Her name is listed as Jane E. on the 1860 and 1870 censuses, on her mother's affidavit for her marriage to James Rogers and in his Pension application.
In the 1900 US Census for Cleveland Ward 41, Cuyahoga County, Ohio Jane Elizabeth Barnum (using her maiden name) and her daughter Cora N. Rogers were enumerated with the family of Edward Bartholomew, as follows:
Dwelling #124; Family #145 (1057 Detroit Street)
Bartholomew, Edward; Head; W; M; b. Dec. 1857; 42; Married 22 years; b. Ohio; Both parents b. Ohio; Mason and Jobber; Employed full year; Can read, write and speak English; Rents non-farm home
Bartholomew, Cornelia; Wife; W; F; b. Jan. 1860; 40; Married 22 years; Mother of 1 child; 1 child living; b. Ohio; Father b. New York; Mother b. Ohio; Can read, write and speak English
Bartholomew, Guy E.; Son; W; M; b. Mar. 1879; 21; Single; b. Ohio; Both parents b. Ohio; Tobaconist; Employed full year; Can read, write and speak English
Bartholomew, Louisa; Mother; W; F; b. Aug. 1832; 67; Widowed; b. Ohio; Both parents b. New York; Can read, write and speak English
Rogers, Cora N.; Niece; W; F; b. Jun. 1875; 24; Single; b. Ohio; Both parents b. Ohio; Stenographer; Employed full year; Can read, write and speak English
Barnum, Jane L.; Mother-in-law; W; F; b. Dec. 1825; 74; Widowed; b. Ohio; Father b. New Hampshire; Mother b. Vermont; Can read, write and speak English
She died of Typhoid Fever.