The (2,0) and (3,t) C13N14 bands of the red CN system have been rotationally analyzed in the laboratory. Wavelengths are presented for a total of 437 rotational lines of which 259 pertain to the (2,0) band and 178 lines to the (3,1) band. The wavelengths are compared with the theoretically predicted values of Utsumi. A systematic difference is in the residuals, which arises from uncertainties in the molecular constants. If a precision of 0.1 A is to be achieved, the theoretical calculations must be extremely accurate. Perturbations are indicated for the first few rotational levels in the R1-branch. The laboratory wavelengths have led to a positive identification of numerous individual rotational lines of the isotopic (2,0) and (3,1) bands in the spectra of five carbon stars, which range in type from Cl2 to C92. The normal (2,0) band has been scrutinized for regions hetween C12N14 line groups where only C13N14 lines fall. Twenty-five such regions have been found, which may provide C22 , useful for surveys of the C13 content in late-type stars on medium-dispersion spectra (50-100 A/mm). Relative abundance ratios of C12 to C'3 have been derived on the basis of the observed llne strengths of two cleanly isolated, single rotational lines, the isotopic P2(19)i line at 8019.351 and the normal R1(40) line at 8038.125. The derived values for the five carbon stars range from well below the equilibrium ratio (3.4:1) of the CNO cycle to well above it (2:1 < a < 11:1). The vibrational temperatures show little correlation with spectral class and are below 2400 K. The exceptionally high C'3 content (a = 2:1) in such stars as Y CVn and `vZ Cas cannot be explained as a product of the equilibrium ratio of the CNO cycle. We suggest that C'3 in carbon stars is partially synthesized by spallation and processes of neutron irradiation either in the atmospheres of Woll-Rayet stars or in the carbon stars themselves.