Edisto Island, South Carolina and Alexander Bache's

My wife and I took a trip to Edisto Island, South Carolina this June, camping a couple of miles from the beach in a rented, teardrop camper. The campsite adjoined Botany Bay, a plantation-cum-nature-preserve with gorgeous beach access.

In hiking Botany Bay's grounds, just past the Bleak Hall Ice House, we followed a sign for the Bache monument, neither of us having any idea what the Bache monument was - or how to pronounce Bache. After a fair number of twists, turns, spider webs, and uncertain left and right turns, we came upon a two and a half foot tall, four-sided, low-slope peaked granite monument inscribed with the name Bache and a few other things that meant nothing to us.

Heck, we didn't even take a photo, the monument was so uninteresting and unassuming.

Until we hiked through Edisto Beach State Park the next day, finding ourselves at the education center in the far, western edge of the park. There we found a second Bache monument, thankfully along with educational placards explaining just why that unassuming granite tower was remarkably important and interesting.

I'll start with the informational placards then follow up with my explanation and interpretation.

See, Alexander Bache, great grandson of Ben Franklin and superintendent of the United State Coast Survey, invented (or at least improved upon) the bar of invariable length.

I know, you're as excited as I was before I read that first placard up top. The Coast Survey was trying to measure a few lengths on the coast with great precision, knowing - as the last placard shows - that a single accurate length measurement plus two angles to a third point would allow for the calculation of other lengths and areas up and down the Atlantic coastline. But a first length had to be measured, and the longer, the better.

The issue at hand, however, was that any measuring tool invariably expanded in the hot, South Carolina summer. What was needed was a bar of invariable length.

As Alex Hebra shows, a bar of two metals constructed correctly could compensate for the expansion of each other.

And that's what we see in the first two placards above, Alexander Bache's bar of invariable length. I don't, admittedly, understand Bache's diagram, but I understand the idea that he solved the problem of expanding and contracting measurement standards, allowing for precise and accurate measurements of great length.

As NOAA records...

Bache carried this principle one step further by coating the bars with a lacquer that was meant to assure that the bars and the different metals making them up absorbed heat equally, thus minimizing any expansion during changes of temperature. Although improvements in accuracy of measurement of this type of bar over Hassler's apparatus were questionable, the increased efficiency of this new instrument was proved beyond a doubt. Bache personally directed the measurement of the first baseline to be determined by this instrument on Dauphin Island, Alabama, in 1847. The greatest length measured on one day was nearly seven-tenths of a mile, while the whole seven-mile base line was measured in seventeen working days. By remeasuring portions of this base line and comparing the observed differences, Bache ascertained that the base line had a probable error in length of only 0.5 inch. The Bodie Island, North Carolina, base line was measured in late 1848. This base line was 6 and 3/4 miles long and required only 10 working days to complete. The greatest progress per day on this line was 1.06 mile and Bache's estimate of the probable error of measurement over the whole line was 0.1 inch.

Or, as The Post and Courier wrote...

Miller says surveyors recently used GPS to calculate the accuracy of Bache's work, and they discovered that its 6.68-mile length was a tad off.

By about 2.5 inches.

2.5 inches over 6.68 miles?

That's 2.5 inches in 423244 inches.

That's 5.91 x 10^-4 percent error.

I'd be okay with that.

And I'd think that deserves a few historical markers. Here are the photos of the one in Edisto Beach State Park. The one in Botany Bay was identical but without any explanation.

Notice how excited my wife is about the whole story.

It was only after doing some reading that I realized how important those posts are.

And don't even get me started on the pervious concrete nearer the education center...

The bar of invariable length had its remarkable era, and I'm glad I got to see it.