Scaling of the elastic proton-proton cross-section

We discuss scaling properties of the elastic $pp$ cross-section both at the ISR and the LHC. We observe that the ratio of bump to dip positions of the differential cross-section $d{\sigma }_{\mathrm{e}\mathrm{l}}\mathrm{/}dt$ is constant over a wide energy range. We next study the consequences of this property, including geometric scaling at the ISR and new scaling laws at the LHC.