next, on average it has been practically constant since 1600CE. 4. Most of the other battle parameters (specifically the initial force strengths, initial force ratios, casualty numbers, casualty exchange ratios, battle durations, and distances advanced by the attacker) have changed so slowly since 1600CE that only the most acute observers would be likely to notice any change over their nominal 50-year military career. 5. Bitterness (logeps), casualty fractions (FA and FD in the above notation), and intensity (loglam) also changed slowly before 1939CE. But since then they have followed a startlingly steeper declining curve. Some observers have noticed a similar post-WWII decline in casualties at the level of wars instead of battles. There is currently no explanation for this newly-discovered phenomenon. How long the steeply declining rate will persist is uncertain, but because it is so important for military planning, considerable effort should be devoted to determining its causes and to making more certain forecasts of its future values. See also Attrition warfare Lotka–Volterra equations similar mathematical model for predator-prey dynamics Maneuver warfare Petrie multiplier similar mathematical model for sexism Lewis Fry Richardson Salvo combat model General and cited sources Citations External links "Kicking Butt By the Numbers: Lanchester's Laws", a Designer's Notebook column by Ernest Adams in the Gamasutra webzine Lanchester Equations and Scoring Systems, appendix to "Aggregation, Disaggregation, and the 3:1 Rule in Ground Combat" by Paul K. Davis, Rand Corporation publication MR-638-AF/A/OSD Lanchester combat models, Mathematics Today, 2006, Vol 42/5, pages 170–173. N-Squared Law: An Examination of one of the Mathematical Theories behind the Dreadnought Battleship by Joseph Czarnecki at Naval Weapons of the World Differential equations Predation