  Let $d\ge 2$ be an integer, let $c(t)$ be any rational map, and let $f_t(z)
:= (z^d+t)/z$ be a family of rational maps indexed by t. For each algebraic
number $t$, we let $h_{f_t}(c(t))$ be the canonical height of $c(t)$ with
respect to the rational map $f_t$. We prove that the map $H(t):=h_{f_t}(c(t))$
(as $t$ varies among the algebraic numbers) is a Weil height.

Number Theory