For sure, you cannot access s1.s2.s3.s4 address from inside. I don't know any way to achieve that. Your URL should use "host name" instead of IP address. It's a best practice to use "host name" or i should write a mandatory practice when designing a web site, "never use ip addresses directly". When you use host name in URL, i know two ways to convert them to real address, as seen by internal users. The way you choose is depending of your DNS position and configuration:
1- You have internal DNS only just for internal users, this way, you write the real address in this DNS. Outside users use an ISP DNS where your primary and your secondary DNS are hosted.
2- Don't have a dedicated internal DNS, use public DNS (primary & secondary), hosted by an ISP or in your DMZ, then that way you must use "alias" command.
Regards,
Ben