  We reconsider the Euclidean version of the photon number integral introduced
in ref 1. This integral is well defined for any smooth non-self-intersecting
curve in $\R^N$. Besides studying general features of this integral (including
it s conformal invariance), we evaluate it explicitly for the ellipse. The
result is $n_{ellipse}=(\xi^{-1}+\xi)\pi^2$, where $\xi$ is the ratio of the
minor and major axes. This is in agreement with the previous result
$n_{circle}=2\pi^2$ and also with the conjecture that the minimum value of $n$
for any plane curve occurs for the circle.
