First of all I found the Johnson-Cutshall Family Tree, http://trees.ancestry.com/tree/21704170/pers
... which contains your Ray family. Of course you need to verify all of the information before you enter it in to your database.
A William Ray married Mary E. Dunkin 12 March 1850, Nodaway Co., Missouri.
Source: Missouri Marriage Records 1805-2002.
In 1870 the family lived in Yell, Boone, Iowa.
William L. Ray, b. MO, 39, farmer
Mary E., wife, b. MO, 38.
John W., b. IA, 18, farm laborer.
Elizabeth M., b. IA, 16.
Keziah A., b. IA, 14.
Mary F., b. IA, 12.
Otic C., b. IA, 2.
Thomas E. Ray, b. IA, 2/12ths.
In 1880 the family was living in Kirwin, Phillips, Kansas.
Wm. L. Ray, b. OH, 48, jeweler.
Mary E., b. MO, 48.
Thomas E., b. MO, 10.
Lettie J., b. IA, 7.
I didn't find Thomas Ray living at Fort Duchesne in 1900 but then I didn't find him anywhere on the Census.
There is an article about Fort Duchesne at www.archives.state.ut.us/research/indexes
. "Fort Duchesne declined in use from 1890 to 1910. By 1893 the four infantry companies were removed to Ford Douglas. By 1909 there was only one company of cavalry left. . ." In 1910 after an Army inspection the fort was shut down.
I'd look in the Utah Archives for more information about the Fort.
I'd also order a copy of the obituary for the Thomas E. Ray who died in Kansas. William was a military man in the Mexican American and Civil War. Thomas might have followed in his footsteps and moved around with the military so he isn't found in the Censuses. Successful Searching!