I think with it being a 40-hole, it will specifically NOT be a Schwinn rim. It will probably take the smaller size 26x1-3/8" tires. (Possibly marked EA-3 British Rims).
The difference in size is 7mm. Schwinn's 26x1-3/8" S-5 and S-6 used 597mm rims. The "rest of the world" used 590mm rims and tires.
One won't fit the other. The reason I don't believe it will be the Schwinn size is that Schwinn never used anything but 36 hole rims on these bikes. The Raleighs (and many other brands they owned) used the 40 hole in the rear.
The 40 hole is not good for much other than parts or for actually fixing an English bike. There's not really any other spoke pattern that can use this rim.
--Rob
EDIT: corrected tire sizes, 590mm and 597mm for non-S6 and S6 sizes. Both are labeled the same on rims and sidewalls "26x1-3/8"