T scales with an ST scale for small angles, the idea of having a double-length scale with the R1 and R2 scale for square roots instead of the half-size A and B scales, and a triple length scale with the Q1, Q2, and Q3 scales instead of the K scale were all originated.

The scale marked as CF' was a folded C scale that started at pi/4 instead of at pi.

Unfortunately, it had a number of drawbacks that limited its popularity.

The slider was narrow, with only a C scale on it, so the advantage of using the second boundary between the slider and the body for more accurate calculations without the cursor was lost.

The two R scales and the three Q scales were in inverse order on the rule, making the scale harder to read. As well, the way in which they were labelled on this rule was quite off-putting, to say it lightly. It appeared that those scales had to do with some extremely complicated mathematical expression.

The drawing given on the patent for this slide rule (U. S. Patent 1,168,059) accurately represents how the System Cuntz slide rules actually manufactured and sold appeared, so, rather than attempting to describe the indescribable, here is that image:

which I have slightly retouched by removing the lines by which parts of the slide rule were labelled with letters to which the patent description referred.

Note also that on the right there were numbers for the purpose of indicating which of the two R scales or the three Q scales would be the right one on which to find the square or cube root of a number on the D scale, depending on the location of its decimal point. Some Pickett slide rules attempted to do something similar.


Duplex slide rules, even excluding those made for special purposes, offered such a wealth of possibilities that usually their only names were the trademarks of the individual maufacturer. The modern duplex slide rule was invented in 1890 by William Cox for the Keuffel and Esser company in the United States.

Duplex slide rules had many different assortments of scales. Some might only have the main set of three log-log scales, LL1, LL2, and LL3, and others would have four log-log scales in both sets of scales. But at each level of complexity, each manufacturer had its own arrangement of scales; this was particularly distinctive at the highest end of the line, where such flagship slide rules as the Pickett N4-ES, the Keuffel and Esser Deci-Lon, the Faber Castell Novo-Duplex 2/83, the Aristo HyperLog 0972, and the Post (Hemmi) Versalog each displayed radical differences in design philosophy.

The Circular Slide Rule

It is possible to move one logarithmic scale relative to another by using a rotating disk as well as a slider. The very first circular slide rules designed, almost immediately after the invention of the ordinary slide rule, instead used a single circular scale, with a pair of cursors whose relative position could be fixed. The Gilson Binary slide rule was a 20th-century slide rule designed on that principle, and it even had a log-log scale.

An image, from an old catalog, of a slide rule of this type (a smaller slide rule made by the makers of the Gilson Binary slide rule) is shown at right. It works on the principle that if one moves the cursor which is in contact with the surface of the disk, the upper cursor will go with it; this is achieved by making the pivot holding the spring holding the two cursors to the disk free to easily rotate.

Most recent circular slide rules did have a rotating disk and a single cursor instead, however. Each of these two forms of slide rule have their own vocal advocates. The advantages and disadvantages of each form of slide rule are, however, relatively obvious:


Straight Slide RuleCircular Slide Rule
SizeIn one direction, it must be as long as its scales, but in the other it can be quite narrow, depending on how many scales it has; the number of scales it can have is unlimited.It can have scales over three times as long as its largest dimension, but it must be the same size in two directions. The more scales that are added to such a rule, the shorter they have to be compared to the rule's longest scale.
Ease of UseAll the numbers on every part of the rule are upright when in use.One never has to worry about choosing the wrong index for a calculation so that the result goes off the end of the scale.

Thus, from this table, the actual history of the slide rule is not surprising; the overwhelming majority of slide rules used for serious work during the heyday of the slide rule were straight slide rules, but special-purpose slide rules designed for use by people who would otherwise not use a slide rule were often circular, and the last slide rules still being manufactured after the pocket calculator are circular slide rules as well.

That is because the advantages of the circular slide rule applied to people new to slide rules and to slide rules with a limited number of scales, while the advantages of the straight slide rule were relevant to people who were trying to calculate rapidly and to slide rules with a large number of scales.

Some other differences between straight and circular slide rules vary with the type of circular slide rule being considered:

Straight Slide RuleConventional Circular Slide RuleBinary Circular Slide RuleClear Plastic Overlay Circular Slide Rule
Scales in ContactEither two pairs of scales, on a one-sided rule, or four pairs of scales, on a two-sided rule, slide against each other.Either one pair of scales, on a one-sided rule, or two pairs of scales, on a two-sided rule, slide against each other.Because the separation between the two cursors can be taken from any scale, and applied to any other, this slide rule acts as if any scale on the rule is sliding against any other scale.If one set of scales is printed on a clear plastic overlay, instead of on a rotating disk within the rule itself, the number of scales that can be in contact with a scale on the body of the rule is arbitrary.
ParallaxAll scales are in the same plane, and the cursor line can be printed on the back of the cursor window.

All scales are in the same plane, and the cursor line can be printed on the back of the cursor window.

The cursor lines can be printed on the back of both cursors, but the thickness of the first cursor separates the second cursor from the scales.The second set of scales can be printed on the back of the plastic overlay, but its thickness separates the cursor from the scales.
Required MotionsIndex to operand; cursor to other operand if scales involved do not touch.Index to operand; cursor to other operand if scales involved do not touch.First cursor to index; second cursor to operand; both cursors together so that first cursor is on second operand.Index to operand; cursor to other operand if scales involved do not touch.

Incidentally, one could put a cursor line aligned with the indexes of the scales on a plastic overlay slide rule to create a slide rule that can be used as a binary circular slide rule for calculations involving sets of scales other than those which are paired. Files in PDF format for making such a slide rule yourself on a laser printer are available here.

Also, a few years after they invented the duplex slide rule, Keuffel and Esser brought out a slide rule which used the braces holding the two pieces body of the slide rule in a duplex slide rule to also hold a middle portion of the body, so that the slider could consist of two sliders joined by a flat plate, so that instead of four pairs of scales, eight pairs of scales were in contact on the rule. This slide rule, the Universal, is now extremely rare and expensive. The principle does not seem to have been used again, although it would have been useful to allow specialized scales to coexist with the full complement of scales on a conventional duplex log-log slide rule.

More Precise Slide Rules

The precision of calculations on a slide rule is, of course, quite limited. From time to time, various measures have been attempted to ameliorate this problem.

A straight slide rule can have a long scale split into several pieces in order to fit its length, leaving the user to either estimate the result or count scales to choose the correct answer. Hemmi made two slide rules of this type, the Hemmi 200 and the Hemmi 201.

The Hemmi 201 split the scale into four parts, and, in addition, it was 20 inches long instead of 10 inches long. The scales were:

L2,4 L1,3 A2,4 A1,3 | C4 C3 C2 C1 | D1 D2 D3 D4
K4 K3 K2 K1 | CF4 CF3 CF2 CF1 | DF1 DF2 DF3 DF4

Thus, it had L, A, C, D, K, CF, and DF scales, each split into four parts. Since the A scale is the same scale repeated twice, only two parts were needed, and thus those two pieces were called A1,3 and A2,4 to show that the first part was also the third part, and so on. Two parts of the L scale were also provided to make it easier to read the scales and label them.

The Hemmi 200 was only 16 inches long, but split the scale into six parts, making it somewhat longer, at 96 inches. The scales it provided were:

D6 D5 D4 | C6 C5 C4 C3 C2 C1 | D3 D2 D1
DF6 DF5 DF4 | CF6 CF5 CF4 CF3 CF2 CF1 | DF3 DF2 DF1

limiting it to just multiplication and division.

A humbler example from Britain was the Unique Ten-Twenty, a ten-inch slide rule with scales split into two parts.

A circular slide rule can have a long spiral scale placed on it.

The Cylindrical Slide Rule

The quest for a slide rule with a very long scale has, however, led to the design of a third type of slide rule, the cylindrical slide rule.

Three basic types of cylindrical slide rules are well-known, and are listed under the names of their most famous representatives.

The Thacher Slide Rule

In this type of slide rule, there is a cylinder which contains a long scale split into several segments, each segment fitting within the height of the cylinder, and the segments being uniformly distributed about its circumference.

This cylinder slides within a cage in which the bars have the segments of a corresponding scale on them.

Thus, the cylinder is rotated to place the required portions of the two long scales in contact, and then slid to bring the appropriate numbers in contact.

Since each bar has two sides, and the bars will generally be thicker than the minimum possible distance between scales, this design lends itself to a more complex type of rule with multiple scales, similar to a conventional slide rule; also, its manner of operation is very similar to that of an ordinary slide rule.

An old drawing of this slide rule is shown below:

In addition to Edwin Thacher's invention of 1881, in which the inner cylinder and the cage both carried overlapping double-length segments of the divided scale for convenience in avoiding off-scale results, the Swiss company Loga produced a slide rule based on this principle which continued to be manufactured quite some time after Thacher's instrument ceased to be produced; it was patented in 1894, and was different in that the cage only had a single copy of each part of the scale, and was half the length of the cylinder, and it was the cage, rather than the double-length inner cylinder, was the component that slid, helping to make the instrument more compact. In addition, because the cage was placed on a cylinder of transparent plastic, the bars were much narrower, so there were 50 of them instead of 20, but the top side only of the bar was used, so the logarithmic scale was split into 50 parts instead of 40.

An earlier design belonging to this general group was the first known cylindrical slide rule, invented by the same Colonel Amédée Mannheim who revised the basic slide rule layout.

The Otis King Slide Rule

This slide rule consists of a body with a helical scale, within which a sleeve with a similar helical scale could both slide and rotate. An outer sleeve then slid and rotated on the helical scale on the body, being narrower at the other end so as to approach closely to the sleeve with the other helical scale. Marks at the two ends of the outer sleeve constituted the cursor of the slide rule; thus, instead of placing the two helical scales in coincidence, points on the two scales separated by the distance between the two cursor marks were treated as corresponding.

Below is an old drawing of this cylindrical slide rule:

The Otis King cylindrical slide rule was perhaps the most popular and inexpensive cylindrical slide rule made.

A special-purpose cylindrical slide rule made for use in sight reduction for celestial navigation, the Bygrave position-line slide rule, was based on the same general principle, although it was constructed differently, so that it looked more like the Fuller slide rule, which will be described next.

As I may have stimulated your curiosity by even mentioning this device, I will also recount an explanation of how it worked that I once gave, in a later section of this page.

The Fuller Slide Rule

An old schematic drawing of this type of slide rule appears on the right.

This slide rule, in its basic form, operated somewhat like a binary circular slide rule; a single scale, helical like those on the cylindrical slide rule of the Otis King type, was positioned between two cursors, then moved to bring one number to one cursor so that the result could be read at the other cursor.

The body of the rule bore the stationary cursor, which had two indicating points, separated by the length of the scale. A cylindrical sleeve, normally bearing tables and formulas rather than scales, had the second cursor, a single point, attached to it, and the scale itself moved on an outer cylindrical sleeve.

A later model then had indicating marks placed on the sleeve with the original scale, such that when these marks were placed against a scale on the sleeve attached to the second cursor, the corresponding point on the main scale would be at the second cursor. That sleeve had room for two additional scales, and in addition the L scale could fit in a single circuit of the cylinder, given a suitable number of turns to the helical scale.

Although complicated, it did have the advantage of making the most use of each moving part, and was perhaps the best-known cylindirical slide rule.

The Bygrave Cylindrical Slide Rule

This special-purpose cylindrical slide rule was so designed that in three calculation steps on the rule, with some addition done by hand, it assists in what is termed sight reduction, the conversion of sextant observations for use in celestial navigation.

As noted above, although it was about the same size as the Fuller cylindrical slide rule, it actually worked according to the basic principle of the Otis King cylindrical slide rule instead. During its lifetime, there were three different basic versions of the device, illustrated at left.

The first version placed the two pointers inside of a window in the collar which contained the instructions for use of the device. This meant that the separation between the two pointers was limited, and therefore the two cylinders with spiral scales were also limited in height.

The second version solved that problem by placing the two pointers on top of the collar with the instructions. But it created a new problem: because now the lower pointer was on top of the collar with the instructions, an equivalent space on the bottom of outer one of the two cylinders with spiral scales was wasted.

The third version solved that problem as well, by bringing back a window, but this time only for the lower pointer.

The two scales are a T scale on the main cylinder (apparently, despite that scale being everywhere described as a scale of tangents, those who have examined actual specimens of the device have noted that it is, in fact, marked as a scale of cotangents) and an S scale, but labelled so as to show cosines rather than sines, and which runs in the reverse direction, on the outer cylinder (which I shall therefore call the CSI scale).

The three steps in its use are as follows:

Given the declination (or latitude in the sky) and the hour angle (or longitude in the sky: quite literally, as this is produced by applying the sidereal time to the right ascension of the object sighted), an intermediate value YLOWER is calculated from the expression

YLOWER = ATAN( TAN( DECLIN ) / COS( HRANG ) )

by (in straight rule terms) placing the index of the T scale over DECLIN on the CSI scale, and then reading YLOWER on the T scale over HRANG on the CSI scale.

The modified intermediate value YUPPER is then 90 degrees minus your current latitude, and either plus YLOWER if the declination and latitude are both in the same (north or south) hemisphere, or minus YLOWER if they are in opposite hemispheres.

One then calculates the azimuth to the star from the equation

AZIM = ATAN( COS( YLOWER ) * TAN( HRANG ) / COS( YUPPER ) )

by placing HRANG on the T scale over YLOWER on the CSI scale, and then reading AZIM on the T scale over YUPPER on the CSI scale.

Finally, the altitude (which is normally what one obtains from a sextant in the first place, but the difference between the altitude calculated with this instrument from the estimated position of your ship and the actual altitude seen with your sextant is what you plot on a chart in celestial navigation) is calculated by

ALT = ATAN( COS( AZIM ) * TAN( YUPPER ) )

which is done by placing YUPPER on the T scale over AZIM on the CSI scale, and then reading AZIM on the T scale over the index of the CSI scale.

A Slide Rule for Multiplying Complex Numbers

A derivative of the Fuller slide rule was used for multiplying complex numbers.

When expressed in polar coordinates, multiplying two complex numbers becomes multiplying their radii, and adding their angles; using the logarithms of their radii, this reduces to adding two independent numbers, which can be done mechanically.

Thus, one can take the following area on the complex plane:

and map it to a rectangular area, which could serve as the slider of a slide rule, with a corresponding area on its base:

The slide rule actually built used a single scale of this type, rather than two scales, one still and one moving, but it used all four quadrants of the complex plane, wrapping them around a cylinder. It was made by W. F. Stanley and Company in 1961, having been designed by one D. J. Whythe to fill a request from the BBC, and resembled the Fuller cylindrical slide rule in general design.

One could make the angular coordinate correspond to the radius, and the radius correspond to the angle, around a circular slide rule for complex multiplication.



Since this was written, I've learned from a page on the web site of the International Slide Rule Museum that the Faber-Castell 989 Complex Slide Rule Calculator also used a scale of this type; it was stationary on a flat surface, with a cursor having a pivoting arm to allow calculation.

There's considerably more information about complex number slide rules on this page.

A Little History

Logarithms were originally invented by John Napier in 1614. In 1620, Edmund Gunter first noted that a logarithmic scale could be used in combination with a compass for measuring out distances along it to perform multiplication. And then the slide rule itself was invented in 1632 by William Oughtred. The modern form of the slide rule, in which two pairs of scales slide against each other, so that the rule is composed of a slider and a stock, was at one time credited to Seth Partridge in 1657, but it is now known he was describing an earlier invention, believed to be that of Robert Bissaker in 1654.

Unlike logarithm tables, which remained an important aid to calculation ever since their invention and until the emergence of the pocket calculator. the slide rule appears to have languished in relative obscurity from Oughtred to Mannheim. Although a few scientists and engineers did make use of the slide rule, its chief popularity in the first part of its existence appears to have been as a tool for calculating taxes on barrels of alcoholic beverages in Britain.

Before Mannheim, the typical scale layout on a slide rule would be what we would call in modern terms:

A/B B/D

Thus, the A and B scales were used for multiplication, and the bottom pair of scales could be used for multiplying one number by the square of another number. This arrangement avoided the need for a cursor, but limited the accuracy of a 10-inch slide rule to that of a 5-inch slide rule with C and D scales.

It takes some effort to learn how to multiply with the C and D scales, and making a cursor whose hairline remains accurately perpendicular to the scales requires some effort. But all these things were possible long before 1859.

The cursor, also known as a runner or index, although perhaps invented either by Robert Bissaker or Isaac Newton, became known around 1778, in a slide rule designed by John Robertson, and the use of C and D scales for multiplication had been introduced even earlier, by a British excise examiner named J. Vero (or Verie).

Thus, it must be concluded that before Mannheim, there was not enough potential demand for the slide rule for this type of innovation to succeed. Prior to this, the popularity of the slide rule had been growing in some countries, while in other countries in Europe, it still remained almost unknown, during the first half of the nineteenth century; it was after Mannheim that the slide rule could no longer be ignored: that generations of schoolchildren might be trained in the use of the slide rule changed from impossible to inevitable.

It was not until 1886, however, that the firm of Dennert and Pape, later responsible for the quality plastic slide rules that sold under the Aristo brand name, invented the slide rule construction involving putting the scales on a thin layer of celluloid, then attached to a wooden base, greatly improving the legibility of slide rules.

The first slide rule with a scale the length of which was a multiple of the length of the rule itself, to permit more precise calculations to be performed, was proposed by William Nicholson in 1787.

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An Independent Mind, Knot Logic

An Independent Mind, Knot Logic

Title: iMMEDIATE ATTENTION TO THE 2025 State of Indian Nations Address

ABOUT US Ma | , Welcome to NCAI.org Founded in 1944, the National Congress of American Indians (NCAI) is the oldest, largest, and most repre...

Karen A. Placek, aka Karen Placek, K.A.P., KAP

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Presents, a Life with a Plan. My name is Karen Anastasia Placek, I am the author of this Google Blog. This is the story of my journey, a quest to understanding more than myself. The title of my first blog delivered more than a million views!! The title is its work as "The Secret of the Universe is Choice!; know decision" will be the next global slogan. Placed on T-shirts, Jackets, Sweatshirts, it really doesn't matter, 'cause a picture with my slogan is worth more than a thousand words, it's worth??.......Know Conversation!!!

Know Decision of the Public: Popular Posts!!