plotted as constant); the curve might equally well have been plotted directly to this law as by the process given. A simple proof of the truth of the above law as arising from the differential equations (1) and (2), §21, is as follows:—
In Fig. 6, let the numerical values of the "blue" and "red" forces be represented by lines b and r as shown; then in an infinitesimally small interval of time the change in b and r will be represented respectively by db and dr of such relative magnitude that db / dr = r / b or,
b db = r dr (1)
If (Fig. 6) we draw the squares on b and r and represent the increments db and dr as small finite increments,
_-_Fig._6.png)
Fig. 6.
we see at once that the change of area of b2 is 2b db and the change of area of r2 is 2r dr which according to the foregoing (1), are equal. Therefore the difference between the two squares is constant
b — r2 = constant.
If this constant be represented by a quantity q2 then b2 = r2 + q2 and q represents the numerical value of the remainder of the blue "force" after annihilation
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