Plotting Quasi-War captures is not an exact science. My methods are a combination of primary-source research, computations, and intelligent estimation. I largely gathered the data from the seven volumes of the Naval Documents Related to the Quasi-War Between the United States and France (Washington: U.S. Govt. Print. Office, 1935), as well as from the document collection American State Papers. You can see the data I collected, including sources, here.
Ships are always moving; therefore, tracking their exact location in any given span of time is virtually impossible. No capture is instantaneous, so tracking where a ship was at the exact time of its capture is not feasible. The best we can do is to record where the two ships first engaged. This is, in itself, an inexact measure--most commanders did not take their exact bearing while being attacked (though some did). Even these more specific records cannot possibly be verified. But then again, up to a certain point, the exact location is not really critical.
Some commanders, particularly those of official ships, did take scrupulous bearings every day and whenever anything interesting happened. Thomas Truxtun, possibly the most verbose officer in the U.S. Navy, was responsible for detailed and (as far as I can tell) accurate bearings; a few others followed his lead.
More frequently, though, locations looked more like this:
Nevis WSW 5 leagues,
under the lee of Guadeloupe, or
16 or 17 leagues from Cape Clear, lat 51o20'N.
In order to figure out where these locations really are, it's necessary to do some calculations. I used this script to calculate a location based on one point (e.g., Nevis), a bearing (WSW), and a distance (5 leagues). (I used a simple click on Google Maps to get the latitude and longitude of the reference point, though I could have easily written an R script to do all the geocoding.)
But even finding the reference point is not an entirely simple process. The place names recorded by ships' captains have often either changed or completely disappeared, and so merely searching in Google, or writing a script for geocoding, only throws up errors. While a Google search can often illuminate historical name changes (for instance, Cape Francois, a very important port in the Quasi-War, is now called Cape Haitien), sometimes the places are too obscure, or the name used is too unusual (or badly spelled), to yield any answers from a simple search.
To figure out where these places are, the easiest place to turn is to a historical map. In order for a historical map to be useful, however, it needs to be georectified, or aligned with a modern coordinate reference system. Nineteenth-century maps are remarkably inaccurate, so georectification is a difficult process.
Historical Map
I chose this map for two reasons: first, it was the map in the collection that was closest in date to the time period of the Quasi-War. Second, the map is intended to be a sea chart of the Caribbean region, which makes it a logical choice to plot ocean locations on. However, the map's accuracy is quite low. You can see from the map that the coast of Latin America, for instance, and a good number of islands in the Windward and Leeward Islands, are highly distorted, despite my use of almost 300 control points. The shape of islands and coastal peninsulas are particularly inaccurate. These irregularities remind us how illusory is our quest to plot exact locations on the ocean. Nevertheless, the historical map is valuable, partially because it is in English, and thus the place names on it are more likely to coincide with ones used by the American navy. Seeing the inaccuracy of the maps also gives us a sense of how important a knowledge of the waters of the Caribbean were: presumably the privateers who were based in the islands had a better sense of the ocean geography than anyone trying to use a chart like this as his primary navigational aid.
A georectified map can't tell us everything, though. Some locations, like "under the lee of Guadeloupe," don't have enough information to be able to calculate a location. Instead, with these locations, I just had to make my best guess. I considered spatial information such as "on my way from Barbadoes to London" as to vague to be plottable, but "under the lee of Guadeloupe" was much easier to estimate. Using what I know about the way prize-taking worked, I estimated locations with the best accuracy I could.
Historic Place Names
One place that kept coming up in the primary sources was variously spelled "Desada," "Deseada," "Descada," and probably other ways. None of those spellings yielded any search results. But this place was very commonly used as a reference by sailors, so it was important that I figure out where it was. I had a few hints (I knew it was in the Caribbean, possibly close to Guadeloupe), but it was not until I had investigated the georectified map that I found it: spelled "Deseada" on the 1787 map, and in slightly the wrong place, it is the modern name of the island La Desirade. This is just one example of the usefulness of a georectified map.
A note about St. Domingo: Just previous to this time, the island of Hispaniola was divided into two colonies, the French Saint-Domingue and the Spanish Santo Domingo. The French gained control of the whole island in 1795. During the Quasi-War, commanders of captured ships often referred to being sent to "St. Domingo," a mix of the two names. This name could refer to either the whole island of Hispaniola, or to the port of Santo Domingo, previously capital of the Spanish colony of Santo Domingo. Given the number of prizes sent into Cape Francois, and the lack of references to Santo Domingo in other contexts, I have assumed that, as when commanders use "Guadeloupe" to mean "Basseterre, Guadeloupe," in this case they are referring to the major prize court in Saint-Domingue, Cape Francois.
I plotted the prize courts using a different data set (from the same sources). Often, when a ship is captured, its capture location is unknown, but the location it was sent to and tried at is known. Some of the captures that make up this data set are the same as the ones in the plotted encounters, but many of them are not. There is also some uncertainty here, as many times the records say only that a ship was sent to a specific place for adjudication, but the outcome of the hearing was not recorded. It's a pretty good guess that a majority of those cases resulted in condemnation, but rather than make that assumption, I merely recorded those captures as having an "uncertain" outcome. Additionally, sometimes captures made it to a port but were abandoned or permanently sequestered; I have counted those instances as condemnations because the result, the loss of the ship, was the same. Likewise, there is a legal difference between the condemnation of a cargo and the condemnation of both ship and cargo. For the purposes of this map, I have not delineated the two, since the loss of all cargo almost always meant the loss of the ship as well; masters were forced to sell the ship because they had lost all the money they were going to make from the cargo.
This map does have some obvious limitations. With a little more time, I would have made it animated over time, which would have been a helpful way to consider the data. The data, though, is much fuller for the years just before the war and in its early days and less so for the latter part of the war. So perhaps time animation would also give us a distorted picture.
More significantly, this map does not have a large number of recaptures, which we know the navy achieved with much greater frequency than they did captures of French ships. Generally speaking, the data on recaptures are without spatial clues, and a recapture meant that the ship never made it to a prize court. Recaptures were nonetheless a significant part of the navy's role in the Caribbean.
It isn't conceivable to record all captures of private vessels, but surprisingly, it is almost as difficult to track down captures by U.S. naval vessels. For instance, Richard Valentine Morris wrote on January 20, 1800, that his squadron had captured 17 vessels; John Shaw wrote of 13 captures at his hands by December 12, 1800. There are no records of most of these captures, though Morris and Shaw may very well have been including recaptures in that number. We also know next to nothing about the courts in which these captures might have been tried.