Darwin entered Trinity College, Cambridge in 1906 and was fourth Wrangler in the Mathematical Tripos. In 1910 he became Reader in mathematical physics at Manchester, where he joined the now legendary group working with Rutherford. Here he worked on the theory of the scattering of a-particles and of the diffraction of X-rays by crystals. The latter work was remarkable for its discussion of the effects of imperfections in crystals on the width of the diffracted beams. At that time almost nothing was known about the arrangements of atoms in crystals and it is only in the last few years that the departures from regularity have been properly understood. It must have needed great insight and originality to take up such matters fifty years ago and to get important results.
The work in Manchester was brought to an end by the outbreak of war in 1914. During the war, Darwin worked on sound ranging and flash spotting and was awarded the M.C. In 1919 he returned to Cambridge as a Fellow of Christ's College, but in 1923 moved to Edinburgh where he became professor of natural philosophy. Here he worked on electromagnetic theory and on quantum and statistical mechanics. In collaboration with Fowler he simplified the basis of statistical mechanics by dealing with averages instead of most probable states. He was elected to the Royal Society in 1922 and was awarded the Royal Medal in 1935. He became a Fellow of the Royal Astronomical Society in 1919. He married Katherine Pember in 1925 and had four sons and one daughter, all of whom survive him.
In 1936 he returned to Cambridge as Master of Christ's College, but left, to become Director of the National Physical Laboratory in 1938. In 1941 he went to Washington as Director of the British Central Scientific Office. He returned to the National Physical Laboratory in 1942 but spent most of his time, till the end of the war, as scientific advisor to the War Office. His main contribution to the work of the National Physical Laboratory was perhaps the formation of the Mathematics and Control Mechanisms Divisions and the decision to form the Engineering and Radio Divisions into separate establishments. He was knighted in 1942.
In 1949 he retired to Cambridge, where he lived in the house in which he had spent his childhood. In his retirement he travelled and lectured widely and wrote a book, The Next Million Years, in which he maintained that over-population is the greatest of our problems and that, on the reasonable assumption that philoprogenitiveness is an inherited characteristic, our chances of dealing satisfactorily with it are small.
Darwin was a man of great intelligence and charm with a most engaging habit of deliberately saying the wrong thing when he thought it would stimulate a discussion. I well remember talking to him about the post-war difficulties in Cambridge when he suddenly said "I think the best thing would be to get the Ministry of Education to run the place"; this was particularly effective since he was at the time a member of the University Grants Committee. His cheerful pessimism will be greatly missed in Cambridge and in many other places.