Here's the telegraph security diagram I shared in class today. To better understand it, consider the following scenarios.
Scenario 1a - Messages Sent via Horses, Agent C Decrypts Messages
In this scenario, once Agent C intercepts the ciphertext as it travels via messenger between Agents A and B, he'll decrypt it, then get on his own horse and travel to Agent B's location to cause trouble. (There is no Agent D in this scenario.) How much time does Agent B have to act on the message before Agent C shows up? Assuming Agent C and the messenger are riding horses with equal speeds, Agent B has precisely as much time as it takes Agent C to decrypt the message.
Scenario 1b - Messages Sent via Telegraph, Agent C Decrypts Messages
Now, after Agent C intercepts and decrypts the message, he sends it along via telegraph to Agent E, who then causes trouble with Agent B. How much time does Agent B have to act on the message before Agent E shows up? Again, precisely as much time as it takes Agent C to decrypt the message. Switching from horses to telegraphs doesn't make Agents A and B any more vulnerable.
Scenario 2a - Messages Sent via Horses, Agent D Decrypts Messages
Now suppose that Agent C merely intercepts the message and gets to Agent D. Agent D decrypts it, then travels via horse to Agent E, who causes trouble for Agent B. How much time does Agent B have to act before Agent E shows up? That would be the time it takes to decrypt the message and the travel time between Agents C and D and Agents D and E. Assuming Agent D isn't located along the A-B route, this means that Agent B has more time than in Scenarios 1a or 1b.
Scenario 2b - Messages Sent via Telegraph, Agent D Decrypts Messages
Same thing, but with telegraphs. Now there's no travel time involved, so Agent B is back to having only the time it takes to decrypt the message as his lead time.
What's the takeaway here? If you're Agent A, then the advent of the telegraph means your buddy Agent B has less time to act on your messages, assuming the other side has to get their intercepted messages to Agent D for decryption. If there's no Agent D, then it doesn't matter if you're sending messages via horses or telegraph, but if there is an Agent D, then you'll want stronger encryption than you used to have.