  The paper deals with two issues. First, we explore the quantitiative
importance of higher multiplets for properties of the $\Delta$ decuplet in
chiral perturbation theory. In particular, it is found that the lowest order
one--loop contributions from the Roper octet to the decuplet masses and
magnetic moments are substantial. The relevance of these results to the chiral
expansion in general is discussed. The exact values of the magnetic moments
depend upon delicate cancellations involving ill--determined coupling
constants. Second, we present new relations between the magnetic moments of the
$\Delta$ decuplet that are independent of all couplings. They are exact at the
order of the chiral expansion used in this paper.
