Martial Mathematics

Last week Japan was again threatening China while Italy was mobilizing 45,000 more men for possible war service against Abyssinia. Also last week Lewis Fry Richardson, D. Sc., F. R. S., principal of Paisley Technical College, showed in the British journal Nature how the approach of any two nations toward war can be reduced to mathematical equations:

dx(1) /dt= k(1)(2)sbx(2)- SQRT (1) + D(1)

dx(2)/dt=k(2)(1)sbx(1)- SQRT (2)sbx(2)+D(2)

The symbol d, common in calculus, operates to make the left side of the equation a quantity containing the element of change. The suffixes (1) and (2), explains Dr. Richardson, identify the symbols which they follow as the opposing nations or groups of nations; x denotes preparedness for war, a variable; t is the length of time during which the nations have been coming together as enemies; k is a "defense-coefficient"; SQRT is a "fatigue and expense" coefficient; D "represents those dissatisfactions-with-treaties, which tend to provoke a breach of the peace."

Thus the first equation simply means that the approach of Nation (1) toward war with (2) is equal to the product of the defense-coefficients of both nations multiplied by the preparedness of (2), minus the preparedness of (1), multiplied by its fatigue-and-expense coefficient, plus the dissatisfactions-with-treaties of (1). The second equation can be translated conversely.

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