Joseph Morgan was a noted pioneer rancher and leading settler of the Panhandle in the early 1880s. His life was brief, and little is known of his earlier years. He arrived with his bride in the Panhandle in 1877 after their marriage in La Junta, Colorado. With his brother-in-law, Mose Wesley Hays, Morgan went to Padre Island and purchased 800 cattle bearing a Mexican brand called the Chicken Foot H. Hays bought 100 head of this stock, which he and Morgan trailed back to the Panhandle. There Morgan rebranded his cattle with a Quarter Circle B on the left side and a crude triangle on the hip, while Hays used the Lazy T brand. Morgan located his spread in Lipscomb County twenty-five miles north of the Springer Ranch on a Canadian River tributary. Hays had a spread six miles down the Canadian valley from Morgan on Big Timber Creek in northern Hemphill County. Morgan was a charter member and executive committeeman of the Panhandle Stock Association, organized in 1880 at Mobeetie. He served on the Wheeler County grand jury in 1882. By the summer of that year he was reported to have significantly increased his rangeland. Because of his triangle brand, his ranch became known locally as the Triangle, although several other ranches throughout the state later adopted triangle brands in various forms.
In February 1883 Morgan went to Kansas City to close out a trade contract in which he planned to sell his cattle for $100,000. This deal fell through, however, and he returned to the ranch, where in March he and his two small sons came down with smallpox. Edward H. Brainard, who had been working at the Triangle for two months, rode thirty-five miles to Mobeetie for a doctor while another ranchhand, Frank Biggers, rode 150 miles to Fort Dodge, Kansas, to try to find a doctor there in time to save his employer's life. Though both doctors came, it was too late to save Joe Morgan, who died at the ranchhouse on March 16. Brainard and another cowboy, John Dilly, drove Mrs. Morgan and the two boys to Fort Dodge with the doctor in hopes of saving them there. Six-month-old Johnny recovered, but his three-year-old brother died and was buried at Dodge City. Mrs. Morgan eventually sold the ranch to Henry W. Cresswell, who added the property to his Bar CC Ranch. Later Morgan's former ranchland became the property of E. E. Polly, of David M. Hargrave, and then of the brothers Jesse and Otto Yokley, whose family still owns it. Morgan is buried at the ranch. The Masonic order, of which he was a member, has erected a marble shaft over the spot and surrounded it with an iron fence.