I think Wikipedia is correct, except they left something out.
The Pratt truss uses the intersection of the verticals and the lower horizontal tension members to anchor the supports for the short-span girders under the tracks (among other things). With the Baltimore truss, there are almost twice as many points for this to happen because the short verticals will also be used to anchor the supports. Thus the short-span girders can be made lighter because their span is shorter.
When the short-span girders are loaded, they will place the short (and long) verticals in tension. Note that the short verticals are anchored mid-span of the diagonal compressive beams. To lessen the deflection of these beams (this is where the Wikipedia comment comes in) by the short verticals in tension, additional compressive beams are added--the short diagonals.
If you didn't have the short diagonals, the loaded short verticals would add a nasty bend into the diagonal compressive beams.
If you didn't have the short verticals, there would be very little purpose for the short diagonals. Possibly the compressive beams could be made a little lighter duty.
Note also the Waddell "A" truss, above. And compare it to a kingpost truss, of which there is not a drawing. But a kingpost truss looks just like the Waddell "A" truss if you remove the short verticals and diagonals. Which do exactly the same thing that they do in the Baltimore and Pennsylvania trusses. So, just as a kingpost truss is a simplified version of a Pratt truss; so it the Waddell "A" truss a simplifed version of the Baltimore/Pennsylvania.
Ed
PS: notice in the above drawings of bridges that the Baltimore and Pennsylvania are really the same bridge. It would be interesting to do an analysis of each and see the numbers. Perhaps the Pennsylvania is slightly more efficient.
