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son of John Handley Knibbs, was born at Sydney on 13 June 1858. He joined the land survey department of New South Wales in 1877, in 1889 resigned to take up private practice as a surveyor, and in 1890 became lecturer in surveying at the university of Sydney. He was elected a member of the Royal Society of New South Wales in 1881, became a member of the council in 1894, from 1896 to 1906 was almost continuously honorary secretary, and in 1898-9 was president. He was also taking an active interest in other societies, and was president of the Institution of Surveyors at Sydney for four years in the period between 1892 and 1901, and president of the New South Wales branch of the British Astronomical Society in 1897-8. He had begun contributing papers to the Royal Society of New South Wales at an early age, at first on matters arising out of surveying, and then on problems of physics. In his presidential address delivered on 3 May 1899 he showed that he had given much time to the study of mathematics. In 1902 and 1903, as a royal commissioner on education, Knibbs travelled through Europe and furnished a valuable report, which led to his being appointed director of technical education for New South Wales in 1905. He was also in this year acting-professor of physics at the university. In 1906 the Commonwealth bureau of census and statistics was created and Knibbs was made its first director.

Before the establishment of the Commonwealth bureau valuable work relating to the statistics of Australia had been done by H. H. Hayter (q.v.) of Victoria, and T. A. Coghlan (q.v.) of New South Wales; but there was need for co-ordination, and beginning on 30 November 1906 a conference of statists from the different states and from New Zealand was held with Knibbs presiding. As a result of the conference it was agreed that the information collected by each state should be made available to the Commonwealth, and that, as far as possible, there should be uniformity of methods. In 1908 Knibbs issued No. 1 of the Official Year Book of the Commonwealth of Australia, an invaluable work issued yearly ever since, which has established the highest reputation among publications of its kind. Knibbs was in charge of the bureau for 15 years, but was also employed in other activities. In 1909 he represented Australia at five European congresses which discussed such diverse subjects as life assurance, the nomenclature of diseases, the scientific testing of materials, and statistics. During the 1914-18 war he was on the royal commission dealing with problems of trade and industry, and was a consulting member of the committee on munitions of war. In 1920 he represented Australia at the empire conference of statisticians in London. In March 1921 he was made director of the newly-founded Institute of Science and Industry. At the 1921 meeting of the Australasian Association for the Advancement of Science he was president of the social and statistical science section, and took as the subject of his address "Statistics in regard to World and Empire development". Two years later he was president of the association and spoke on "Science and its service to man". He resigned his directorship of the Institute of Science and Industry in 1926, and lived in retirement until his death at Camberwell, a suburb of Melbourne, on 30 March 1929. He was created C.M.G. in 1911 and was knighted in 1923. He contributed 29 papers to the Royal Society of New South Wales, and several of his monographs, largely on statistical subjects, were published as pamphlets. In 1913 he published a volume of verse, Voices of the North and Echoes of Hellas, largely translations, carefully written but not important as poetry, and in 1928 appeared a work on population, The Shadow of the World's Future.

Knibbs was a man of wide culture with a thirst for knowledge. He was deeply interested in more than one department of science, but will be remembered chiefly for his work as a statistician. He married in January 1883 Susan Keele, daughter of L. O'D. James, who survived him with three sons and a daughter. One of the sons, S. G. C. Knibbs, lived for some time in the Solomon Islands, and was the author of The Savage Solomons, published in 1929.