Spin gap in a quasi-one-dimensional $S=$$\frac{1}{2}$ antiferromagnet: ${\mathrm{Cu}}_2$${\mathrm{}(1,4-\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{z}\mathrm{a}\mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{e})\mathrm{}}_2{\mathrm{Cl}}_4$

${\mathrm{Cu}}_2$(1,4-diazacycloheptane)${}_2{\mathrm{Cl}}_4$ contains double chains of spin-$\frac{1}{2}$ ${\mathrm{Cu}}^{2+}$ ions. We report ac susceptibility, specific heat, and inelastic neutron-scattering measurements on this material. The magnetic susceptibility $\chi \mathrm{}\left(T\right)\mathrm{}$ shows a rounded maximum at $T=8\mathrm{}$ K indicative of a low-dimensional antiferromagnet with no zero-field magnetic phase transition. We compare the $\chi \mathrm{}\left(T\right)\mathrm{}$ data with exact diagonalization results for various one-dimensional spin Hamiltonians and find excellent agreement for a spin ladder with intrarung coupling $J_1=1.143\mathrm{}\left(3\right)\mathrm{}$ meV and two mutually frustrating interrung interactions $J_2=0.21\mathrm{}\left(3\right)\mathrm{}$ meV and $J_3=0.09\mathrm{}\left(5\right)\mathrm{}$ meV. The specific heat in zero field is exponentially activated with an activation energy $\Delta =0.87\mathrm{}\left(1\right)\mathrm{}$ meV. A spin gap is also found through inelastic neutron scattering on powder samples that identify a band of magnetic excitations for $0.8<\mathrm{}ħ\omega <1.5\mathrm{}$ meV. Using sum rules we derive an expression for the dynamic spin-correlation function associated with noninteracting propagating triplets in a spin ladder. The Van Hove singularities of such a model are not observed in our scattering data, indicating that magnetic excitations in ${\mathrm{Cu}}_2$(1,4-diazacycloheptane)${}_2{\mathrm{Cl}}_4$ are more complicated. For magnetic fields above $H_{c1\mathrm{}}\simeq 7.2$ T specific-heat data versus temperature show anomalies indicating a phase transition to an ordered state below $T=1\mathrm{}$ K.