I keep getting email bounced back to me, so I'll reply here on the public forum. . .
There wasn't anything in the 51st Infantry book about a Jesse Thompson, but I looked at an online Civil War database for information.They had 6 Jesse Thompsons serving from Indiana, none in the 51st or 61st.If you're right about the Co. I part, then it was probably the one in the 63rd Infantry.Says he mustered into Co. I of the 63rd on 8-9-1862 and was discharged 5-26-1865.
There were 9 Mcpheeters from Indiana listed-- two from Washington County, one each from Bloomington, Logansport, Fredericksburg, Livonia, Monroe County, and Cass County, and one without a residence listed.None was listed as Welcome, although the one without a residence listed was a William who was discharged in Indianapolis, so at least we're in the right part of the state.