Peary’s acceptance of Cook as his surgeon on his first full-scale expedition started the two men down a path that would intertwine their lives forever.  The expedition sailed from New York aboard the Kite in June 1891.  Its other members were a Norwegian skier, Eivind Astrup, Langdon Gibson, Peary’s choice for second in command, John Verhoeff, who had training at Yale’s Scientific School and who had contributed money to the expedition, Matthew Henson, Peary’s manservant, and Peary’s wife, Josephine. 
    On the outward voyage Peary’s leg was fractured in an accident, but it was no test of Cook’s medical skill, as the break did not need to be set.  Rather, Cook gained Peary’s confidence through his patience and unruffled calmness in every circumstance.  By the time Peary’s leg had healed in the spring, Gibson had fallen from Peary’s favor and Cook became his second in command.  

    After landing the expedition members constructed a partially pre-fabricated house and settled in for the winter. 
    Cook, who was appointed the expedition’s nominal anthropologist, quickly established contact with the Inuit living in the area and during the winter took careful measurements of all of the members of the tribe who visited “Redcliffe House.”  The Inuit were astonished at the white men’s house and contents.  There seemed no limit to its wonders and what the strangers might be capable of.  They called the oil lamp on the table “baby sun” and wanted to know if Cook was making his measurements so that he could create other people like them. 
    The object of the expedition was to cross Greenland west to east and to determine how far it extended northward.  In May 1892, Peary, Gibson, Astrup, Cook and Henson set out.  Henson froze a heel early on and returned, but the others went about 130 miles before Peary chose Astrup to complete the trek with him.  
     Cook and Gibson returned to Redcliffe House without incident, and the summer passed.  In August, when the Kite reappeared, Peary and Astrup had not, but they were sighted the next day, having accomplished their object, and had a dramatic reunion with a party from the ship that had gone up on the icecap to look for them.
     The expedition might have been a perfect success had not John Verhoeff disappeared shortly before the time of departure.  Although his body was never found, it appears that he fell down a crevasse while crossing a glacier alone.  Apparently, Verhoeff had planned to stay in Greenland and establish an independent reputation as an explorer and did not intend to return with the expedition.   
    Cook was recognized in Peary’s book, Northward over the “Great Ice,” for both his medical and anthropological work.
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