A search was made for new isotopes of the elements lithium through nitrogen produced in the high-energy (4.8-GeV) proton irradiation of a uranium target. The fragments were identified by $\ensuremath{\Delta}E\ensuremath{-}E$ and time-of-flight techniques. An electronic pulse-width discriminator greatly reduced the background allowing high sensitivity. A new method for analyzing time-of-flight data and a new algorithm for particle identification were introduced. Two new isotopes, $^{14}\mathrm{Be}$ and $^{17}\mathrm{B}$, were observed to be particle stable and the existence of $^{19}\mathrm{C}$ was confirmed. It was shown that $^{12}\mathrm{Li}$ and $^{16}\mathrm{B}$ are particle unbound. Approximate production cross sections were determined for $^{14}\mathrm{Be}$, $^{17}\mathrm{B}$, $^{18}\mathrm{C}$, and $^{19}\mathrm{C}$, and upper limits estimated for $^{13}\mathrm{Li}$, $^{19}\mathrm{B}$, $^{20}\mathrm{C}$, and $^{22}\mathrm{N}$.[NUCLEAR REACTIONS $\mathrm{U}(p,x)$, $E=4.8$ GeV; $^{14}\mathrm{Be}$, $^{17}\mathrm{B}$, $^{18}\mathrm{C}$, $^{19}\mathrm{C}$ measured $\ensuremath{\sigma}$; $^{13}\mathrm{Li}$, $^{19}\mathrm{B}$, $^{20}\mathrm{C}$, $^{22}\mathrm{N}$ $\ensuremath{\sigma}$ upper limits.][NUCLEAR STRUCTURE $^{14}\mathrm{Be}$, $^{17}\mathrm{B}$, $^{19}\mathrm{C}$ observed particle bound; $^{12}\mathrm{Li}$, $^{16}\mathrm{B}$ particle unbound.]