To estimate how thick your cob walls are going to be, and therefore how wide to make the foundation, see the wall building section (page 86).
Make the ditch for the foundation as wide as the foundation will be, plus enough room to work in comfortably.
Where the ground touches the foundation, the cold or heat of the earth will be transferred into the foundation and into your dwelling. Where temperatures are extreme, insulate the outside of the foundation with something that blocks the transfer of cold or heat and does not absorb water. Modern construction folk use that blue Styrofoam stuff. In the United States, it's called 'Formular'. We've yet to come up with something natural that works well as an outside foundation insulation. Even gravel might help, though. (Refer to page 55 to see where insulation goes.) If you plan to insulate the foundation, leave room for that, too.
For strength, make the base of the foundation wider than the top. You can do this by tapering the sides steeply, or by making the first couple layers underground a foot or more wider than the rest of the foundation.
A tree trunk is wider at the base to give it strength. If you like the cave look with a rounded connection between the wall and the floor, build the foundation extra wide at the bottom with a steep taper. This could be done on the inside or the outside or both.