Francis stayed active on all levels of involvement in the city of Lowell, and served as an
alderman from 1862 to 1864. In 1865, Francis researched and published his findings on cast iron, and its use in structural columns in "The Strength of Cast-Iron Columns". In 1874, Francis served on the American Society of Civil Engineers committee to investigate the cause of the breach of the Mill River dam in
Massachusetts. Also on the committee were engineers Theodore Ellis and William Worthen. The investigation proceeded quickly and its report was published within a month of the disaster. It concluded that no engineer was responsible for the design and that it was the “work of non-professional persons”. “The remains of the dam indicate defects of workmanship of the grossest character.” Francis originated
scientific methods of testing
hydraulic machinery, and was a founding member of the
American Society of Civil Engineers and its president in 1880.
Francis formula In 1883, Francis completed his calculation standards for water flow rates, now known as the
Francis equation or
Francis formula, usually used in
fluid dynamics in conjunction with calculating
weirs. The equation is Q = 3.33 h_1^{3 /2} (L-0.2h_1) where: Q is the discharge in cubic feet per second over the weir, L is the length of the weir in feet, and h1 is the height of the water above the top of the weir. He remained at the
Locks and Canal Company for his entire career, until retirement in 1884 at the age of 69, and remained on as a consultant right up until his death. His son James took over as chief engineer. The rest of his life he spent with his wife Sarah, and their six children in their home on Worthen Street, which was Whistler's old home and now is the
Whistler House Museum of Art. Francis was called to duty in 1889 as a member of an ASCE committee to examine the cause of the
Johnstown Flood disaster when the
South Fork Dam in Johnstown, Pennsylvania, broke, killing over 2,200 people. Although the report was completed by January 1890, it was immediately suppressed and not released to other ASCE members or the public until mid-1891, two years after the 1889 flood. Francis himself presented the results of the investigation at the ASCE convention in Chattanooga, Tennessee. The other three committee members did not attend. Although Francis’ name headed the report, the
de facto chairman of the committee was Max Becker, a railroad engineer based in Pittsburgh with virtually no experience in dams or hydraulic engineering. According to Francis, it was Becker who delayed the release of the report. A detailed discussion of the South Fork investigation, the participating engineers, and the science behind the 1889 flood was published in 2018. Francis died on September 18, 1892, at the age of 77, and is buried at
Lowell Cemetery under a massive pillar of cut granite stones, symbolizing the stones used to make the canals. ==Honors==