 Before electronic computers, people built mechanical computers to perform specific mathematical operations. One such machine was this, Albert Michelson's Harmonic Analyzer. This 19th-century machine adds together cosines to create intricate patterns. Amazingly, it also does the inverse operation. It can take a pattern and reveal the cosines that, when added together, will approximate it. This operation is called Fourier analysis and is possibly the most important mathematical technique of the past 100 years. Without Fourier analysis, there would be no MP3s, JPEGs, or cell phones as we know them today. To celebrate this stunning machine and to gain a greater insight into what Fourier analysis is and how it works, I'll share in this video some history of this analyzer and then in three additional videos detail its operation. In synthesis, I go step by step and examine the key components of the machine and how each plays its part in adding cosines. In analysis, I show you how the machine uses the same mechanical motions to find the frequency components of a signal you want to analyze. And in operation, I show the steps an operator of this machine must go through to perform these calculations. This machine's designer, Albert Michelson, was famous for measuring the speed of light. Yet he also measured many other properties of the universe precisely, like the diameter of stars or the rigidity of the earth. In the late 19th century, he performed Fourier analysis by hand to help resolve fine details of the light emitted by vaporized elements. He was doing an early version of Fourier transform spectroscopy. These hand calculations were laborious, so he invented this machine to automate these calculations. He built a prototype machine similar to this one in 1897 and then a larger prototype four times the size a year later. The machine was then commercialized by William Gartner and company. They made precision scientific instruments often designed by Michelson. In their 1904 catalog, they advertised this machine, which can add up to 20 different sinusoids, as well as a larger version that calculated with 80 sinusoids. We know that in the early 20th century, Gartner sold at least four of these machines, and based on that, it seems this 20-element machine sold for around $225, and that it was likely made between 1901 and 1910. After this period, the machines are mentioned only occasionally. We found pictures of several different configurations until it made one last public appearance in an improved form at the 1933 World's Fair in the Great Hall of Science in an exhibit called The Magic of Analysis. Our machine has an unknown history. We're not sure when it arrived here on the University of Illinois campus. We only know that for at least the last 40 years it is set in a glass case in Altgeld Hall. It's gears completely still. Join me as I bring back to life this stunning mechanical computer. I'm Bill Hammack, the Engineer Guy. In this series, synthesis, analysis, and operation. Click here to learn more about the book and posters that accompany the videos. Here we go page by page through the entire book and point out some extra details. And here you can sit back and watch the rocker arms move up and down over and over.