  In this note, we use scaling principle to study the boundary behaviour of the
span metric and its higher-order curvatures on finitely connected Jordan planar
domains. A localization of this metric near boundary points of finitely
connected Jordan domains is also obtained. Further, we obtain boundary sharp
estimates for this metric on $ C^2 $-smooth bounded domains and consequently,
this metric is comparable to the Carath\'eodory and the Kobayashi metrics on
these domains.
