Raimey already knows my answer to a similar question:
Now, to the term Rouxdrilling: None of these were designed by one of the two Rouxes! The monicker comes from a disdainable habit of German gunmakers and -dealers: In their catalogs they more often than not a break-open action is described only after the position and movement of the opening lever. They continued to use the name of the first one who had used such a lever, regardless of the lockup such a lever worked on. Their avarage customers only wanted to know how a gun handled, regarding strength of the lockup they relied on the words of their trusted gunsmith/dealer.
So every gun with the familiar toplever was described as a "Scottverschluss", wether the lever worked on W.M.Scott's spindle or another type of lockup.
Every side-swinging lever under the foreend was a "Lefaucheuxverschluss", even if it worked a Teschner/Collath slide-and tilt action.
A side-swinging lever around the triggerguard was a "Lancasterverschluss", though the real slide-and-tilt Lancaster action was virtually unknown. Even recently Norbert Klups stepped into this trap, set up more than 100 years ago by the German catalogs: In his book on double rifles he always misnames the familiar Jones action as "Lancasterverschluss"! (The French were not better: The 1896 MAS catalog calls the Jones action "Systeme Beringer"! Beringer's capping breechloaders used a seperate chamber turned sideways by an underlever around the triggerguard.) Sometimes this was even topped: both side-turning underlevers, the Lefaucheux- and the Lancaster-type, were often lumped together under "Excenterverschluss", albeit only the early slide-and-tilt actions used an excentrical cam.
Now to Roux: Jacques Roux, fabricant d'armes a Liege, in the 1850s patented an improvement to Lefaucheux' pinfire guns, which were inert actions to be closed by hand. Roux's design was the first snap-action gun to see widespread use. Roux locked his gun with a round underbolt, which went lengthwise into a round hole bored into the barrel lug. To open the gun this bolt was withdrawn against spring pressure by pushing forward a lever which was in front and partly over the triggerguard. In 1861 Roux' lockup was used by Francois Eugene Schneider/Paris and George Henry Daw/London on the first true centerfires to become known in England. In Germany the name "Rouxverschluss" was stuck on all actions which were opened by pushing down/forward an underlever. All the "Rouxdrillinge" I know are practically variations of Purdey's 1863 patent, 2nd variation: Double underbolts withdrawn by Roux's lever in front of the triggerguard, most of the time only with a doll's head as a top "fastener". By the way, the side-lever drillings, which are identical in all respects except lever shape to the so-called "Rouxdrillinge" were never called such.
Hoping to have cleaned up something