These differential equations must be solved simultaneously, either analytically or numerically. We can only argue about something that can be analytically or empirically verified. Such an assessment may be performed either experimentally or analytically. The values encode a composite of many subtle factors difficult to quantify analytically. But there are some analytically tractable cases. This fact leads to an analytically tractable compound distribution. Sometimes it is too cumbersome solving the differential equation analytically. The differences are both analytically and normatively important. Nonetheless, Holmes inspired future generations of forensic scientists to think scientifically and analytically. The method is useful for obtaining numerical solutions to problems too complicated to solve analytically. It is possible to derive analytically the point of maximum efficiency. This is possible by approximating the analytically correct functions whenever needed. Analytically, fractals are usually nowhere differentiable. For some simple capacitor geometries this additional capacitance term can be calculated analytically. However, such systems tend to be analytically intractable.