Well, that’s not strictly true. It took an extra day, because I’d accidentally reset the Time Capsule in the middle of backing up. Apple warned that such an interruption would take a long time for Time Machine to validate the backup the next time. I let this run overnight and it hadn’t completed by morning. So I reformatted the Time Capsule’s hard disk.
Tonight I started a brand new backup, and that’s what took 5 hours. When I add other machines, I’ll make sure to have them wired, and try real hard not to interrupt!
I think this may actually have been the fastest way to back up the MacBook Air — it reports a wireless rate of 130 (I assume that's Mbit/s, which is faster than using the USB Ethernet connector, which maxes out at 100BASE-T).