Correlation of Tunneling Spectra in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{O}_{8+\delta }$ with the Resonance Spin Excitation

New break-junction tunneling data are reported in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ over a wide range of hole concentration from underdoped $(T_c=74\mathrm{K})$ to optimal doped $(T_c=95\mathrm{K})$ to overdoped $(T_c=48\mathrm{K})$. The conductances exhibit sharp dips at a voltage, $\Omega /e$, measured with respect to the superconducting gap. Clear trends are found such that the dip strength is maximum at optimal doping and that $\Omega$ scales as ${4.9kT}_c$ over the entire doping range. These features link the dip to the resonance spin excitation and suggest quasiparticle interactions with this mode are important for superconductivity.