Reply#1 - Monica - yes, this fits well with what I have and am sure it is the same family. Thanks!
Reply#3 - Dod - Walter was still alive in 1885, living in Boone County, Iowa, age 61 with son, Robert and family. On Oct 23, 1882, there is a marriage record, Boone County, listed on Family Search for Walter m. Euphema Japp, where he lists his parents as James and Margaret. In the 1885 census he lists as widowed, but another researcher has Euphema Japp still living and never has him married to Walter. Perhaps they were married only a short time and divorced? I see the Japp name ties in many years before to a Beveridge line in Scotland.
Looby - thanks for these replies - it does appear that perhaps Jean/Janet was Robert's mother (and other children) and Walter's first wife, as you say would take more research. Interesting there was a Janet Beveridge listed in the 1851 census with Margaret and Walter, but perhaps his sister's name was Janet also.