Later in history, the Roman Empire conquered all of the Celtic people except those in the British Isles (mainly Ireland). The traditions and culture of the Celtic people outside of the safety of the islands all but disappeared with other cultures. The natural barriers of the ocean and English Channel made it easy for the Celtic culture to flourish with the least amount of interruption. However, one of the few cultures to bother the Irish Celts were the Vikings. Their raids destroyed many of the written records of the Irish arts and dances. One of the surviving books was the famous Book of Kells, which has many of the original knots and arts recorded in it. The Viking raids ended in 1014.
The next group to interrupt Ireland's sheltered culture were the English. They spread their own culture among the Irish. The best example of this can be seen in language. For centuries the Irish had their own language which thrived. However, it resembled no other language on earth and because of that, most found it difficult to pronounce and impossible to understand. So, when the English brought along the English language, it spread throughout Ireland like wildfire. That is why most of eastern Ireland speaks English, and western Ireland speaks Irish, or Gaelic. Now, I know that this has nothing to do with dance, however in an indirect way, it does. Along with the English came the Roman Catholic Church and dance instructors called "Dance Masters".
These dance masters, who came mainly from France, began teaching the Anglo-Irish (the landowners and lords) the royal court dances of France. Eventually these court dances spread throughout the social classes to the bottom, until peasants were eager to learn the dances. So, dance masters set up classes wherever there was space, including barns, kitchens, and even in the streets. Soon everyone knew variations of the French dances. Now, you must understand that the dances that were taught were not exactly the court dances. Many factors came into the teaching of the dances.
First of all, the dance masters had to shorten the dances in order for them to fit the available music. And also, the Roman Catholic Church came into play by changing the look of the dances in order to fit the new morals of the church and Europe. Dance was transformed from open styled dancing (such as in ballet) to closed and moral styles (such as the crossed legs and straight arms in Irish). Although no one really knows why Irish dancers use straight arms.To read more, check out "Irish dancing: Past, Present and Future" by Kelly A. Brown.