The 5-1 band of the recently discovered B'->B system of N₂ has been photographed under large dispersion and a rotational analysis has been made. The upper state has been shown to be of species ³Σ_u^- and the lower state has been confirmed to be B³Π_g. The rotational constants derived from the analysis are B' = 1.381₆ cm^-1, D' = 4.6 × 10^-6 cm^-1, Bdouble prime = 1.610₄ cm^-1, Ddouble prime = 5.4 × 10^-6 cm^-1. The spin structure of the ³Σ_u^- state has been determined and a discrepancy between theory and experiment noted.