Let $f$ be a $C^{2}$ function on an open set which contains $\overline{B(x, r)} .$ We can use first Green's formula and then differentiation under the integral sign to obtain $$ \int_{B(x, t)} \Delta f d \lambda=\int_{S(x, t)} \frac{\partial f}{\partial n_{e}} d \sigma \quad(0<t \leq r) $$ where $\partial / \partial n_{e}$ denotes the exterior normal derivative, and then $$ \int_{B(x, t)} \Delta f d \lambda=t^{N-1} \int_{S} \frac{\partial}{\partial t} f(x+t y) d \sigma(y) $$ Source : Classical Potential Theory, Armitage and Gardiner.
I didnt understand what they mean by exterior normal derivative and how they get the second formula ? Any help is really appreciated !