Log tables - I remember them well - a sign of my age I suppose. In fact I’d rather like to own a good one. (I did last year pick up a 1933 Collins Wireless Diary which has much useful information about postage, telegraphy, electronics, wireless (aka radio), a little on television, and also some log and trig tables.)
But here, courtesy of @sohkamyung, is Charles Petzold’s online book, a work in progress, all about logarithms. The first chapter covers log tables, the slide rule is sure to appear later - but many chapters are not yet present.
This type of long division is known as the column division method. It is not the type of long division I was taught in grade school. I was taught the partial quotients method (also known as chunking or hangman), and I don’t know what kids are taught these days. But the important (and depressing) point is that division is so bad that nobody is really sure of the best way to do it!
I don’t know of this other method - perhaps someone here learnt it?
I can almost guarantee that my great-grandfather contributed to that! Peter S. Caldwell was professor of Mechanical Engineering at the Royal Technical College in Glasgow. He contributed all sorts of technical tables for Collins and Letts diaries for a very long time. He’s unlikely to be credited, though.
I just looked up column division and partial quotients, and I don’t think either of those are the method I learned in school – although partial quotients is rather similar in some respects. (In fact, I feel like it’s kind of a generalization of the specific method I was taught, and it’s more similar to what I tend to do in practice to approximate long divisions in my head.) I have no idea what the method I was taught is called, we just called it “long division”.
Like Ed (and probably many others!) I used “3 figure tables” at school too - they had more than just Logs in them with sin/cos/tan, etc.
Luckily I was given a slide rule and was allowed to use it if I could demonstrate it’s correct use, so off I went…
This was on the cusp of electronic calculators and got one in ~1976 although I wasn’t allowed to use it in maths - but in engineering and physics they didn’t mind.
A few years later, I went to Napier Uni. to (initially) do computing and while we did a bit of maths they never really went into Napiers rods method of calculations although his originals were on display in a part of the building I latterly worked in.
Here’s my Chambers Four-Figure Mathematical Tables (with Proportional Parts for Tenths card insert). It has 65 pages, and cost me 50p in about 1981, when it was already practically obsolete - my edition was printed in 1974.
I may have just placed an order for second hand copies: one of four-figure and another of five-figure tables. I quite like the older ones, even the ones from before my time.
There’s a scan of Knott’s four-figure tables on the Internet Archive - it contains lists of primes and factorisations as well as the expected tables. And it has some physical constants. And a bonus table of just 30 six-figure logarithms, for numbers which look like plausible interest rates.
Here’s a clip of the page giving factors of odd numbers up to 999:
The fact it was acquired by the U. Alberta library in 1988 as a historical book shows how quickly log tables faded away. The Archive has a huge array of log tables, from huge 7-figure tomes down to little 3-figure booklets. As I’m firmly of pocket calculator age, we had the Blackie & Chambers Three-figure tables made available for exams, but with its weird logo mostly scribbled upon by bored students.
I may need to re-read Petzold’s website, but I found it rather fragmented. It seemed to spend much more time on calculations of sines and cosines than logs. I know it’s a draft website, so it’s still a decent piece of work.
PS He worked on binary arithmetic and mechanical computing. I like to think he was the first computer scientist in our family and I was the second after a short delay Check out his Promptuary. (There’s a wikipedia article on it but this system won’t let me post if I include the URL to it) See the notes on location arithmetic and his use of a chessboard in one of the articles on Napier's Binary Chessboard Calculator - Napier's 'Rabdologiae' | Mathematical Association of America
My Dad gave me my own copy of Chambers Seven Figures tables and a slide rule when I was around 11 or 12. (I think I still have the book, not so sure about the slide rule.) I remember being allowed to keep the slide rule in a maths exam, while a few of the richer kids with the early calculators were not allowed to use them That would have been around '73 or '74 I think. My first ever computer program (written when I was in 2nd year at high school, on coding sheets which Moray House students then punched on to cards) was to print out a few pages of logs in formatted columns. Actually I think my (BASIC) program would have tried to print an entire book’s worth but the folks at Moray House were smart enough to put a very small output limit in the JCL to stop stupid programs just like that. I think the actual jobs ran remotely at UMIST on the 360 down there. Turnaround time for the high-school student jobs was between one and two weeks. The Moray House students who were paid to rekey the coding sheets onto punched cards were not allowed to fix any mistakes they spotted so even a trivial syntax error would invoke the week+ delay!
We still had card punches in my first year at Edinburgh (1976) which were used for applied maths (eg things like the Simplex algorithm) but they were gone some time in the next 2 years, plus or minus 1. By my second year when I switched from Chemistry to Computer Science, we (i.e. computer science students) were allowed to use the interactive terminals, and since the card punches were only in one building that I no longer had any need to go to (Alison House) I didn’t personally note exactly when they were removed.
I seem to remember being told that the IBM 1130 at System Source - which came out of Ontario Hydro’s billing centre, perhaps in Markham - was in use until the mid-80s
We used optical mark cards in our high school in the west coast mountains of Canada right into the eighties. Initially the optical card reader was part of a DEC Classic system but replaced with an Apple II lab with a Chatsworth optical card reader circa 1980. The primary use was BASIC assignments on optical mark cards that would be batch processed.
