Die Numbers On International Machine Cancels

Does anyone know what the die numbers denote? (4 in the wavy lines in the example)?

It's a machine number. Larger cities had multiple machines working simultaneously in their main offices, and sometimes in larger stations (the numbers do not, however, serve as a station identifier).

Thanks paperhistory.

So, it would really be up to the post office as to whether and how the dies of the different machines were set up. For example, I have the same cancellation (an International machine cancel for first class mail) with just the wavy lines (no machine number and no little "c"), which could mean the office had only one machine or, perhaps, that the office hadn't bothered to distinguish machines by customizing the cancellations for each one.

That's commonplace on later international machines in particular, after in many cases the machine number was moved into the postmark dial. (or, as you note, the office only had a single machine).