The fact that the earth wobbles was expected/predicted long before it was observed, which makes for a couple stories about the nature of science and the people who do it. The story of the Chandler wobble starts up almost a century before Chandler was born. In 1765, the Swiss mathematician Leonhard Euler, whose name appears throughout mathematics and physics, was examining the mathematics for conservation of angular momentum on a rotating spheroid -- i.e., something like the earth. It turned out that such a body could have a wobble on top of its regular rotation. Given what was known about the shape of the earth then, Euler predicted a period for his wobble of about 305 days. (Modern information doesn't change this number much.)
The magnitude of such a wobble could also be estimated from the law of conservation of angular momentum, and was somewhere around 0.1 seconds of arc. That made for a difficult observation in 1765, and it wasn't until 1841 that astronomers started trying to observe this 10 month (305 day) wobble. Given data analysis methods of the day -- pencil and paper -- analyses were done looking to see if there was a signal with a 10 month period. No such signal was found, even though several people looked. Side note being that one of the astronomers who looked in to this was Friedrich Bessel, who was the first person to measure the parallax (thence distance) to a star. Quality of observing skill was not an issue in his failure to detect the wobble.
Enter, then, in the late 1880s the next start of our story, and some options of how to tell it. I could tell the story about a 'lone genius, toiling in obscurity until his great moment'. It would be doing some fair amount of violence to reality, but that hasn't stopped all story tellers. Chandler was indeed not being paid to do science. He made his living as a merchant. But keep in mind, though, that in the 1800s, 'scientist' even as a label was fairly new, and very few people who were scientists, or rather, who were doing science, did it full time. Many were men of independent means who used their free time to try to understand the world.
Chandler was one such, but his roots in astronomy extended far back -- to high school.
In his last year of high school, he performed mathematical computations for an astronomer. After graduation, he become the assistant of another astronomer. Later, he worked in the US Coast Survey -- later named the US Coast and Geodetic Survey. The science of determining the size, shape, orientation, and rotation of the earth is Geodesy (belated spoiler alert). Then he changed areas of work, married, had children and other usual things. But he was still pulling out his telescope to observe the stars, and in touch with at least one major astronomer.
His story gets more active in the 1880s, by which time he's over 40. He invents his own instrument to measure the passage of stars overhead. The reason for concern about this is that all astronomical observations were made from the earth, so knowing that it was the earth that moved rather than the stars, is crucial. Getting more precise understanding of the earth's orientation, then, helps interpret all other astronomical observations -- the kind of calculations that Chandler was doing for his astronomer mentors, and in the Coast Survey.
After collecting a bunch of data, ensuring that it was high quality data by making improved instruments himself, Chandler made the key different choice from Bessel and others. Rather than look just at the expected period of 10 months, he took on the far greater workload of analyzing the data for variation at all periods. Out came a peak at 428 days (~14 months), not the expected 305. Chandler then extended his work to look at the data collected by other people in the previous century, again finding an about 14 month period in the earlier data.
So the real key was not the quality of the data, but doing the analysis without expectation. Rather than thinking ill of any of the previous researchers, congratulate the amateur. Analyzing without expectation meant doing thousands of computations by pencil and paper. No computers in 1891!
The follow up is that within the next year Newcomb presented the physics that explained why the wobble's period was so much longer than expected. In doing his computations, Euler had worked with a rigid earth. But the earth is not exactly and entirely rigid. It has some give to it. This was known to be true before Euler, but there was no reason to consider it to be important for the wobble, so no computation. Given the observations and analysis of real wobble by Chandler, Newcomb took up that extra calculation -- applying Euler's mathematics but to an earth that is somewhat elastic. Bingo. As the earth flexes a little bit while wobbling, it slows down the speed of the wobble.
This is an opportunity that amateurs missed. The calculation of wobble for a flexible earth could have been done any time between 1765 and 1891. But nobody did. This strikes me as a recurring theme in the history of science. Observations make something theoretically interesting, so then a theoretician is motivated to work on an explanation. The converse is also illustrated in this story -- a theoretical calculation (Euler's) motivates observers to perform particular observations and analyses.
For more than a century (this is a really slow moving story), the effort on Chandler Wobble turned to trying to explain why it's still around. So more blogging to come.
In the mean time, a bit of opinion about amateurs. One of the situations in which I think amateurs have the most room to contribute is what Chandler did -- being able to analyze data without preconceptions. Professionals these days have to propose what they're going to find, and that what they're going to find is significant. The 'no preconceptions' doesn't fit well with that. You might not find anything, and if you do, it may not be significant. The professionals then move on to what they expect to be the richer area.
If you're doing something because you love it, on the other hand, even if you don't find anything, you've been doing something interesting, so a win. If you find something, but it isn't interesting to the professionals, it's still interesting to you, and you did find something. Even bigger win. And every so often, like Chandler, you'll find something that is very important.
I'd also suggest emulating Chandler in a different way. Namely, he was in regular contact with the professionals in the area. While his work wasn't something many were interested in doing themselves, it was worth discussion.