His birth is probably listed in a Swiss parish register.The LDS church has microfilmed many of them, and you can view them in Salt Lake City or in a local LDS family history center. I looked at the LDS site, www.familysearch.org, and did not find a Charles Meyer born about 1852, but you might check that again.Unfortunately, with a common name like "Meyer" it can be difficult to find the right parish.. The book "Zürcher Familiennamen" often tells what village or villages a name comes from. It has about 1.5 inches of listings about "MEYER" naming about 40 villages. The name MEIER, which might be the correct spelling, has about 18 inches of village names. And those are only for Canton Zurich! So that doesn't seem like much help.( More information like this athttp://www.eye.ch/swissgen/gener-e.htm)http://www.eye.ch/swissgen/gener-e.htm).
I assume you have exhausted all information in the US that might give a village name: death records, church records, naturalization records, prrobate records. You need to search these for him and also any siblings, as they might list a village when his doesn't. Maybe even for close friends! Perhaps a distant cousin would know the information, if you could make a connection there.If you are confident about the immigration date, you might search the imigration indices for NY, Baltimore, etc. They are available at the National Archives and may be obtainable other places.