We derive the equation of state of a dilute atomic Bose gas with an in
teratomic interaction that has a negative scattering length and argue
that two continuous phase transitions, occurring in the gas due to qua
ntum degeneracy effects, are preempted by a first-order gas-liquid or
gas-solid transition, depending on the details of the interaction pote
ntial. We also discuss the consequences of this result for future expe
riments with magnetically trapped spin-polarized atomic gases such as
lithium and cesium.