Euclidean magnitude-limited source count

For identical luminosities, uniform spatial density, and no extinction, the inverse-square law gives limiting distance $r\propto F_{\min }^{-1/2}$. The number in the enclosed volume is therefore $N\propto F_{\min }^{-3/2}\propto 10^{0.6m_{\lim }}$. Increasing the sample by a factor $b$ needs a magnitude-limit increase $(5/3){\log }_{10}b$. This relation need not hold with evolving source populations, dust, or cosmological distance effects.