Assuming that the total cross sections tend to finite nonvanishing limits as $s\to \infty$, it is shown in axiomatic field theory that the scattering amplitudes $f_1(s, t)$ and $f_2(s, t)$ for processes $A+B\to A+B$ and $\overline{A}+B\to \overline{A}+B$ must satisfy either or both of the relations $\frac{{\sigma }_1\mathrm{}\left(s\right)\mathrm{}}{{\sigma }_2\mathrm{}\left(s\right)\mathrm{}}\to 1$ and $\frac{\left[\frac{d{\sigma }_1(s, t(s\left)\right)}{\mathrm{dt}}\right]}{\left[\frac{d{\sigma }_2(s, t(s\left)\right)}{\mathrm{dt}}\right]}\to 1$ as $s\to \infty$, where ${\sigma }_i$, and $\frac{d{\sigma }_i}{\mathrm{dt}}$ are the total and elastic differential cross sections and $t\left(s\right)=-C{\left(\ln s\right)}^{-2\mathrm{}}$. Since ${\sigma }_i$ and $\frac{d{\sigma }_i}{\mathrm{dt}}$ are both measurable, this result enables us to subject axiomatic field theory to an experimental test.

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