BigC the dimensions are as follows: #1 = 1 1/8 X 1 at the center, 3/4 X 3/4 mid limb, 1/2 X 1/2 at the tips. #2 is slightly flatter in profile at 1 3/16 X 7/8 middle, 1 X 3/4 mid limb, 1/2 X 1/2 at the tips.
The limb cross section is a D with the flat being the back of the bow and rounded belly.
One definition of "D" bow is that the limb cross section must conform to the "5/8 Rule" which states, "The thickness of the limb must be no less than 5/8 of the limb width" (or 0.625 in decimal). Bow #2 is 19/16 X 14/16 at the center (~0.737 decimal ratio) - well within the "5/8 Rule".
The problem of string alignment - that is not only at rest but at full draw as noted by 4est T above - is that the closer to round your limb cross section, the less stable the limb is to torque.
Osage is a great wood for this style of bow. Yew is lighter in density but much less durable. The old saying that "A full drawn bow is 7/8th broken" is about yew. They did not have osage in Europe or they would have been using it. Yew is good stuff and very "lively" because of the light weight of the material, but if you have ever have a piece of yew blow up in your hand you will find it pretty exciting.