We complete the verification of the 1952 Yang and Lee proposal that

thermodynamic singularities are exactly the limits in ${\mathbb R}$ of

finite-volume singularities in ${\mathbb C}$. For the Ising model defined on a

finite $\Lambda\subset\mathbb{Z}^d$ at inverse temperature $\beta\geq0$ and

external field $h$, let $\alpha_1(\Lambda,\beta)$ be the modulus of the first

zero (that closest to the origin) of its partition function (in the variable

$h$). We prove that $\alpha_1(\Lambda,\beta)$ decreases to

$\alpha_1(\mathbb{Z}^d,\beta)$ as $\Lambda$ increases to $\mathbb{Z}^d$ where

$\alpha_1(\mathbb{Z}^d,\beta)\in[0,\infty)$ is the radius of the largest disk

centered at the origin in which the free energy in the thermodynamic limit is

analytic. We also note that $\alpha_1(\mathbb{Z}^d,\beta)$ is strictly positive

if and only if $\beta$ is strictly less than the critical inverse temperature.