On July 12, 1931, Francis P. Farquhar led a Sierra Club climbing school on Unicorn Peak near Yosemite National Park's Tuolumne Meadows. Dawson and Eichorn completed the first traverse of Unicorn Peak that day, and continued on to make the second ascent of Cockscomb Peak. They then joined up with young climber Walter (Bubs) Brem, hiked to Sawtooth Ridge and made a first ascent of Finger Peaks, a new route on the northwest face of Matterhorn Peak, and the first ascent of (later named) The Dragtooth. Returning to Tuolumne Meadows, Dawson and Eichorn climbed Cathedral Peak on July 24, and made the first ascent of its prominent west pinnacle, later named Eichorn Pinnacle. Joined by Brem, the trio then made the first ascent of Echo Ridge, later renamed Matthes Crest.