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PROVO - Pioneer children sang as they walked and walked and walked - 1,032 miles along the Mormon Trail from Winter Quarters, Neb., to the Salt Lake Valley.
Not 1,031 miles, not 1,033, but 1,032.
They knew because a few of them kept track using a remarkably accurate odometer affixed to one of their wobbling wagon wheels.
This wooden "roadometer" was the precursor to the modern mile tracker. Unfortunately, the original device no longer exists.
So Brigham Young University engineer Larry Howell decided to bring the historical distance counter back to life.
Blending historical information from pioneer travel records with a mathematical algorithm, Howell used his gear-mechanism know-how to build an exact replica of the 1847 creation.
"It's the first time since the original was made that we have the right dimensions," Howell said. "They were considered to be unknown for all these years."
Howell's excitement about the specifics is important because he's not the first to build a replica.
The Pratts - of Pratt Wagon Works in central Utah's Cove Fort - have built a bunch, including one attached to a replica wagon that sits in the LDS Church's Museum of Church History and Art in downtown Salt Lake City.
"We knew the number of teeth on the wheel, and the dimensions of the box, but we didn't have the diameter of the gears," Ben Pratt said. "We made the box the right size and made the gears to fill the space, and that's it."
Howell has seen those replicas, but said his work, teamed with the craftsmanship of BYU student Joey Jacobsen, is a bit more precise.
Still, Howell believes what he has done doesn't measure up to what the original pioneer cast created 159 years ago.
"They were out in the forsaken wilderness of Nebraska and did what I consider to be a research-and-development project," Howell said. "The fact that they were willing and had the vision to do that in the circumstances that they were in, I think, was really pretty amazing."
The brains behind the original odometer was Mormon pioneer Orson Pratt. With sponsorship from then-LDS Church President Brigham Young, Pratt had craftsman Appleton Harmon build the device and sent William Clayton out to use it.
Clayton had the arduous task of watching each notch-turn of the odometer, then tracking the results. In the end, he was able to mark the distance between watering holes and camps for future wagon teams.
Jacobsen said he and Howell went the extra mile to remember their forefathers' sacrifices during the replica-building process.
"We tried to put ourselves in their footsteps," Jacobsen said. "We asked ourselves: How would they have done this, what would they have done?"
"But it took us a lot longer to build than it took them," Howell added. "We have modern engineering tools and computers, but it still took many times longer. Of course, we were trying to figure out how it was done."
Howell's project was more than the culmination of his personal curiosity.
Research from the BYU professor's historical rebuild will be published during a symposium this September for the American Society of Mechanical Engineers.
It was a matter of coincidence Howell and Jacobsen finished their work in time for Pioneer Day. As nifty as they think the resurrected device is, however, the two concede not everyone is turning cartwheels over it.
"We are at the dinner table and my 15-year-old son, Nathan, looks up at me and says, 'Dad, nobody cares about 150-year-old gears,' " Howell said.
Then again, Nathan Howell wasn't one of those pioneer children who sang as they walked and walked and walked and - walked.