  In the present paper we find explicit formulas for the degrees of Heegner
divisors on arithmetic quotients of the orthogonal group $\Orth(2,p)$ and for
the integrals of certain automorphic Green's functions associated with Heegner
divisors. The latter quantities are important in the study of the arithmetic
degrees of Heegner divisors in the context of Arakelov geometry. In particular,
we obtain a different proof and a generalization of results of Kudla relating
these quantities to the Fourier coefficients of certain non-holomorphic
Eisenstein series of weight $1+p/2$ for the metaplectic group $\Mp_2(\Z)$.
