1855 September 27th. Born at 14 Albert Terrace, Bayswater, London, the fourth son of the judge Sir John Charles Frederic Sigismund Day (1826–1908) and his first wife, Henrietta Rosa Mary, née Brown (1824–1893).
1868-73 Attended Beaumont College, a Catholic school at Windsor
1873-74 Trained as an engineer at the School of Practical Engineering at Crystal Palace in London
1874-77 Worked at Stothert and Pitt in Bath
1878 With J. W. Lampard he started an iron foundry in the Victoria Ironworks, off the Upper Bristol Road, Bath, making cranes, mortar mills and compressors amongst other things and most work came from his former employer.
He advertised a new design of “valveless air compressor” which he made on licence from the patentee, Edmund Edwards.
1879 May 10th. Married at Midford Castle near Bath to Margaret Anne (1853–1933), eldest daughter of James John Parfitt of Bruton. They had nine surviving children
1881 Living at 9 Devonshire Buildings, Wells Road, Bath, Somerset (age 25 born London), Mechanical Engineer. With wife Margaret A. (age 27 born Brecon) and son Thomas S. L. (age 9 months born Bath). Also James J. Parfitt (age 23 born Brecon) his Brother-in-Law. Two servants. 
1885 Advertisement for portable hand cranes, mortar Mills and valveless air compressors by Day and English
1888 Director of the Western Counties Steam Bakeries and Milling Co when it was formed
1889 He was working on an engine design which would not infringe the patents that Otto had on the four-stroke, and that he eventually called the Valveless Two-Stroke Engine. On the original design there were two flap valves - one in the inlet port, where you would probably find a reed valve on a modern two stroke, and one in the crown of the piston, because he did not come up with the idea of the transfer ports until a couple of years later. He made about 250 of these first two-port motors, fitting them to small generating sets, which won a prize at the International Electrical Exhibition in 1892.
1891 Living at 14 North Parade, Bath (age 35 born London), Manufacturing Mechanical Engineer and Employer. With wife Margaret (age 37 born Brecon, Wales) and children Margaret (age 9), John (age 8), Charles (age 7), Ethel (age 6), Joseph (age 1) and Arthur (age 2 months). Also Sister (wife's?) Ada Reynolds and four servants. 
1891 April. Applied for a patent of the engine which was granted the following year (June 1892).
1892 One of Joseph Day’s workmen, Frederick W. C. Cocks, who made the modification which allowed the skirt of the piston to control the inlet port and do away with valves altogether, giving rise to the classic piston ported two stroke. This design was patented in October 1892.
1892 January. Exhibited a two-port engine at the International Electrical Exhibition at Crystal Palace
His company in Bath was a general engineering one, and his engines were a sideline. Much of his money came from the manufacture of bread making machinery, and the prices of wheat were very turbulent around the turn of the Century. The profitability of Day’s factory fluctuated just as wildly. These were early days for the idea of the limited company, and shareholders, then as now, could panic and bring down a company that they thought to be under threat. The problem was made worse by the publication of rumours, or the deliberate orchestration of publicity campaigns in the press.
A flurry of lawsuits followed, with Day as both plaintiff and defendant. The Treasury Solicitor even tried to have him extradited from the USA where he had gone to try to sell his US patents in order to raise money. The case was eventually settled when the jury found that Day had no case to answer, but it all came too late, and he went into virtual retirement by the seaside. The development of his engine then passed to his licence holders in America, whose royalties restored his finances sufficiently to allow him to launch a spectacular new venture after the First World War.
1893 September. Declared bankrupt
1894 May. Works and stock of the business auctioned
1894 June. Verdict returned of 'not guilty' to fraudulent accounting. 
The first American patent was taken out in 1894, and by 1906, a dozen American companies had taken licences. One of these, Palmers of Connecticut, managed by entrepreneur Julius Briner, had produced over 60,000 two-stroke engines before 1912. Many of these early engines found their way into motorcycles, or onto the back of boats.
c1896 He moved from Bath to Weston-super-Mere
1898 Involved in legal action against the Millbury Engineering Co and the Valveless Gas Engine Syndicate regarding the 1892 patent rights on the engine he had sold them. He claimed it was only for the first gas powered version of the engine and not for the later oil type which he had developed some years after the 1892 patent. 
1901 Living at 1 Paragon Villas, Weston-super-Mere (age 45 born London), Civil Engineer working on own account. With with Margaret (age 45) and children Margaret A. (age 19), Joseph (age 11), Arthur (age 10), Wilfrid (age 5 born Bath) and Gwendoline (age 4 born Weston-super-Mere). Three servants. 
1905 October. Formed the Day Inventions Co in New Jersey with his cousin Thomas Fleming Day (1861-1927).
1906 Discharged from bankruptcy and opened Day Motor Co, an engine making business at Barking and then later at Putney
Became involved with a new enterprise for the exploration for oil in shale at Norfolk. He joined the board of English Oilfields but resigned in 1923
1946 December 25th. Died at 1 St. George's Road, St Margaret's-on-Thames aged 91
Buried at Teddington Cemetery
Sources of Information
- 1881 Census
- 1891 Census
- Manchester Times, Friday, June 15, 1894
- The Bristol Mercury and Daily Post, Wednesday, December 21, 1898
- 1891 Census