How does a switch's MAC layer behave when both nodes are at different speed and duplex

I have a network which is coected like this :

PC1 | | (auto neg) | Switch1 | | (10 Mbps Half) | Switch2 | | (auto neg) | PC2

then everything works fine. Now I just want to know how does switches pass on the traffic when 2 nodes are at different speed (like here, PC node at 1Gbps, another switch's node at 10 Mbps Half). There must be two MACs involved in the switch both ruing at different speeds. So how does it work ?