Gadsden Purchase: How the US gave up a Vermont (and got part of it back)

The history of the US is mostly one of expansion, sometimes through military acquisition and sometimes via purchase. When the US had an opportunity to buy land, they have normally taken it.  Normally. There are a few times in US history that the country gave up territory (the Panama Canal zone, The Philippines, US Trust Territories and Corn Island, for examples) and a couple of times that places came looking for annexation and were rebuffed (part of the Dominican Republic did so), but only one time that the US had a deal in hand to buy land and  turned that land down. That came during the Gadsden Purchase. 

As the State Department describes it

Gadsden met with Santa Anna on September 25, 1853. President Pierce sent verbal instructions for Gadsden, giving Gadsden negotiating options ranging from $50 million for lower California and a large portion of northern Mexico to $15 million for a smaller land deal that would still provide for a southern railroad....

Santa Anna refused to sell a large portion of Mexico, but he needed money to fund an army to put down ongoing rebellions, so on December 30, 1853 he and Gadsden signed a treaty stipulating that the United States would pay $15 million for 45,000 square miles south of the New Mexico territory....  

With a great deal of difficulty resulting from the increasing strife between the northern and southern states, the U.S. Senate ratified a revised treaty on April 25, 1854. The new treaty reduced the amount paid to Mexico to $10 million and the land purchased to 29,670 square miles.

The original copy of the treaty that Gadsden negotiated defined the border as "From the existing border at the Colorado River, south along that river to a point two marine leagues north of the most northern part of the Gulf of California; then in succession a right line to the intersection of the 31st parallel of latitude north with the 111 degree of longitude, whence another right line to the 31deg 47' 30" north latitude, where the same will cross the boundary line, descending to the Rio Grande to the Gulf of Mexico." There was a contingency if it was discovered that the boundary bisected Lake Guzman, but the lake turned out to be far south of the defined line.[1]

The boundary was then modified by Congress on April 10, 1854 to appease northerners who wanted as little future slave territory as possible.  The change was approved by Mexico and the President and that deal created in the current boundary - a smaller land acquisition than was originally intended. 

So how much land did the United States give up? It's unclear that anyone has accurately calculated this.

Reported sizes of the Gadsden Purchase

It's first important to note that at the time no one was really clear on how much land the United States was buying (and no one would be for more than 90 years) - or how much land it was choosing not to buy by modifying the treaty. Negotiators weren't even sure where Lake Guzman was.  For many years, the official measurement for the size of the purchase was given by the Census Bureau in 1870. They used official government estimates for the size of the New Mexico territory before and after the purchase, without realizing how those numbers were calculated (and the maps at the time were of low quality). The number they came up with was 45,535 square miles, which they got by subtracting the estimated area of the territory in 1850 (215,807) from that in 1860 (261,342).[2] This would be the official estimate for more than 40 years (though starting in 1900, the Census Office's Statistical Atlas of the United States began reporting it as 31,017. It isn't clear where they got this number.). It was also off by more than 50%.

One reason this number was flawed is that the southern border with Mexico wasn't determined in 1850. Due to the flawed Disturnell map (below) used in setting the border in the treaty of Guadalupe-Hidalgo, Mexico claimed the border was farther north than the United States did, and not without good cause. A controversial agreement, the Bartlett-Garcia Conde Compromise, defining the border wasn't signed until 1851.

 
Oddly enough, a more accurate measurement was available at the time the Census Bureau made its error. An 1857 Interior Department Survey by William H. Emory calculated the area as 26,185 square miles.[3] Though some publications reported this number for years, the larger number was far more common.

In 1912, Frank Bond, chief Clerk of the General Land Office, recalculated the size of the Gadsden purchase using the more modern methods of the time, and the value he came up with was a much more accurate value of 29,670 square miles.[4]

Finally, in 1940, the Census Bureau recalculated the sizes of all territorial acquisitions and determined that the 1912 number was slightly off. They determined that the actual size of the Gadsden Purchase was 29,640 square miles.[3][5]

Interestingly, each of the numbers and the errors that most of them represent, are so pervasive that they can still be found reported in books published today. Even the State Department historian used an old number in the quote above.

Amount by which the Purchase was reduced.

I could only find one attempt to answer the question about the size of the area by which Congress reduced the purchase. That number is 9,000 sq. mi. It comes from a 1923 thesis on the Gadsden Purchase written by historian Paul Neff Gabor. That thesis includes a map of the area and states the number definitively based on a citation. But that number does not seem accurate when the area is calculated using tools available today. The source of the 9,000 sq. mi. claim is from the "United States and Mexico Claims Commission, 1868, pub of the Department of State, III, 38" however a search for the original document indicates that the citation is flawed. Volume III does not include a case #38 and case #38 (found in another Volume) does not mention the size of the reduced area. It is unclear why a border dispute decision would contain this number and it's unlikely they would have accurately calculated it at that time. Thus I can't figure out how Garber determined the size of the reduced area, and the number he determined makes little sense.

The line that Gadsden negotiated started at a point farther south on the Colorado and then created a wedge shape going south to a point below the current border south of Nogales and then back north in a straight line to the point where the current border reaches its northernmost point along the Rio Grande. The new line removed from the sale two pieces, in black on the map below, and added a small wedge, in red, of what is now the south east corner of New Mexico's boot heel.

There are a few problems with trying to determine the size of the area by which the Purchase was reduced.

One is that the treaty is not the final say on where the border is. The Border Commission was. In fact, the markers on the ground, placed by agreement between Mexican and American survey teams, are the definitive word on where the border is, not the treaty or any map. Without such a survey and agreement on what the border would have been, we can only rely on the treaty.

Another problem is that the treaty set the boundary as departing the Colorado River at a point "two marine leagues north of the most northern part of the Gulf of California." Not only is it difficult to determine what would have been considered the "most northern part of the Gulf of California" in 1854, but when setting the border elsewhere, commissioners couldn't agree on how far a marine league was.[6]

That being said, using the area defined by the treaty and the standard 3-mile long modern definition of a marine league, the area winds up looking like the one in the map above. In that map, more than 10,000 sq. mi. in the Mexican states of Sonora, Baja California And Chihuahua were originally to be part of the Purchase, and 300+ sq. mi. in New Mexico and Arizona was not, for a total change of ~9,750 sq. mi. which is not too far off from the 9,000 sq. mi. reported by Gabor, but enough to be wrong. [How far north along the Colorado River the line goes matters, as drawing it at the current departure point results in an area ~4,200 sq. mi. and at the mouth of the Colorado results in an area of ~10,300 sq. mi.]

What was given up

The United States gave up ~9,750 sq miles of land, an area larger than 6 states, and in return saved $5 million, which would be worth more than $135 million today.

Had the US made the larger purchase it likely would've come out ahead. The US would have gained land that contained the sizable cities of Nogales (population 232,000), San Luis Rio Colorado (population 180,000+) and Aqua Prieta (pop. 84,000) in Sonora as well as dozens of smaller towns spread across three Mexican states. It would have gained all of the fertile farm land in the Mexicali Valley east of the Colorado and some of the farm land in the Rio Sonoyta Valley. It would have gained most of the El Pinacae y Gran Desierto de Altar Biosphere Reserve and part of the Upper Gulf of California and Colorado River Delta Biosphere Reserve, both of which are UNESCO sites.  In addition, Mexico is currently entitled to 1,500,000-acre-foot of Colorado River water (less in times of drought, or more in surplus) which is based on the amount of water they were believed to be using in 1944.[7] If Mexico had access to less Colorado River water - a reasonable assumption if the border went farther south along the river - they would've been given a smaller share. A foot-acre of water in California goes for $70, and the larger purchase would have reduced Mexico's Colorado River shore by 40%. A 40% reduction in river water would have gained the United States $42 million dollars of water per year. 

In addition to the $5 million dollars, Mexico would have gained a sliver of New Mexico's boot heal, and about 5 acres of Arizona's southeast corner. It's a small sparsely populated area and the largest town in it is the border town of Antelope Wells, NM (population: 2).

Not only did Mexico retain land and water, it avoided being nearly cut in half. Had the original purchase gone through, it would have left Mexico with a narrow band of land along the coast of the Gulf of California that would have made connecting Baja to the rest of Mexico more difficult. This would have been particularly ironic since the primary point of the purchase was to make connecting the United States to California easier. The two major east-west Mexican highways and the one railroad both pass through the are retained by the reduction. Without the reduction, Mexico would have been forced to build transportation links that go through the United States or build roads on less desirable routes close to the coast and through the Colorado River delta.

And what was accidentally given back

Marking the border was a matter of science, but at the time the science was still in its infancy. The Boudary Survey performed in the 1850's set several key monuments in the wrong place, and always to the benefit of the United States.  Monument #40, the marker along the New Mexico border that defines the spot where the border turns south, is about a mile too far east, resulting in the unintended transfer of about 30 square miles to the United States.[8] The monument that set the point where the 111th meridian of longitude west meets the parallel of 31° 20', and where the boundary turns north along the Arizona border, was erroneously placed at a point 4 miles to the west of where it should have been. This gave the United States another 297 square miles of unintended land.[9] Altogether, surveying cost Mexico an area equal to about one-fourth the size of Rhode Island. 

Had the boundary been surveyed correctly, the reduction of the purchase would have been more than 10,000 square miles. 

1. And should the line from 31, 111 to the Rio Grande traverse Lake Guzman (which is actually Laguna de Guzman or the Guzman Basin) the line was to be "broken so as to form an angle at a point one marine league south of the most southern part of the lake." This was done to ensure that there was space around the southern end of the lake for a railroad to be built.
2. Compendium of the 9th Census, Page 542
3. Manifest Opportunity and the Gadsden Purchase, Louis Bernard Smith, Arizona and the West, Vol. 3, No. 3, page 264, 1961 Size and supporting evidence was submitted to World Almanac in 1953
4. Historical Sketch of "Louisiana" and the Louisiana Purchase, Frank Bond, 1912, page 13
5. Statistical Abstract of the United States 1941, page 1 and Statistical Abstract of the United States 1942, page 1
6.Disagreements arose immediately, since there was no standard measurement for a marine league." Monuments, Manifest Destiny and Mexico, Prologue Magazine, Summer 2005, Vol. 37, No.2, Michael Deer.
7. Water and the West: The Colorado River Compact and the Politics of Water in the American West; Norris Hundley, 2009, page 296
8. Border Spaces: Visualizing the U.S.-Mexico Frontera, page 41
9. La Gran Línea: Mapping the United States–Mexico Boundary, 1849–1857, Paula Rebert, page 129.