let $\frak{b}$ be a borel subalgebra of a complex semisimple lie algebra $\frak{g}$. let $\frak{h}\subset\frak{b}$ \ be a cartan subalgebra and let $\frak{n}$ be the nilradical of $\frak{b}$. let $\delta_{+}\subset\frak{h}^{\ast}$ be the set of positive roots corresponding to $\frak{b}$. then there is a distinguished maximal set $b\subset\delta_{+}$ of strongly orthogonal roots called the cascade of orthogonal roots. the center, cent($u(\frak{n})$), of the enveloping algebra of $\frak{n}$ is a module for $h=\exp\frak{h}$. \noindent{\bf theorem.} cent($u(\frak{n})$) {\it is a polynomial ring in }$m$ {\it generators} $u_{1},...,u_{m}$ {\it where} $m=$ card$b $. {\it furthermore, all} $h$-{\it weights in} cent($u(\frak{n})$) {\it are of multiplicity} $1$ {\it and the} $u_{i}${\it can be chosen so that the weight vectors are all the monomials} $u_{1}^{k_{1}}\cdots u_{m}^{k_{m}}$. {\it the} $u_{i}$ {\it are characterized up to scalar multiple as the weight vectors which are also irreducible polynomials}. we also have \noindent{\bf theorem.} {\it the set of weights in} theorem 1 {\it is exactly the set} $d_{cas}$ {\it of elements in the semigroup generated by the linearly independent set} $b$ {\it which are also dominant.} the construction of the weight vectors can be given in terms of matrix units for $u(\frak{g})$. applications of the results are given to the determination if minimal generalized exponents and the proof that a borel subgroup of $g$ has open coadjoint orbits when $m=rank{\frak g}$.