The nature and multipolarity of the 4.45 MeV γ-ray from carbon-12^* are obtained from the angular distribution of the positrons and electrons of internal conversion pairs photographed in a cloud chamber. The transition is found to be of electric quadrupole origin. Accordingly, a spin of 2⁺ is ascribed to the first excited level in ¹²C and a decay scheme is proposed for ¹²C^* at the lower energies.A transformation formula is given which relates the spatial angular distribution of cloud-track pairs to the distribution of pair-angles projected on to a plane of reference.