Carbon and Emery Counties were once one county called Emery County. In fact, originally both those counties were part of Sanpete County.
In 1894 the territorial legislature separated the two eastern Utah districts creating the map we know today.
When this was done Carbon was primarily a coal mining and railroad county while Emery had an agricultural base.
Once the division was done Carbon ended up with 1,476 square miles of property within its borders. Emery has 4,439 square miles.
If one does the math, Emery is just barely three times bigger than Carbon, but it's total population is only half of its northern neighbor.