There is a Great deal of Difference between "Riding Breeches/Jodphurs" Cavalryman & the Upper Classes wore for riding & "Short Pants" that Little Boys worn that came to just above the knees or "Knickers" that Sportmen wore that came to just below the knees.
First & Foremost "R.B./Jodpurs" came all the way down to ones ankles, they were buttoned or lacied there so as not to ride up ones leg. They were also cut loose fit from Hip to Knee for comfort, some more snugly or loosely, depending on the fashion trend @ the time & Fit Snug from Knee to Ankle worn w/ Hunt/Riding/Field/Hussar/Lancer/Wellington Boots.
"Short Pants" for little boys were cut loose from hip to just above the knees & did not fasten @ all any place around the knees & were worn w/ cotton Knee Socks.
"Knickers" worn by Sportsmen fastened just below the knee via Buttons or Buckle & Billit, were worn w/ Heavy Wool Knee Socks, along w/ Gaitors made out of Heavy Duty Cordaroy, Canvas, Wool, Leather or combinations there of.
Jodphurs came out of JODPHURA, India & were worn originally by the Ruling Class Indians during Tiger Hunts, Polo Matches & just in general riding from the 1830's on, in the classic style as we know them today.
There are actually 2 distinct styles of Jodphur Breeches, one is as discribed above & one that does not Button or Lace-up just above the ankle. This style Flares slightly from just above the ankle & reaches just below the Arch of the Foot, w/ a Buckle & Billit on either side to be Strapped under the instep of an ankle boot, supprisingly enough called the "Jodphur Boot".
Oh, & by-the-by, Frederick Burnham was an American that Learned his Craft as a Scout in the South West while growing up & was hired by the U.S. Army as such. He was propecting for gold in Az. & was also around the happenings between the Earps & the Clantons.
He went to South Africa to make his fortune in the Gold Fields there, when some of those "Little Wars" broke out. So F.B. Already Having Fought against the Apaches, Kiowas & the like, did rather well using those same learned Scouting Skills successfully against the Native African Tribesman, as well the Boers of the Transval & Orange Free State & as you know the Boers were a Modern Equipted & Trained fighting force or you should.