I wrote to the Disstonian Institute about the one I found. I got the following three responses from Erik:
1) This is in the 1932 catalog:
The Disston No. 344 Hand Saw for Wood or Metal is made for cutting soft
meal placed over wood; iron bolts; nails imbedded [sic] in wood, etc.
Blade of Disston steel, high temper, taper ground. The have a slight
set.
Beechwood handle, varnished edges, three screws.
24" blade, 12 ppi, 6 3/4" at heel, 2 1/8 at point. $31 per dozen.
It was intended to do the job of a Sawz-all.
2) Thecatalog illustrations show the 340 and 342 with 4-screw handles with
waterproof lacquer finish. The 344 has 3 screws with varnished edges, a
downgrade, I'd say. The 240 is similar to the the 342 in its purpose,
to cut like a hacksaw in steel. The others were discontinued
altogether. I think the changeover from 3xx to 240 model numbers was
around WWII. Your saw has a Disston Phila medallion, I'm guessing.
3) The 1914 catalog shows a hand hacksaw which is identical to the 340 with
no model number. The 1923 catalog has Nos. 340, 341, 342, 343 hand hack
saws. No. 343 is for cutting kalamein, which was a soft metal put over
wood. The teeth could be set on the 343. 340, 341 and 343 were
available in lengths from 16 to 30 inches.
The same catalog shows backsaws for metal. No. 440 cut steel or iron
with lengths from 20 to 32 inches, available with 4 or 5 inch width.
441 was for copper, 442 for metal trim, 443 for kalamein.
I described the 1932 catalog offerings last time. The 240 was sold
after WWII. The saws changed over the time from 1914-1954. Disston
tried out different models. Apparently some did not sell and were soon
discontinued. After the war, Disston offered a much narrower range of
saws than earlier. That trend started in the late 1920's and continued
for the remainder of the company's history.