Mass per logarithmic size bin
= Mass per logarithmic size bin
{title2=$m_{\log}\propto D^{4-\alpha}$}
For equal-density spherical bodies with differential number distribution $n(D)\propto D^{-\alpha}$, a fixed logarithmic bin has width $dD=D\,d\log D$. Multiplying the body mass proportional to $D^3$ by $n(D)dD$ gives $m_{\log}\propto D^{4-\alpha}$. Distinguishing differential-number and logarithmic-mass slopes is essential in <collisional cascade> plots.