Unenforceable Trusts and the Rule against Perpetuities

Bequests upon trust to use the income thereof each year in keeping a monument or grave in repair, or in saying masses,8 or in having a brass band to play at the testator's grave each year on the anniversary of the testator's death9 have been held invalid, and the reason given is that the gift is a "perpetuity"1 or is in "violation of the rule against perpetuities."11 What do the courts mean by calling such a gift a "perpetuity?" And in what way, if at all, could the bequest be so changed as to avoid the "rule against perpetuities" and thus make the gift valid?