Can't find ip addresses of devices on LAN

[Thomas George <lists@tomgeorge.info>]

I have tried ping 192.168.1.225 followed by arp -a

and I have tried netstat -r

Neither report ip addresses of attached devices.

I know there are two devices besides this pc and I know the address of 
one of these devices. I can ping it and it responds.

How to find the address of the second device other than ping each 
address from 192.168.1.2 to 192.168.1.255?