A limiting diagram for the Segre classification of the energy-momentum
tensor is obtained and discussed in connection with a Penrose special
ization diagram for the Segre types. A generalization of the coordinat
e-free approach to limits of Paiva et al to include non-vacuum spaceti
mes is made. Geroch's work on limits of spacetimes is also extended. T
he same argument also justifies part of the procedure for classificati
on of a given spacetime using Cartan scalars.