"Blood" is an old timey word for pedigree or ancestry, short for Bloodlines. So there are things like blue blood
and pure blood.
I breed Thoroughbreds, and the use of the word "blood" is still very much used in the original meaning in this industry.
So "Running Blood" would be a reference to the racehorses in the bloodlines of the horses I breed. While I don't breed
for racing, I think the Thoroughbred is the ultimate horse. Here is a poem by Paul Mellon that sums it up nicely.
Thoroughbreds:
The day my final race is run,
And win or lose, the sinking sun,
Tells me it's time to quit
the track,
And gracefully hang up my tack,
I'll thank the Lord the life I've led
Was always near a thoroughbred.
Though
some may think, and I'll agree
That only God can make a tree.
Before He thought of trees it's said,
His mind was
on the thoroughbred.
