Langley focused on aeronautics experiments, while Abbot became acting director of the SAO in 1896. When Langley died in 1906, Abbot succeed him as director (in 1907), and Charles Walcott became Smithsonian secretary. Abbot, recognizing that the solar constant was badly approximated, proposed a more accurate value of 1.93 cal/cm²/min for the solar constant (the modern value is measured in watts per square meter).
Abbot was secretary of the Smithsonian Institution from 1928 to 1944. Responsible for the observatory's solar observations, he designed and built devices for measuring solar radiation, including a greatly improved bolometer which measured the Sun's inner corona at the 1900 solar eclipse in Wadesboro, North Carolina.
In 1918 Abbot became Assistant Secretary of the Smithsonian Institute. He succeeded Walcott as Secretary in 1928, and guided the Institute through the turbulent years of the Great Depression and World War II.
From 1941 he was an original standing committee member of the Foundation for the Study of Cycles.
Abbot retired as both SAO director and Smithsonian Secretary in 1944, being the first Smithsonian Secretary not to die in office. He delegated the National Museum largely to his Assistant Secretary, Alexander Wetmore, who succeeded him as Secretary in 1944.
Abbot, like Langley, pursued the idea that the Sun's radiation was variable and that this variability could influence weather. He persistently searched for variations in the solar constant, hoping that these could be used for weather forecasting, and believed that he had detected such variations, on the order of 3% to 10%. However, modern measurements of greater accuracy indicate that such variability does not occur, apart from tiny variations due to sunspots and faculae.
He completed the mapping of the infrared solar spectrum and carried out systematic studies of variation in solar radiation, its relation to the sunspot cycle, and its effect on weather variation. He also studied the nature of atmospheric transmission and absorption. Abbot perfected various standardised instruments now widely used for measuring the sun's heat, and he invented devices utilizing solar energy.
In 1938, Abbot authored perhaps his most singular study, although anonymously. This was his contribution to the Journal of Parapsychology, detailing his studies into clairvoyance. Here he stated that clairvoyance had become as evidential to him as gravitation. His findings were later recognized to represent the first statistical identification of the "displacement effect" in parapsychology. He published a replication of his findings, this time under his own name, in the Journal in 1949.
Abbot crater on the Moon is named after him; an exception was made and it was named for him while he was still alive. He obtained his last patent at the age of 101, the oldest inventor to ever receive a patent. He died in Washington D.C..