The Sept. 26, 1907 NYT reports on the accidents of the mass transit systems in the greater New York City area. The story reports, "[t]he traction companies, steam, electric, and horse, surface, Subway, and elevated, kill or seriously injure every month about 200 persons."

The story reports that from Aug. 5 through Aug. 31, there were 5,500 accidents reported in the Greater New York area:

Persons injured in car collisions...............145
Persons injured in collision with vehicles...465
Persons struck by cars............................405
Persons injured boarding cars..................641
Persons injured alighting from cars...........1,263
Employes injured....................................641
Derailments............................................33
Injuries on stairways...............................26
Other accidents......................................1,881

The paper counted each injury as a separate accident, so we don't really know how many separate incidents in which the 5,500 individuals were injured.

However, in the same time period, 189 persons were either killed or seriously injured:

Persons killed.............42
Fractured skulls...........10
Amputated limbs.........10
Broken limbs...............44
Other serious injuries...83

It's not clear that the August of 1907 was a typical month on the transit system. Moreover, we don't know how many people rode the transit system over the same period - perhaps the system was much safer (in percentage terms) than is portrayed in this article. Nevertheless, it seems that during that month it was rather dangerous to ride the trains in New York City.