It is a particularly poor design as the tension in the tubing is concentrated into a few small spots where it isn't thicker from the other welds etc. No wonder the poor thing cracked.
It probably always goes on the clamp arm side as that's the one that moves inward; the stress is slightly unequal around the seat tube due to friction between the tube and seatpost.
Modern clamps are a far superior approach, putting all the stress into an easily-replaced collar with the seat tube itself in compression.
Ride it or milk it!