Answer by taking a quote from the following article:

Theodore Roosevelt Jr. ( ROH-z@-velt; October 27, 1858 - January 6, 1919) was an American statesman and writer who served as the 26th President of the United States from 1901 to 1909. He also served as the 25th Vice President of the United States from March to September 1901 and as the 33rd Governor of New York from 1899 to 1900. As a leader of the Republican Party during this time, he became a driving force for the Progressive Era in the United States in the early 20th century. His face is depicted on Mount Rushmore, alongside those of George Washington, Thomas Jefferson, and Abraham Lincoln.

Theodore Roosevelt Jr. was born on October 27, 1858, at East 20th Street in New York City. He was the second of four children born to socialite Martha Stewart "Mittie" Bulloch and businessman and philanthropist Theodore Roosevelt Sr. He had an older sister, Anna (nicknamed "Bamie"), a younger brother, Elliott, and a younger sister, Corinne. Elliott was later the father of First Lady Anna Eleanor Roosevelt, the wife of Theodore's distant cousin, President Franklin Delano Roosevelt. His paternal grandfather was of Dutch descent; his other ancestry included primarily Scottish and Scots-Irish, English and smaller amounts of German, Welsh, and French. Theodore Sr. was the fifth son of businessman Cornelius Van Schaack "C.V.S." Roosevelt and Margaret Barnhill. Theodore's fourth cousin, James Roosevelt I, who was also a businessman, was the father of President Franklin Delano Roosevelt. Mittie was the younger daughter of Major James Stephens Bulloch and Martha P. "Patsy" Stewart. Through the Van Schaacks, Roosevelt was a descendant of the Schuyler family.  Roosevelt's youth was largely shaped by his poor health and debilitating asthma. He repeatedly experienced sudden nighttime asthma attacks that caused the experience of being smothered to death, which terrified both Theodore and his parents. Doctors had no cure. Nevertheless, he was energetic and mischievously inquisitive. His lifelong interest in zoology began at age seven when he saw a dead seal at a local market; after obtaining the seal's head, Roosevelt and two cousins formed what they called the "Roosevelt Museum of Natural History". Having learned the rudiments of taxidermy, he filled his makeshift museum with animals that he killed or caught; he then studied the animals and prepared them for display. At age nine, he recorded his observation of insects in a paper entitled "The Natural History of Insects".  Roosevelt's father significantly influenced him. His father was a prominent leader in New York's cultural affairs; he helped to found the Metropolitan Museum of Art, and had been especially active in mobilizing support for the Union during the Civil War, even though his in-laws included Confederate leaders. Roosevelt said, "My father, Theodore Roosevelt, was the best man I ever knew. He combined strength and courage with gentleness, tenderness, and great unselfishness. He would not tolerate in us children selfishness or cruelty, idleness, cowardice, or untruthfulness." Family trips abroad, including tours of Europe in 1869 and 1870, and Egypt in 1872, shaped his cosmopolitan perspective. Hiking with his family in the Alps in 1869, Roosevelt found that he could keep pace with his father. He had discovered the significant benefits of physical exertion to minimize his asthma and bolster his spirits. Roosevelt began a heavy regime of exercise. After being manhandled by two older boys on a camping trip, he found a boxing coach to teach him to fight and strengthen his body.

What was significant about his fourth cousin?
the father of President Franklin Delano Roosevelt.