Not of my lines but here goes.
1930 US Census for Nebraska, Cherry County, Evergreen Precinct, ED# 16-13, Page 155 (1B), 15/15
William Ballard, Head, 56, M28, IA, MO, US, Rancher, Ranch
Catharine, Wife, 48, M28, NE, US, Ireland, None
Walter, Son, 25, NE, IA, NE, Teacher, Public school,
Ester M., Dau, 20, NE, IA, NE, None,
Dudley F., Son, 19, NE, IA, NE, Ranch hand, At home,
Ruth C., Dau, 18, NE, IA, NE, None
Thomas C., Son, 16, NE, IA, NE,None
James, Son, 15, NE, IA, NE, None
Billy, Son, 12, NE, IA, NE, None
Vera M., Dau, 11, NE, IA, NE, None
John R., Son, 9, NE, IA, NE, None
Neal, Son, 6-2/12, NE, IA, NE, None
Helen, Dau, 4-2/12, NE, IA, NE, None
Theodore Chaffin, Boarder, 18, NE, US, US, Ranch Hand, Ranch
Cecil Hamilton, Boarder, 33, NE, US, IA, Ranch Hand, Ranch
"Mr. Latta's next well was made for W. H. Stratton at its store at the Oasis Post Office, midway between Simoen end Kennedy, but later discontinued. News of the success of these two wells soon spread to all parts of the county and Mr. Latta was in much demand to make wells which were sorely needed. To show what this meant to the early ranchers, during the winter of 1894-95 at the homestead of the author, one hundred head of mature cattle were watered by pumping the water with a wooden pump by hand from a shallow well."
This is in Cherry County south-west of Valentine and does not appear on a current Nebraska Atlas.Two other land marks are the Samuel R McKelvie National Forest (to the North-west) and Valentine National Wildlife Refuge (to the South-east).
1920 US Census for Nebraska, Cherry County, Evergreen Precinct, ED# 16-13, Page 166 (1A), 1/1, (William IA, TN, IA, Catharine, Walter, Ester M., Dudley F., Ruth C., Thomas C., James, Billy, Vera M.).It looks like his brother at 2/2 (Edward IA, TN, IA, Mary, and Edmond).
I didn't see them in 1910 in Evergreen Precinct.