1. a. trans. To hit or strike hard; to drive with blows. Also fig., to assail violently.
b. Cricket. To obtain (runs) by hard hitting.
2. intr. To walk heavily or doggedly.
Halliwell's ‘Slog, to lag behind’ probably belongs to
3. a. To deal heavy blows, to work hard (at something), to labour away, etc.
Somehow all that cricket terminology makes slogging seem much more vigorous than what I had in mind. The 1876 quote under usage #2 was more what it feels like, trudging laboriously through puddles. A combination of sludge, effort, and sloth = slog. Or at least I thought so. But perhaps I can now reconfigure my mental attitude and go "assail" some papers "violently." Or something.