I looked up more in The Big War series. Google had all but one scanned and available as a free e-book.
The order of the series is:
1.) The Search for the Spy
2.) The Air Scout (this is the one Google didn't have)
3.) Dodging the North Sea Mines
4.) With Joffre on the Battle Line
5.) Fighting in France
6.) Battling on the Somme
7.) With Pershing at the Front
8.) Smashing the Hindenburg Line
The last in the series was published in 1919, so the author and readers knew how it all turned out. I'll see if it gets more jingoistic once Earl and Leon are fighting with American troops. The Army Boys series was quite jingoistic, from what I read of that. Fighting in France was rather more subtle. Ross Kay seemed to be quite a decent writer. He must have been turning the books out pretty quickly to stay up to date, but he was using dispatches to portray the kinds of things that actually happened. I found it interesting that the books in the series were coming out at the beginning and middle of the war as well, when they didn't know what was going to happen. The Army Boys books seemed to have all come out in 1919, when they did know how it all turned out.
As I looked at some of the other series I had noted, like the Motor Boys ones, I saw that many of the boy heroes in boys' adventure stories had gone to war by 1917 or 1918. It reflected what was sweeping over the nation. It went from The Motor Boys in 1906 to The Motor Boys in the Army in 1918 and The Motor Boys Bound for Home; or Ned, Bob and Jerrry on the Wrecked Troopship in 1920. So much for the very early part of the century's joy in automobiles. Times had changed.
(Added later: Actually, there had been a number of the books before the army ones, and apparently the boys had gone from everything from motorcycles to automobiles to "aeroplanes" to motorboats, and all over the world. There was a series about them going to college, as well.)
The Motor Boys in the Army was about them enlisting and having basic training, or whatever it was called in 1918, in a made-up Army camp in the South. They had a few adventures, but it was a book full of description of Army life and drills. And -- oh, dear -- they star in a minstrel show given on base. I guess it was a very popular thing at the time. It was a shock to modern sensibilities.
Apparently they go overseas in the next book in the series, which is not an e-book. The next e-book available is The Motor Boys Bound for Home, which I skimmed a bit. I wonder if that's where the series ends, or if it continues further.
I got out of the house a couple of times, once to pick up pizza for dinner and once to go to the grocery store. They weren't fun trips, but it's good for me to get out.