The book is indeed among the Broome County Historical Society holdings in the Broome County Library in downtown Binghamton, NY. Alas, I do not have the specific book's title as it literally was the last item we were looking at and the facility was closing just as we found this bit of information. If you are familiar with the facility, you know there are bookcases on the right wall of the room (from the perspective of its entrance). The book is shelved with other books covering wars (from the middle toward the end of the bookcases - though it is not the last bookcase) and is among the books covering the civil war. It is not a large book and is small in comparison to many surrounding it and in the same bookcase. It is soft-covered, white being the “background” color. It covers Broome County Civil War enlistments. The exact means by which we searched in the book, I do not quite recall – not sure if was by surname or if it was by searching under Kirkwood, NY enlistments and found Oliver listed. Somehow, I think it was more the latter than the former. We didn’t get a chance to delve further in the book itself nor any other books the society may have covering the men who enlisted from the area during the civil war.
As to living in Champaign, OH, I need to correct that information to be Paris Township, Edgar, Illinois as I misinterpreted what my niece communicated to me as it was in the same conversation I had regarding the Baxters in Ohio. But it was poking around the Champaign Ohio Baxter information that did give us the lead on Oliver and his wife.
What led us to search in Champaign. OH was information contained in the book, Memorial of the Baxter Family by Joseph Nickerson Baxter published in 1879 (freely available on the internet, BTW) as it listed Amelia being located there at the time the book was published. For your reference here is the paragraph from that book on page 113 covering this information
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Stephen Baxter, b. 1781, Fairfield County, Conn., m. Nancy Couch, living with Mrs. Cheney, 1878, over 93 years old ; then moved, early in this century, into Duchess County, New York. Afterwards moved to Broome County, North Binghamton ; there lived till 1839 ; then moved to Champaign County, Ohio. Large family, — one daughter, Mrs. Martha Cook, now resides near Binghampton, N. Y. Two sons, Abraham C. and W. H., now reside at Urbana, Ohio. Stephen, jr., d. from wounds received at battle of Port Republic, Va., June, 1862. Two daughters, Mrs. Charrie A. Cheney and Mrs. Amelia Owen, both widows, live at Mechanicsburg, Champaign County, Ohio. Mrs. Nancy Rogers resides at Hume, Edgar County, I11. Mrs. Abbie D. Hoor, Urbana, Ohio ; husband, V. Hoor. Samuel removed to Broome County, N. Y. ; some of his descendants still reside in New York State. Two sons of Stephen d. after reaching middle age. Seven of Stephen's children living in 1878, youngest over 50.
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Oliver married, September 8, 1887, a first cousin (daughter of Philander R and Amelia S (Baxter) Owen; Amelia (also went by Abby) was a younger sibling of Martha Darling Baxter. Oliver’s wife’s name was Charity D Owen. We surmise she likely was named after another of Abigail’s and Martha’s sisters named Charity who went by Charrie (we also have seen it spelled Charry). It was via her use of this same nickname (Charrie) we found the marriage information.
With that information, and the fact that Oliver married, if you will, within the scope of the Baxter family line, we then searched for him and Charrie on Ohio census records and Illinois census records and found them in the location noted above. (from 1900, 1910, and 1920 Illinois census records – so far)
As FYI, here is a url providing information on Martha’s immediate family, in the event you do not have it. http://archiver.rootsweb.ancestry.com/th/read/BAXTER/2011-03/1299446257
May I ask, are you in this family or by happenstance bought the CDV and bible in the estate auction from which you obtained the items? We are in the Vesalius Cook family line.