Slide rule anyone?
Slide rule anyone?
A couple of slide rules are in my desk and are used from time to time, primarily for mental exercize.
Anyone else out there in Bogelheadland use slide rules? It is a great way to combine mental math with an early calculator. Back in the day ( early 70's) I used it for basic multiplication and division, primarily to check my work on long hand calculations. Now, it is interesting to review exponential and logarithems. I never really understood logs except it made x and / much easier on complex problems.
Anyone know of great sites for self help on slide rules?
Ed
Anyone else out there in Bogelheadland use slide rules? It is a great way to combine mental math with an early calculator. Back in the day ( early 70's) I used it for basic multiplication and division, primarily to check my work on long hand calculations. Now, it is interesting to review exponential and logarithems. I never really understood logs except it made x and / much easier on complex problems.
Anyone know of great sites for self help on slide rules?
Ed
Re: Slide rule anyone?
I did a Google search and came up with this site which looks helpful or at least interesting. I plan to check it out more later.
http://sliderulemuseum.com/SR_Course.htm
http://sliderulemuseum.com/SR_Course.htm
Re: Slide rule anyone?
I have a K & E slide rule sitting on the shelf above my computer that was used by both my father and older brother in their engineering studies at Lehigh University. My Dad graduated in 1920 and my brother in 1952. My memory is not too good, but I seem to remember using or being introduced to slide rule use in high school in the early 1950s.
Tom D.
Re: Slide rule anyone?
Lehigh is a great school. My wife was born in Bethlehem and her uncle graduated from LU. We live in NW Indiana (her family were part of the Bethlehem  Burns Harbor migration in the 60's) and return each year. We drove thru the campus last summer.
I would like to use the SR for finanical calculations...shouldnt be too hard, just need to familiarize myself with the formulas. The issue now is the review of math from 40 years ago. My son is taking calculus in HS and just rolls his eyes when I pull the SR out.
Ed
I would like to use the SR for finanical calculations...shouldnt be too hard, just need to familiarize myself with the formulas. The issue now is the review of math from 40 years ago. My son is taking calculus in HS and just rolls his eyes when I pull the SR out.
Ed
 nisiprius
 Advisory Board
 Posts: 37328
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Slide rule anyone?
John C. Bogle does.MP173 wrote:Anyone else out there in Bogelheadland use slide rules?
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Slide rule anyone?
I managed to graduate as an engineer from Drexel University in 1965, using a $2.00 plastic circular slide rule. It was about 4 inches in diameter, and was quite the novelty. I told anyone who asked that I used it because I never 'ran off the ends' or had to use the 'folded scales'. It cracked when I was a Senior and I discarded it. Wish I still had it. Finished senior year using a 'Post' 6 inch rule that got me thru finals. Still have that one, but haven't used it since.
I also remember having to take a class in Bufftran, (I think that followed Fortran) and using punched cards (Hollerith code?) to load my program into the university's IBM 1620(?), which took up a significant portion of the basement in one of the science buildings.
Ah, nostalgia. It isn't what it used to be.
I also remember having to take a class in Bufftran, (I think that followed Fortran) and using punched cards (Hollerith code?) to load my program into the university's IBM 1620(?), which took up a significant portion of the basement in one of the science buildings.
Ah, nostalgia. It isn't what it used to be.

 Posts: 37017
 Joined: Fri May 11, 2007 11:07 am
Re: Slide rule anyone?
I have just inherited my father's.
I like to tease people that they designed nuclear reactors with these things which they did, and those reactors are still sitting on the shores of the Great Lakes, generating power. A tribute to engineering 'margin of error' .
I no longer know how to use one, but each time I pick it up I think of him.
I like to tease people that they designed nuclear reactors with these things which they did, and those reactors are still sitting on the shores of the Great Lakes, generating power. A tribute to engineering 'margin of error' .
I no longer know how to use one, but each time I pick it up I think of him.

 Posts: 2797
 Joined: Thu Jun 25, 2009 12:50 am
 Location: Vancouver WA
Re: Slide rule anyone?
My dad is a retired science teacher in his mid70s. He collects them. He has some incredibly beautiful ones made of things like ivory and brass. Apparently there is now a collector's market for these things. I'm too young to know anything about them much less how to use them. Although I do remember the days that math and science books had trig and log tables in the back so you could do things like look up the cosine of 22 degrees instead of just typing it into the calculator. Now days even calculators are going obsolete as every smart phone has a scientific calculator included. The main reason why calculators are still sold for school use is because most schools don't let kids have their phones out during class and certainly don't let them out during testing.

 Posts: 7501
 Joined: Mon Dec 17, 2007 7:32 pm
Re: Slide rule anyone?
I finished high school in the 70s, so they still taught us slide rules and I had one. However, in college the first affordable calculators were available, so I never really used one.
Brian
Brian
Re: Slide rule anyone?
We called them a "Slipstick". I used them in the 50's and 60's, but then came the HP Model35 calculator. Essentially an electronic "Slipstick". The Model35 cost $395.00 in 1972 when it first came out. A unit comparable to the Model35 (that does about 1000 more things) today costs about $4.00!
Contrary to the belief of many, profit is not a four letter word!
Re: Slide rule anyone?
Message deleted.
Last edited by Sam I Am on Mon Oct 07, 2013 12:58 pm, edited 1 time in total.
Re: Slide rule anyone?
My wife taught the use of a slide rule during a summer orientation program for incoming college freshmen in the early 70s.
Re: Slide rule anyone?
Texas Instruments soon came out with the SR50 & SR51 that were much cheaper than the HP35. Might I also remind folks that we put a Man on the Moon using slide rules. I have a Pickett sitting in a desk drawer and long ago forget how to use it.
investor
investor
Re: Slide rule anyone?
Even SRs were luxury items for us when I grew up. We used logarithmic and trigonometric tables at the end of math books.
I never had a SR and would really like to have one now, but couldn't find where to buy it (without paying outrageous antique price).
The basic principle of SR is actually very easy: Two ordinary rulers can be used to do addition. For example, to do 3.2+5.6, we line the 0 on the 2nd ruler with 3.2 on the 1st ruler, then read on the 1st ruler the marking lined up with 5.6 on the 2nd ruler.
Taking advantage of the properties of logarithms, we can then do multiplications when we scale 1, 10, 100, 1000, ... (instead of 0, 1, 2, 3, 4, ...) with equal spacing on the two rulers. You can see visual illustrations of these at
http://www.jamestanton.com/wpcontent/u ... ocfile.pdf
I never had a SR and would really like to have one now, but couldn't find where to buy it (without paying outrageous antique price).
The basic principle of SR is actually very easy: Two ordinary rulers can be used to do addition. For example, to do 3.2+5.6, we line the 0 on the 2nd ruler with 3.2 on the 1st ruler, then read on the 1st ruler the marking lined up with 5.6 on the 2nd ruler.
Taking advantage of the properties of logarithms, we can then do multiplications when we scale 1, 10, 100, 1000, ... (instead of 0, 1, 2, 3, 4, ...) with equal spacing on the two rulers. You can see visual illustrations of these at
http://www.jamestanton.com/wpcontent/u ... ocfile.pdf
Re: Slide rule anyone?
"I was born with nothing and I have most of it left."
 cheese_breath
 Posts: 8192
 Joined: Wed Sep 14, 2011 7:08 pm
Re: Slide rule anyone?
I still have my old slide rules from my high school physics (1957) and college physics (1960) classes stuffed away in the bottom drawer of my desk.
The surest way to know the future is when it becomes the past.
 cheese_breath
 Posts: 8192
 Joined: Wed Sep 14, 2011 7:08 pm
Re: Slide rule anyone?
I remember the 1620 well. I did my college senior thesis on a 1620 in 1964. The college didn't have a computer yet, but a few of us had permission to use the 1620 at the Leonard refinery in town after the working folks went home for the night. Also, my second job after college was developing systems on a 1620. (First job used a 1401). The 1620 plus its peripherals took up a consderable amount of space but not nearly as much as some of the other computers of the day.whr19606 wrote:I also remember having to take a class in Bufftran, (I think that followed Fortran) and using punched cards (Hollerith code?) to load my program into the university's IBM 1620(?), which took up a significant portion of the basement in one of the science buildings.
The surest way to know the future is when it becomes the past.
Re: Slide rule anyone?
The biggest problem with slide rules is that the answers are, while correct, only approximate. On a standard 10inch slide rule, you can only get 3 signficant digits. For those who are nontechnical, those are the first 3 digits of a number. So you can get an answer like 4170 or 4180, but you cannot get an answer like 4177. This level of precision is suitable for some applications, but not for others.
Jeff
Jeff
Re: Slide rule anyone?
Sorry, that thread doesn't fit under the current forum guidelines. See: Forum Posting Guidelines  updated 2/27/12NAVigator wrote:Here is an interesting thread about slide rules; Anybody remember slide rules?
Jerry
Neither does this thread  it's a general comment with no personal consumer benefit. This topic is locked. See: Forum Policy
Note that topics must be directly connected to your (or your friend's or family's) life as a consumer. General comments or complaints about these topics will be removed.
Note that this subforum has a much lower threshold for locking or removing posts than the financial and investing subforums. ...
Re: Slide rule anyone?
After receiving a PM, I unlocked the thread.
Re: Slide rule anyone?
LadyGeek:
You are a reasonable person.
Ed
You are a reasonable person.
Ed
 nisiprius
 Advisory Board
 Posts: 37328
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Slide rule anyone?
So, about the appropriate investment of time...
Now, listen my friend, I consider that the hours I spent with a slide rule in my hand were golden. Help ya cultivate horse sense, and a cool head, and a keen eye. Didja ever try to keep an exponent in your head with the slide projectin' to th' right on an inverted folded scale? There's nothin' like a K&E log log decitrig decitrig decitrig. ManTISSA!
But just as I say it takes judgement, brains and maturity t' deal with a slug and a poundal, I say that any boob can mash a button on a calculator. And I call that sloth, my friends, the first big step on th' road to the depths of degradath' next thing you know they've got one that graphs. Graphs, my friend, right there on the screen! Now how ya gonna teach 'em, babes I tell ya, how ya gonna teach 'em to keep their wrist on the inside of the curve?
And the next thing ya' know they're Googling for answers, comin' home from school braggin' to friends about Wikipedia. Not a wholesome hundredandthirtypound set you c'n press cucumbers with, oh no, but a bunch of bits and bytes any fool can edit. Make your blood boil, don't it?
Y'got trouble, my friends, right here in River City, with a capital T and that rhymes with T and that stands for TI!
Now, listen my friend, I consider that the hours I spent with a slide rule in my hand were golden. Help ya cultivate horse sense, and a cool head, and a keen eye. Didja ever try to keep an exponent in your head with the slide projectin' to th' right on an inverted folded scale? There's nothin' like a K&E log log decitrig decitrig decitrig. ManTISSA!
But just as I say it takes judgement, brains and maturity t' deal with a slug and a poundal, I say that any boob can mash a button on a calculator. And I call that sloth, my friends, the first big step on th' road to the depths of degradath' next thing you know they've got one that graphs. Graphs, my friend, right there on the screen! Now how ya gonna teach 'em, babes I tell ya, how ya gonna teach 'em to keep their wrist on the inside of the curve?
And the next thing ya' know they're Googling for answers, comin' home from school braggin' to friends about Wikipedia. Not a wholesome hundredandthirtypound set you c'n press cucumbers with, oh no, but a bunch of bits and bytes any fool can edit. Make your blood boil, don't it?
Y'got trouble, my friends, right here in River City, with a capital T and that rhymes with T and that stands for TI!
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

 Posts: 1317
 Joined: Mon Oct 31, 2011 8:36 pm
Re: Slide rule anyone?
Before lost in a fire, I had a sixinch and fullsize K&E and a titanium circular Pickett that fell off of a camel train in the Spanish Sahara.
Re: Slide rule anyone?
Bravo, Nisinisiprius wrote:So, about the appropriate investment of time...
Now, listen my friend, I consider that the hours I spent with a slide rule in my hand were golden. Help ya cultivate horse sense, and a cool head, and a keen eye. Didja ever try to keep an exponent in your head with the slide projectin' to th' right on an inverted folded scale? There's nothin' like a K&E log log decitrig decitrig decitrig. ManTISSA!
But just as I say it takes judgement, brains and maturity t' deal with a slug and a poundal, I say that any boob can mash a button on a calculator. And I call that sloth, my friends, the first big step on th' road to the depths of degradath' next thing you know they've got one that graphs. Graphs, my friend, right there on the screen! Now how ya gonna teach 'em, babes I tell ya, how ya gonna teach 'em to keep their wrist on the inside of the curve?
And the next thing ya' know they're Googling for answers, comin' home from school braggin' to friends about Wikipedia. Not a wholesome hundredandthirtypound set you c'n press cucumbers with, oh no, but a bunch of bits and bytes any fool can edit. Make your blood boil, don't it?
Y'got trouble, my friends, right here in River City, with a capital T and that rhymes with T and that stands for TI!
Re: Slide rule anyone?
How about 5 place log tables when 2 to 3 figure accuracy was not good enough? What a pain.
Re: Slide rule anyone?
I have an old German book of 20 place logarithms. Unbelievable. I never tried to use it. It's an interesting curiousity.jwvanhoven wrote:How about 5 place log tables when 2 to 3 figure accuracy was not good enough? What a pain.
Jeff
Re: Slide rule anyone?
Love it, Nisi!Y'got trouble, my friends, right here in River City, with a capital T and that rhymes with T and that stands for TI!
You folks are bringing back some memories. I recall an aluminum Pickett, a cheap plastic one, a 6" K&E bamboo (that was my uncle's who graduated college in 1912) and even a circlular one that I never really mastered.
For an online slide rule see http://www.antiquark.com/sliderule/sim/ ... rule.html
Bob
Re: Slide rule anyone?
How many digits are the numbers they're taking the logs of?jsl11 wrote:"I have an old German book of 20 place logarithms. Unbelievable. I never tried to use it. It's an interesting curiousity."jwvanhoven wrote:"How about 5 place log tables when 2 to 3 figure accuracy was not good enough? What a pain."
Re: Slide rule anyone?
Four digits. The method of using it appears to be complex. However, all the instructions are in German which I do not read. The book was published in 1880, and there is a note by the apparently original owner that it cost $1.80 in 1904.555 wrote:How many digits are the numbers they're taking the logs of?jsl11 wrote:"I have an old German book of 20 place logarithms. Unbelievable. I never tried to use it. It's an interesting curiousity."jwvanhoven wrote:"How about 5 place log tables when 2 to 3 figure accuracy was not good enough? What a pain."
Jeff
Re: Slide rule anyone?
Four or five years ago I was watching a news program and the interviewer was talking to an artillary soldier (Marine maybe) in Afghanistan. He asked what was in the soldier's pocket. It was a slide rule. Why did he use that? Because it works every time when needed. Backup to the computers. Smart young man.
Re: Slide rule anyone?
I can do most additions in my head. For other arithmetic, all I need is a piece of paper, which is lighter than a slide rule.Taboose wrote:Four or five years ago I was watching a news program and the interviewer was talking to an artillary soldier (Marine maybe) in Afghanistan. He asked what was in the soldier's pocket. It was a slide rule. Why did he use that? Because it works every time when needed. Backup to the computers. Smart young man.
Victoria
WINNER of the 2015 Boglehead Contest. 
Every joke has a bit of a joke. ... The rest is the truth. (Marat F)
 nisiprius
 Advisory Board
 Posts: 37328
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Slide rule anyone?
Story told my my math teacher as true. College physics lectures, which the professor was frequently doing calculations with the aid of the standard threeplace log table.
The professor would announce, "One point oh five four times ten to the eighth," and a guy with a sixinch slide rule at the back of the room would then call out "One point oh five four TWO." For every calculation, the professor would announce the answer, and then the guy with the sixinch slide rule would announce it to one more decimal place.
The puzzle, for those not old enough to see it, is that a sixinch slide rule isn't even accurate to three decimal places.
It turned out that what he was doing was using the log table, along with the professor, and then using his sixinch slide rule to perform the interpolation to get one more place.
The professor would announce, "One point oh five four times ten to the eighth," and a guy with a sixinch slide rule at the back of the room would then call out "One point oh five four TWO." For every calculation, the professor would announce the answer, and then the guy with the sixinch slide rule would announce it to one more decimal place.
The puzzle, for those not old enough to see it, is that a sixinch slide rule isn't even accurate to three decimal places.
It turned out that what he was doing was using the log table, along with the professor, and then using his sixinch slide rule to perform the interpolation to get one more place.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Slide rule anyone?
...and then Buffy staked Edward. The end.
 Aptenodytes
 Posts: 3751
 Joined: Tue Feb 08, 2011 8:39 pm
Re: Slide rule anyone?
I graduated from High School in 1977, in the hometown of Texas Instruments. Everyone wanted a TI calculator, and the thing to do was get someone's dad who worked there (I only recall dads working there) to get one for you at an employee discount. Getting a TI calculator was an act of local patriotism, a step forward on the march to a better tomorrow, as well an easier way to do math problems.
In spite of all that, my high school chemistry teacher required that we do all our calculations with a slide rule. All labs, homework, tests had to be done using only the slide rule. Even the national standardized tests that affected college placement.
We joked about it and complained about it, but I am really glad she did that. It gave me a tangible connection to a long line of historical practice that was dying out. It got me to think about math in a more visceral way  the different scales used for different calculations helped reinforce the underlying principles. And  this is the most lasting effect  it forced me to think about significant digits. Whereas a calculator would spit out as many digits as the display could hold, and most people who grew up in a calculator/spreadsheet world treat them as equally significant, part of the discipline of using the slide rule was figuring out in your own head how many digits were significant and reporting only those.
In spite of all that, my high school chemistry teacher required that we do all our calculations with a slide rule. All labs, homework, tests had to be done using only the slide rule. Even the national standardized tests that affected college placement.
We joked about it and complained about it, but I am really glad she did that. It gave me a tangible connection to a long line of historical practice that was dying out. It got me to think about math in a more visceral way  the different scales used for different calculations helped reinforce the underlying principles. And  this is the most lasting effect  it forced me to think about significant digits. Whereas a calculator would spit out as many digits as the display could hold, and most people who grew up in a calculator/spreadsheet world treat them as equally significant, part of the discipline of using the slide rule was figuring out in your own head how many digits were significant and reporting only those.
Re: Slide rule anyone?
tomd37 wrote:I have a K & E slide rule sitting on the shelf above my computer that was used by both my father and older brother in their engineering studies at Lehigh University. My Dad graduated in 1920 and my brother in 1952. My memory is not too good, but I seem to remember using or being introduced to slide rule use in high school in the early 1950s.
I too am a Lehigh Engineer (not a Mountain Hawk) and my K&E loglog duplex decitrig hangs over my desk. Cost $18.50 plus $.50 to get engraved with full name by itinerant engraver at Lambert Hall dining facility. Carrying case discarded immediately as only EE's used them to carry it on their belt. Used daily for 18 years and still ocassionaly for a trig or exponential calculation. For those interested and in London there is a large exhibit of SRs at the Science Museum.MP173 wrote:Lehigh is a great school. My wife was born in Bethlehem and her uncle graduated from LU. We live in NW Indiana (her family were part of the Bethlehem  Burns Harbor migration in the 60's) and return each year. We drove thru the campus last summer.
I would like to use the SR for finanical calculations...shouldnt be too hard, just need to familiarize myself with the formulas. The issue now is the review of math from 40 years ago. My son is taking calculus in HS and just rolls his eyes when I pull the SR out.
Ed
 Epsilon Delta
 Posts: 7507
 Joined: Thu Apr 28, 2011 7:00 pm
Re: Slide rule anyone?
My five figure log table is sealed in a case labeled "Break glass in case of Y2K".
The "glass" is actually poly(methyl methacrylate) so accessing the table would take significant effort.
The "glass" is actually poly(methyl methacrylate) so accessing the table would take significant effort.
Re: Slide rule anyone?
Yeah, I figured the input couldn't have too many digits. If a book has 10^n entries, n can't be too big. And if you have x to 4 digits, I find it very hard to believe that that you could ever need log x to 20 digits.jsl11 wrote:"Four digits. The method of using it appears to be complex. However, all the instructions are in German which I do not read. The book was published in 1880, and there is a note by the apparently original owner that it cost $1.80 in 1904."555 wrote:How many digits are the numbers they're taking the logs of?jsl11 wrote:"I have an old German book of 20 place logarithms. Unbelievable. I never tried to use it. It's an interesting curiousity."jwvanhoven wrote:"How about 5 place log tables when 2 to 3 figure accuracy was not good enough? What a pain."
 nisiprius
 Advisory Board
 Posts: 37328
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Slide rule anyone?
Quite possibly the idea is to do an interpolation. I'm way too lazy to do the math but it wouldn't surprise me if linear interpolation between twentyplace logarithms with the mantissa values at fourplace intervals might be good to twenty places, and if not maybe the "complex method" involved quadratic interpolation.555 wrote:jsl11 wrote:"Four digits. The method of using it appears to be complex.555 wrote:How many digits are the numbers they're taking the logs of?jsl11 wrote:"I have an old German book of 20 place logarithms. Unbelievable. I never tried to use it. It's an interesting curiousity."jwvanhoven wrote:"How about 5 place log tables when 2 to 3 figure accuracy was not good enough? What a pain."
Hey, what the heck, let's try the experiment.
Log10(5.000) = 0.698970004336019
Log10(5.001) = 0.699056854547668
Midpoint of the logarithms = 0.69901342944185
Logarithm of the midpoint = 0.699013431612882
So linear interpolation in a fourplace table whose values are given to twenty places should be good to about 78 places, anyway.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Slide rule anyone?
Ah! the old K&E slide rule; graduated from Univ Cincinnati " 1958. Standard math tool for engineers; we M.E.'s didn't carry them on our belt either. As Nisi says made you think.
Worked for a company that designed/built equipment to put a man on the moon, nuclear containment vessels, St.Louis Arch etc. all with a slide rule.
We young engineers also stood in line to use a Monroe calculator (company only had one)that could do square roots to more significant figures. Hard to believe how the world has changed!
Worked for a company that designed/built equipment to put a man on the moon, nuclear containment vessels, St.Louis Arch etc. all with a slide rule.
We young engineers also stood in line to use a Monroe calculator (company only had one)that could do square roots to more significant figures. Hard to believe how the world has changed!
Re: Slide rule anyone?
Enjoying the comments about SRs and their applications. I have been using an online site  Ron Manley's Slide Rule for some advanced instruction.
Here is my question to all the math folks out there....I am looking for either a good book or an online site which explains certain math properties and functions, primarily for everyday use. I am NOT an engineer, but would like to understand how to use the SR for math applications. Without wading thru years of math, I am looking for everyday applications including formulas, logs, exponential use, etc.
Recommendations?
My background...late 50's, four year college degree with last class Trig (no Calculus) with a basic understanding of math functions.
Ed
Here is my question to all the math folks out there....I am looking for either a good book or an online site which explains certain math properties and functions, primarily for everyday use. I am NOT an engineer, but would like to understand how to use the SR for math applications. Without wading thru years of math, I am looking for everyday applications including formulas, logs, exponential use, etc.
Recommendations?
My background...late 50's, four year college degree with last class Trig (no Calculus) with a basic understanding of math functions.
Ed
Re: Slide rule anyone?
Oh, interpolation. I remember log tables (but not slide rules) as a kid, but I didn't remember about interpolation. You probably have an explanation there.nisiprius wrote:Quite possibly the idea is to do an interpolation. I'm way too lazy to do the math but it wouldn't surprise me if linear interpolation between twentyplace logarithms with the mantissa values at fourplace intervals might be good to twenty places, and if not maybe the "complex method" involved quadratic interpolation.
Hey, what the heck, let's try the experiment.
Log10(5.000) = 0.698970004336019
Log10(5.001) = 0.699056854547668
Midpoint of the logarithms = 0.69901342944185
Logarithm of the midpoint = 0.699013431612882
So linear interpolation in a fourplace table whose values are given to twenty places should be good to about 78 places, anyway.
 nisiprius
 Advisory Board
 Posts: 37328
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Slide rule anyone?
What I'd like to know is where the sacred Table of ThreePlace Logarithms came from.
It was always the samesame layout, same format, pretty sure it was the same typeface, and never a copyright notice or source. They'd hand them out when you took exams in many math or physics courses. It wasn't from the sacred CRC Book because that contained a fortyorfiftypage section of four or fiveplace logarithms. If I recall correctly, the standard threeplace logarithm table was a single 81/2x11" sheet with logarithms and antilogarithms on one side, and trig functions on the other.
Parenthetically, can you imagine calculating a booklength table of logarithms by hand, without so much as a MonroeMatic calculator to help you?
It was always the samesame layout, same format, pretty sure it was the same typeface, and never a copyright notice or source. They'd hand them out when you took exams in many math or physics courses. It wasn't from the sacred CRC Book because that contained a fortyorfiftypage section of four or fiveplace logarithms. If I recall correctly, the standard threeplace logarithm table was a single 81/2x11" sheet with logarithms and antilogarithms on one side, and trig functions on the other.
Parenthetically, can you imagine calculating a booklength table of logarithms by hand, without so much as a MonroeMatic calculator to help you?
I wonder if that was the same guy, or if there were many of them? Was the engraving device powered by #6 ignition cells? Did it involve a metal point that scanned across metal type, closing a circuit whenever the point touched the raised outline of the letter, and powering a solenoid that drove a sharppointed scribing device into the slide rule? A physical rasterscan? With the size of the type reduced by the ratio of the scanning movements at source and target?walnut wrote:Cost $18.50 plus $.50 to get engraved with full name by itinerant engraver at Lambert Hall dining facility.
Last edited by nisiprius on Sun Nov 25, 2012 4:30 pm, edited 1 time in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Slide rule anyone?
Pretty sure it was the same guy. Have met others from different schools with same looking ID on rule. I do remember the dry cells but not the mechanism. When finished he rubbed a red chalk or crayon into the letters. Still there along with a couple of burns courtesy of Camel cigarettes (also responsible for setting carbon paper on fire in wastebasket about once a week).nisiprius wrote:I wonder if that was the same guy, or if there were many of them? Was the engraving device powered by #6 ignition cells? Did it involve a metal point that scanned across metal type, closing a circuit whenever the point touched the raised outline of the letter, and powering a solenoid that drove a sharppointed scribing device into the slide rule? A physical rasterscan? With the size of the type reduced by the ratio of the scanning movements at source and target?
[Fixed quote admin LadyGeek]
Re: Slide rule anyone?
I didn't say what you quoted. How did my "name" get there.walnut wrote:Pretty sure it was the same guy. Have met others from different schools with same looking ID on rule. I do remember the dry cells but not the mechanism. When finished he rubbed a red chalk or crayon into the letters. Still there along with a couple of burns courtesy of Camel cigarettes (also responsible for setting carbon paper on fire in wastebasket about once a week).nisiprius wrote:I wonder if that was the same guy, or if there were many of them? Was the engraving device powered by #6 ignition cells? Did it involve a metal point that scanned across metal type, closing a circuit whenever the point touched the raised outline of the letter, and powering a solenoid that drove a sharppointed scribing device into the slide rule? A physical rasterscan? With the size of the type reduced by the ratio of the scanning movements at source and target?
[Not any more, I fixed it (and yours). admin LadyGeek]
 Nestegg_User
 Posts: 1160
 Joined: Wed Aug 05, 2009 1:26 pm
Re: Slide rule anyone?
Anyone need my old Sterling 594? (two sided dec trig loglog includes 121 page instructions) or my Concise No. 320 circular?
Needed it in the mid70's physics classes : 4 bangers were just coming out...but still expensive. I waited until later  SR52 !!
Needed it in the mid70's physics classes : 4 bangers were just coming out...but still expensive. I waited until later  SR52 !!
Re: Slide rule anyone?
Interpolation is the process of estimating a value of a function based on nearby values. Even with computers, interpolation is still a standard technique in numerical analysis. You don't need interpolation to compute logarithms, sines, square roots, or similar functions for which you have a formula. But if you have to do a complicated calculation for each value of a function and you need to compute it for many different values, you might make a table of, say, 1000 values (from 0 to 1 by .001, or from 0 to 1000 by 1), and then use interpolation from the table to get a numerical estimate.555 wrote:Oh, interpolation. I remember log tables (but not slide rules) as a kid, but I didn't remember about interpolation. You probably have an explanation there.nisiprius wrote:Quite possibly the idea is to do an interpolation. I'm way too lazy to do the math but it wouldn't surprise me if linear interpolation between twentyplace logarithms with the mantissa values at fourplace intervals might be good to twenty places, and if not maybe the "complex method" involved quadratic interpolation.
Hey, what the heck, let's try the experiment.
Log10(5.000) = 0.698970004336019
Log10(5.001) = 0.699056854547668
Midpoint of the logarithms = 0.69901342944185
Logarithm of the midpoint = 0.699013431612882
So linear interpolation in a fourplace table whose values are given to twenty places should be good to about 78 places, anyway.
Interpolation can be done with any number of terms. Linear interpolation is most common: you assume the graph from 5.000 to 5.001 is a straight line. But you could also do a quadratic interpolation: the graph from 4.999 to 5.000 to 5.001 must pass through all three points, and you find the quadratic (a parabola) which passes through all three, then use that to estimate values near 5.000; this is usually more accurate. Likewise, you could do a cubic interpolation with four values.
For those familiar with algebra: Given f(a), f(b), f(c), and f(d), the formula for a cubic interpolation is:
f(x)=
f(a)(xb)(xc)(xd)/(ab)(ac)(ad) +
f(b)(xa)(xc)(xd)/(ba)(bc)(bd) +
f(c)(xa)(xb)(xd)/(ca)(cb)(cd) +
f(d)(xa)(xb)(xc)/(da)(db)(dc)
If you plug in x=a, only the first term is nonzero, and it simplifies to f(a); similarly for the other three values. Thus you have a cubic polynomial which agrees with f at a, b, c, and d, and should thus be very close to f for values of x between b and c.
Re: Slide rule anyone?
Thank you, that was interesting.grabiner wrote:Interpolation is the process of estimating a value of a function based on nearby values. Even with computers, interpolation is still a standard technique in numerical analysis. You don't need interpolation to compute logarithms, sines, square roots, or similar functions for which you have a formula. But if you have to do a complicated calculation for each value of a function and you need to compute it for many different values, you might make a table of, say, 1000 values (from 0 to 1 by .001, or from 0 to 1000 by 1), and then use interpolation from the table to get a numerical estimate.555 wrote:Oh, interpolation. I remember log tables (but not slide rules) as a kid, but I didn't remember about interpolation. You probably have an explanation there.nisiprius wrote:Quite possibly the idea is to do an interpolation. I'm way too lazy to do the math but it wouldn't surprise me if linear interpolation between twentyplace logarithms with the mantissa values at fourplace intervals might be good to twenty places, and if not maybe the "complex method" involved quadratic interpolation.
Hey, what the heck, let's try the experiment.
Log10(5.000) = 0.698970004336019
Log10(5.001) = 0.699056854547668
Midpoint of the logarithms = 0.69901342944185
Logarithm of the midpoint = 0.699013431612882
So linear interpolation in a fourplace table whose values are given to twenty places should be good to about 78 places, anyway.
Interpolation can be done with any number of terms. Linear interpolation is most common: you assume the graph from 5.000 to 5.001 is a straight line. But you could also do a quadratic interpolation: the graph from 4.999 to 5.000 to 5.001 must pass through all three points, and you find the quadratic (a parabola) which passes through all three, then use that to estimate values near 5.000; this is usually more accurate. Likewise, you could do a cubic interpolation with four values.
For those familiar with algebra: Given f(a), f(b), f(c), and f(d), the formula for a cubic interpolation is:
f(x)=
f(a)(xb)(xc)(xd)/(ab)(ac)(ad) +
f(b)(xa)(xc)(xd)/(ba)(bc)(bd) +
f(c)(xa)(xb)(xd)/(ca)(cb)(cd) +
f(d)(xa)(xb)(xc)/(da)(db)(dc)
If you plug in x=a, only the first term is nonzero, and it simplifies to f(a); similarly for the other three values. Thus you have a cubic polynomial which agrees with f at a, b, c, and d, and should thus be very close to f for values of x between b and c.
gatorman
 nisiprius
 Advisory Board
 Posts: 37328
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Slide rule anyone?
A standard table of logarithms has a little table in a narrow column on the right called "Proportional Parts." These are a precalculated interpolation table so that you can get one more decimal place than is tabulated. It relies on the fact that successive differences from one entry to the next within the table stay the same for many lines of the table; for example, if I look up log sin 21°, 21° 1', 21° 2', 21° 3', etc. I see 9.55433, 9.55466, 9.55499, 9.55532, etc. The difference between one entry and the next are all 0.00033. So I look at the right where there's a column labeled "P. P." and under the heading "33" I find
1 0.6
2 1.1
3 1.6
etc. So if I need to know log sin 21°1.3' I take the value for 21° 1' and add 1.6 (rightaligned to the edge of the digits), and I suppose roundit's not anything I really did very muchand say "9.55466 + .000016 = 9.554676 rounds to 9.55468"*
Even in the 1950s and 1960s, there were a lot of humble things one did to simplify calculations. There were IBM 1620s and such around, but they weren't for everyone. In 1975 a biguniversity Zoology department had exactly one Monroe rotary calculator for use by grad students, and we thought that was fairly decent of them. It was a very fancy modelit actually had a "memory" feature that would save and restore a single number. And because it was so fancy, it was constantly out of order and being repaired.
One of the more interesting things I ran across, given that the purpose of logarithms is to reduce multiplication to addition, was a book with a fiftyorsopage "Table of Half Squares" in it. Why would you want that? You want to multiply a x b? You add them, a + b, look up the half square, then you subtract them, a  b, look up the half square, then you subtract the halfsquares. See, it's just one addition and two subtractions instead of a multiplication.
It is quite a different world when multiplication and division aren't effortless, instantaneous, and free everywhere for everyone all the time.
*I do believe I screwed up. Did anybody notice? I'm staring that that antique CRC book, and do believe I looked up the proportional parts for 3 seconds of arc, not 0.3 minutes, and that 9.55468 is log sin 21° 1' 3''. And that actually they seem to be adding 10 to the logarithms for some good reason I no longer know.
1 0.6
2 1.1
3 1.6
etc. So if I need to know log sin 21°1.3' I take the value for 21° 1' and add 1.6 (rightaligned to the edge of the digits), and I suppose roundit's not anything I really did very muchand say "9.55466 + .000016 = 9.554676 rounds to 9.55468"*
Even in the 1950s and 1960s, there were a lot of humble things one did to simplify calculations. There were IBM 1620s and such around, but they weren't for everyone. In 1975 a biguniversity Zoology department had exactly one Monroe rotary calculator for use by grad students, and we thought that was fairly decent of them. It was a very fancy modelit actually had a "memory" feature that would save and restore a single number. And because it was so fancy, it was constantly out of order and being repaired.
One of the more interesting things I ran across, given that the purpose of logarithms is to reduce multiplication to addition, was a book with a fiftyorsopage "Table of Half Squares" in it. Why would you want that? You want to multiply a x b? You add them, a + b, look up the half square, then you subtract them, a  b, look up the half square, then you subtract the halfsquares. See, it's just one addition and two subtractions instead of a multiplication.
It is quite a different world when multiplication and division aren't effortless, instantaneous, and free everywhere for everyone all the time.
*I do believe I screwed up. Did anybody notice? I'm staring that that antique CRC book, and do believe I looked up the proportional parts for 3 seconds of arc, not 0.3 minutes, and that 9.55468 is log sin 21° 1' 3''. And that actually they seem to be adding 10 to the logarithms for some good reason I no longer know.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
 Epsilon Delta
 Posts: 7507
 Joined: Thu Apr 28, 2011 7:00 pm
Re: Slide rule anyone?
The general approach is:nisiprius wrote:Parenthetically, can you imagine calculating a booklength table of logarithms by hand, without so much as a MonroeMatic calculator to help you?
1) Some high grade mathematician works out an infinite series that approximates the function.
2) A midgrade mathematician generates the coefficients for a number of finite polynomials that approximate the function with sufficient accuracy over intervals that cover the range needed.
3) A calculator (it was a job title) evaluates the polynomials for all values using only addition/subtraction.
4) Typesetter takes output and sets type and prints tables.
5) Captain runs ship aground because one of the above messed up.
This is why they invented difference engines. These avoid errors at step 3 and by automatically typesetting the results avoid errors at step 4. Furthermore because they eliminate some of the premium on short polynomials they help the first two steps as well.

 Posts: 9488
 Joined: Fri Mar 02, 2007 2:39 pm
Re: Slide rule anyone?
Ah, the juxtaposition between slide rules and calculators. Reminds me of a time long ago and a place far far away. Midseventies, "A" and "C" schools. Slide rules and newly released TI SR50 red LED calculator (bought one for 50% of my monthly military pay).
Deployment to a body of water were we did not exist and there were no sharks Computational failure of both primary and secondary navigation systems during blind hispeed transit. In danger of "buying" a "piece of the rock", and I don't mean Prudential. My new calculator failed, senior SINS tech did continual complex computations from raw data using a military issue circular slide rule.
That was 35 years ago. Imagine how much more dependent we are on technology. Who among the general population could survive without modern technology. I still have that circular slide rule. I haven't touched it in over thrity years. Might be time to break it out and exercise the mind.
Deployment to a body of water were we did not exist and there were no sharks Computational failure of both primary and secondary navigation systems during blind hispeed transit. In danger of "buying" a "piece of the rock", and I don't mean Prudential. My new calculator failed, senior SINS tech did continual complex computations from raw data using a military issue circular slide rule.
That was 35 years ago. Imagine how much more dependent we are on technology. Who among the general population could survive without modern technology. I still have that circular slide rule. I haven't touched it in over thrity years. Might be time to break it out and exercise the mind.