Our two study species are Melophorous bagoti, a Central Australian desert ant and Cataglyphis fortis, a North African desert ant. Both are highly thermophilic and forage solitarily in the heat of the day of summer. Like many animals, they can keep track of the distances and directions travelled from their starting point (home) to compute a direct vector home. a process called path integration. We studied their memory for the outbound distance travelled on a journey by having them run down a contsrained narrow channel to a feeder. In testing, ants were given a bit of food and released in a long channel to run back towards home. The first point at which they turned back provided their odometric estimate of the outbound distance. The following predictions may be made about odometric memories. They shoudl be good even without training and improve little with practice at the same outbound distance; they need to be good enough to get home even on the first trip. As one journey rarely lasts more than two h, odometric memories should be erased and not integrated with the current estimate. All three predictions were confirmed in both species.