Blue View - The Great Mechanical Computer

Marcie wrote a blog earlier this week about visiting the Kinzua Skywalk, the remains of the magnificent railroad trestle that crossed the Kinzua Valley in Pennsylvania. When it was completed in 1882, it was the longest and tallest railroad bridge in the world. In fact, until it was partially destroyed by a tornado in 2003, it was still the fourth highest railroad bridge in America, 121 years after it was built.

It was designed by the brilliant engineer Octave Chanute. He used a new technology, hollow iron tubes called “Phoenix Tubes”, to construct the support towers, which were supported by sandstone masonry piers.

I have the highest respect for civil engineers in general. As an electrical engineer, if I make a mistake, maybe I’ll fry a resistor or blow a fuse, whereas if a civil engineer makes a mistake, his bridge falls down. I can only imagine the number of calculations Mr. Chanute completed to ensure his iron towers and footings could withstand the worst case winds in the valley and/or flood waters of the river below, coupled with the weight, vibration and wind resistance of a loaded coal train working its way across the top of the trestle. In addition, he made all those calculations without the help of a calculator or computer.

As I was contemplating all this, it occurred to me that a good slide rule would have made his job a whole lot easier, and that it was unfortunate that slide rules hadn’t been invented yet. Or were they? When were slide rules invented, anyway?

If you were born after 1965 or thereabouts, you probably don’t even know what a slide rule is. In its simplest form, a slide rule was used to multiply or divide two numbers. They could also be used to calculate square or cube roots, trig functions and logarithms. Specialized slide rules were also available for aviation, nautical and financial calculations. In high school and college, you could immediately spot the science, math and engineering geeks by the slide rules hanging from their belts.

A slide rule works on the principle that adding the logarithms of two numbers produces the logarithm of the product of those numbers. That’s not nearly as complicated as it sounds. (An aside here. When Marcie proofed this, she asked me whether I should explain what a logarithm was. Good point! By the time I was two or three sentences into my very convoluted explanation, her eyes were glazed over and I realized that you, the reader, either (a) already knew what a logarithm was, or (b) didn’t know and couldn’t care less. In either case, this blog is better without the explanation. If you would like more info on logarithms, here’s a Wikipedia link. Now, back to my blog…). If you wanted to make a very simple adding machine, you could use two rulers, one placed above the other. Let’s say you wanted to add two plus four. Slide the top ruler to the right until its end lines up with the two on the lower ruler, then look to see what number on the lower ruler lines up with four on the top ruler. Most of us don’t need help adding two plus four, but it would be a quick way to find the sum of 3-7/16 and 4-3/8.

Now, what if we calibrated the scales on each ruler using the logarithms of the numbers. For example, the logarithm (log) of two is .301, so we put number two, 0.301” from the end instead of two inches. Likewise, the log of four is 0.602, so number four goes 0.602” from the end, and so on. Once we placed all the numbers between one and ten on our rulers, they would look like the two shown below. If we add two plus three on our new rulers, we’re actually adding the logarithms of the two numbers, and the result will be the log of the product of the two, or six. We can also divide two numbers by reversing the process, so we now have a cool little machine that can multiply and divide. Most actual slide rules looked a great deal more complex than our two rulers, as more scales were added to calculate things like trig functions, but for basic multiplication and division, they were no more complex than our rulers.

So, when was the slide rule invented? John Napier, a Scottish mathematician, began developing the concept of logarithms in the late 1500s. Based on his work, the English mathematician, William Oughtred is credited with inventing the first slide rule in the early 1600s. By the late 1800s, when Octave Chanute was designing the Kinzua railroad trestle, slide rules were well known and widely available, so my guess is he was pretty good on the old slipstick.

BTW, K&E and Pickett were the two biggest slide rule manufacturers in the U.S. When electronic calculators were introduced around 1970, the handwriting was on the wall. When calculators became cheap enough for students to buy in the mid 1970s, the slide rule market totally collapsed, and both companies shut down their slide rule manufacturing plants within just a couple of years. Slide rules are now collectors items. Bummer - I think I sold mine at a garage sale for a quarter, 40+ years ago.

See you next week…