Actually, it is feoil, and they're compound words. Originally they were spelt muicfheoil and mairtfheoil. But, when they reformed the spelling for English speakers, they removed those things that showed how they're related (as well as several other things that disambiguated the language, such as the difference between léim 'I read' and léim 'Jump')
QUOTE: "when they reformed the spelling for English speakers"
That's a very exaggerated comment, galaxyrocker. Danish, Dutch, French, German, Greek, Latvian, Norwegian, Portuguese, Russian, Spanish, and Swedish have all undergone a greater or lesser degree of spelling-reform during the course of the last 200 years. In none of these cases were the reforms introduced for the benefit of English-speakers -- and no more were the changes to Irish orthography made for that reason.