The Dikeman Mfg. Co. whats-it

[Branson]

>They could have been made with a very sharp plane, but it would have to be ground to a very slight radius.

Sounds like a jack planed surface -- at least that's what I expect of planing with a jack.  Jacks are supposed to have slightly radiused blades.  I like the surface they produce.  You find this even on the top cabinet makers  when you check the bottoms of the drawers and other hidden places.

[ron darner]

On surfaces not ordinarily seen (undersides of drawer bottoms, especially) the marks are probably from a scrub plane; it had a more deeply curved edge, for quickly removing wood from rough-sawn - or even split - boards down to a relatively flat surface with shallow grooves.  The jack plane would have far less curvature, and further flatten the surface.  Even planes used for finish flattening are sometimes given a tiny radius at each corner to avoid showing edge marks.  This can be as little as a couple of passes with the stone when sharpening, and it will still be helpful.
Many times, scrub planes were used at an angle to the grain, or even straight across.  A few passes at different angles does wonders for showing where there are still low spots, or twist!  Wikipedia has a nice picture of a disassembled scrub plane, and the article shows links to other types.  "Jack" was the all-purpose type.

[Branson]

On surfaces not ordinarily seen (undersides of drawer bottoms, especially) the marks are probably from a scrub plane; it had a more deeply curved edge, for quickly removing wood from rough-sawn - or even split - boards down to a relatively flat surface with shallow grooves.  The jack plane would have far less curvature, and further flatten the surface.  Even planes used for finish flattening are sometimes given a tiny radius at each corner to avoid showing edge marks.  This can be as little as a couple of passes with the stone when sharpening, and it will still be helpful.
Many times, scrub planes were used at an angle to the grain, or even straight across.  A few passes at different angles does wonders for showing where there are still low spots, or twist!  Wikipedia has a nice picture of a disassembled scrub plane, and the article shows links to other types.  "Jack" was the all-purpose type.

Mostly, in my experience, a jack plane was used to roughly smooth drawer bottoms, etc.  The object was to smooth rather than to reduce.  A scrub plane hogs off a lot of wood at once.   (Still, I have a country made candle table in which the bottom of the table top had been worked with an adze!)

I always put a small radius on my smoothing planes for exactly the reason you give. 

Jacks can also be used for angled passes, and were often used so to take out light twists in a board as well as to even the thickness.