A two-dimensional fluorescence (excitation/emission) spectrum of C2 produced in an acetylene discharge was used to identify and separate emission bands from the d (3)Pi(g)<--c (3)Sigma(u) (+) and d (3)Pi(g)<--a (3)Pi(u) excitations. Rotationally resolved excitation spectra of the (4<--1), (5<--1), (5<--2), and (7<--3) bands in the d (3)Pi(g)<--c (3)Sigma(u) (+) system of C2 were observed by laser-induced fluorescence spectroscopy. The molecular constants of each vibrational level, determined from rotational analysis, were used to calculate the spectroscopic constants of the c (3)Sigma(u) (+) state. The principal molecular constants for the c (3)Sigma(u) (+) state are B(e)=1.9319(19) cm(-1), alpha(e)=0.018 55(69) cm(-1), omega(e)=2061.9 cm(-1), omega(e)x(e)=14.84 cm(-1), and T(0)(c-a)=8662.925(3) cm(-1). We report also the first experimental observations of dispersed fluorescence from the d (3)Pi(g) state to the c (3)Sigma(u) (+) state, namely, d (3)Pi(g)(v=3)-->c (3)Sigma(u) (+)(v=0,1).