Yes, Dave is right. You can do square roots on a Curta. It is a trial and error method of repeated division, but it works quite well and once you've done a few it's not all that hard.
Actually it would have been sufficient for traverse calculations given the instrumentation most people were using when the 4102 came out. Most people were using a one minute transit so this level of caalculation was quite useful.
Me too Dave, but it was 50+ years ago for me when I used to do it.
I realize that the slide rule was a better fit and match for the perceived accuracy of the technology of it's era, but I find myself now trying not to oversell it's application to today's surveyors who have a curiosity about it.
There is no great miracle, but it is another tool that had it's time and place.
On the other hand I did learn slide rule in high school and used it through college in physics. But in most of chemistry and physics 3 places was good enough.
It is always valuable the have testimony from those who have used the tools, as opposed to the assumptions of some of us who are trying to learn about how things were done.
Good information...
There is a video on youtube on a method to do square roots that is pretty good.
Now on to logs? no..
I used one for a couple years until calculators became affordable. I do not miss them.
That was really cool, Rich.
"Now on to logs? no.."
I suppose I'm becoming predictable, Jerry. I just pulled Dad's old Basic Mathematical Tables book out yesterday. I was taught the basic of logs in school (even though their prevalence in everyday math had already passed). But messing with the slide rule I found new appreciation for the logarithms. I read several times that slide rules are logarithmic scales, but it wasn't until I played with one that I really understood that. Since logarithms allow addition to represent multiplication and subtraction for division, it makes sense that two scales could be joined together to add a length (divided logarithmicly) to another length (also divided logarithmicly) for multiplication.
Since I never used logs on a production level (only for the exercise of it), I started wondering if logs of trig functions were available in tables of the day. It seemed this would be a slick way to apply the sine of an angle to a distance very quickly by simply adding two numbers (log of the distance and log of the sine). So I pulled out the old book of tables and sure enough, there they were. Interestingly, the sine and cosine and tangent logs are all expressed as 10 minus the log (a lot of 9.xxxx) Not sure why this was done instead of listing it directly (such as -0.xxxx).
Thanks for all of the replies so far. I certainly don't plan to give up my electronics, but these things stretch the mind. For instance, I had never been taught the odd number subtraction method for determining square root (as the video Rich linked shows with a Curta). So late last night I'm Googling "Square Root Determination by Odd Number Subtraction." You just never know where this stuff will take you sometimes, except that you will likely know more when you're done.
These discussions also make me appreciate the genius of the minds of those left to more crude devices. They built engineering marvels, designed vehicles to traverse the skies and heavens, landed on the moon, and very accurately determined the size and shape of the Earth with these things.
Dave,
I definitely need to get with you. I would love to give a traverse calculation a go on one.
There was an old surveyor here locally that did incredible work. When everyone else was reporting to the degree and sometimes minute, and foot and sometimes tenth, he was reporting to the second and to the thousandth in the 50's. The thousandth was obviously ridiculously optimistic, but he actually was pretty good to the few hundredths - using a chain, even over long distances and uneven ground.
I only mention the chaining work to show just how meticulous he was. He was a very uncommon breed and was probably an SOB to work for to produce those sorts of results (I can only imagine). Another rare thing he did was to put his work on some form of astronomic bearing. Sometimes his bearings would be very, very good. Tens of seconds from true - these times I suspect he observed Polaris. But most of the time he was around 2-3 minutes. Here I think he used the altitude method to observe the Sun. I bring all of this up because I wonder if he reduced those observations on a slide rule like the 4200.
I can only guess, for all of the great work he did, his successors did not take the responsibility of perpetuating his legacy seriously. They have done poor survey work, tarnishing what should have been a sterling reputation, and do not share anything about their progenitor such as old maps or personal history. Basically a legacy lost.
>10 minus the log (a lot of 9.xxxx)
The table gives the log of the function plus 10, or conversely the log sine is the table value minus 10.
The sine and cos, (and for less than 45 deg the tangent) are less than 1 so their log is negative. In order to do as little subtraction and dealing with negative numbers as possible, the table added 10. Note that the sine is an increasing function of angle and the log sine in the table also increases, showing that it can't be 10-log.
yep... you're right.
Square root calculators
Friden mechanical calculators had a square root model. You could key in up to 14 digits, and a row of buttons at the bottom represented the decimal point. Push the key for the decimal point, and the machine would then calculate the square root.
Back in 1972, I used to spend days with a square root Friden computing the diagonals of variance-covariance matrices when preparing to compute a new photo-triangulation block merge with a previously-computed block.
After work that day, it would be a couple of hours before the sound of that calculator stopped ringing in my ears.
Used to use one to solve RC problems in electronic engineering in school. Took a few minutes per problem with the rule as opposed to 30 mins. each longhand.
