Eureka County is between Lander to the west, Elko to the north, and White Pine to the east. U.S. 50 runs through the middle of town, which is also called Eureka. Highway 50 is the Loneliest Highway in America. Until I get a history of these patches, I will simply list them in the order that I think they came in...
Here are the ones I have in my collection.
To the left is the first patch, which is a stock eagle.
To the right is the first of the state shaped Sheriff patches.
To the left is a second of the Sheriff state shape styles.
To the left is the current style. Note that the one above says Sheriff's Dept. unlike the other two.