Well, trying to write what I think (not that I know anything about it) is more Ruby-ish code, here is a mixin for the Array:

class Array
    def mergesort
        return self if (length<=1)
        half = (length-1)/2
        firstHalfOfTheList = slice(0..half)
        secondHalfOfTheList = slice((half+1)..(length-1))
        sortedFirstHalfOfTheList = firstHalfOfTheList.mergesort
        sortedSecondHalfOfTheList = secondHalfOfTheList.mergesort
        merge sortedFirstHalfOfTheList, sortedSecondHalfOfTheList
    end
    def merge(first, second)
        merged = Array.new
        firstlength = first.length
        firstlength.times do
            fp = first.shift
            secondlength = second.length
            secondlength.times do
                sp = second.first
                if sp < fp then
                    merged << second.shift
                end
            end
            merged << fp
        end
        merged + second
    end
end