Hi, and thank you reply,
Why “Generally”, check sounds American for me, and overcheck fits usually with single and tandem. I feel bearing rein was the original word, and then, became sidecheck, and overcheck.
I understand the Black Beauty, especially chapter 23, A Strike for Liberty.
But this means word of bearing rein was popular before 1877.
Horse power era in GB was ended might be 1914, with the end of horse drawn omnibus in London. But the beginning of the end of horse power era started at least 1865, Locomotive Acts (or Red Flag Acts).
So I think, bearing rein must be popular in the first half of 18th century
At that time, what image did people feel with bearing of bearing rein?