Presented in this thesis is the design and characterization of a new, high-flux source of cold atoms based on continuous, post-nozzle injection of lithium atoms into a cryogenic, supersonic helium jet. To date, experiments have been performed with lithium injection fractions up to [approximately equal to]10⁻⁶, where fluorescence spectroscopy reveals successful capture and thermalization of lithium atoms within the helium jet. The observed lithium beam copropagates with the helium jet and has a temperature of less than 10 mK, a brightness of 1.1x10¹⁹ m⁻² s⁻¹ sr⁻¹, and a brilliance of 3.1x10²⁰ m⁻² s⁻¹ sr⁻¹. Lithium atoms contained within a solid angle of [approximately equal to]0.018 sr are good candidates for future magnetic extraction. This results in a potentially capturable lithium flux of 1.1x10¹² s⁻¹, comparable to the existing record for a cold atomic beam. Also presented is preliminary data showing lithium fluorescence nearly 1 m downstream, demonstrating that the cold lithium beam can be successfully extracted from the seeding region. Numerical simulations reproduce capture efficiency to within 50%, suggesting that the process is well understood. We believe that successful seeding may be possible at a fraction up to 10⁻⁴. Seeding at this rate could produce an atomic beam with a flux as high as 1.3x10¹⁴ s⁻¹ at a phase-space density up to 1.6x10⁻⁷, corresponding to brightness and brilliance of order 10²² m⁻² s⁻¹ sr⁻¹ and 10²⁴ m⁻² s⁻¹ sr⁻¹ , respectively. If this novel cooling method performs as well at higher incident lithium flux, it could serve as a pump source and pave the way to the realization of the first truly continuous atom laser. / text