Edward Dobson was born in London, England, probably in 1816 or 1817, the son of Elizabeth Barker and her husband, John Dobson, a merchant. In 1832 his widowed mother apprenticed him to an architect and surveyor. He attended University College, London, obtaining certificates of honour in architecture and civil engineering by 1843. On 7 May 1839, at Shoreditch, London, he married Mary Ann Lough; they had 10 children. Arthur Dudley, their second son, was born in Islington, London, on 9 September 1841. Edward Dobson worked as a railway engineer near Nottingham from 1846 to 1849. When the railway boom ended, he sailed on the Cressy to Canterbury, New Zealand, in 1850, taking the oldest boys, George and Arthur, with him. Mary Ann Dobson and the other children joined them in 1851. Dobson built houses on their land in Christchurch and Sumner.
Arthur Dobson received his early education in Nottingham. From 1851 to 1853 he and George were taught in Tasmania by their uncle, the Reverend Charles Dobson. Family finances improved in 1854 when Edward was appointed provincial engineer for Canterbury, so Arthur returned to New Zealand and attended Christ's College from 1857 to 1858. The boys learnt practical building skills from their father as well as surveying and engineering. Arthur was apprenticed to his father for five years: an early task was assessing the depth of mud in Lyttelton Harbour. Father and son worked together surveying for the Rangiora main drain; their efforts made it possible to drain the 20,000 acre swamp.
Arthur Dobson then spent four months camping and surveying in North Canterbury, reaching Lake Sumner and the Hurunui River. For two years, from December 1860, he worked with geologist Julius Haast. He collected and labelled geological specimens and accompanied Haast exploring and surveying the upper Kowai River. They climbed Mt Torlesse, explored the Southern Alps and the glaciers, and tried to climb Mt Cook.
As provincial engineer Edward Dobson was chosen to superintend the building of a railway tunnel through the hills between Lyttelton and Christchurch in 1860; Arthur drew sectional plans prior to the beginning of construction. One of the first electric telegraphs in New Zealand was installed along the railway.
In 1865 gold was discovered on Canterbury's west coast and Christchurch was eager to share in the new wealth. Immediate steps were taken to build a road to Hokitika. The Dobsons had already helped search for passes over the Southern Alps, and in the early 1860s Arthur had carried out an extensive survey of the West Coast. He survived the rigours of bush surveying with the help of local Maori, whose language he learnt. In March 1864 he had discovered Arthur's Pass, now chosen by his father as the main route to the West Coast goldfields. Edward Dobson offered high wages, creating problems in the labour market, but his drive and energy ensured this difficult road was completed in a year, despite a severe winter in Otira; the road was opened on 20 March 1866. This costly highway was only used once by the gold escort, for the miners soon decided to ship their gold to Melbourne.
Prior to 1868 both Christchurch and Kaiapoi suffered from flooding of the Waimakariri River. The worst flood occurred on 4 February 1868 when water flowed about three feet deep through Christchurch, and the Canterbury Plains resembled a lake. Edward built embankments, and designed a canal through Kaiapoi Island, to straighten the course of the river. He resigned as provincial engineer that year, and river control passed to a board of conservators.
Edward Dobson moved to Australia in 1869, since public works had almost halted in Canterbury. With excellent references he became engineer to a Melbourne railway company, the engineer for water supply, Melbourne, and assistant engineer, Geelong Water Supply. Arthur, meanwhile, had been appointed, on 1 October 1866, assistant provincial engineer for Nelson. On 20 November 1866 he married Eleanor Lewis in Nelson; they were to have four children. In 1867 he explored the Motueka and Karamea districts. He became district engineer for the West Coast goldfields in Nelson province in 1869, provincial engineer in May 1871, and in December chief surveyor for Nelson. In October 1872, while still in the employ of the Nelson provincial government, he was placed in charge of railway construction in Westport by the general government. In 1875 he resigned all his offices in Nelson following a change in the provincial government; he was then appointed district engineer, and had charge of all railway works.
Edward Dobson returned to New Zealand in 1876. He conducted railway surveys until 1878, when he and Arthur formed a partnership in Christchurch. They upgraded the Timaru waterworks, and organised three water supply projects on the Canterbury Plains. In 1884, having surveyed a railway line through the Southern Alps, including '75 miles of the most difficult country in New Zealand,' they launched the Midland Railway Company in partnership with others; the line was not completed until 1923.
Dobson and Son were often called in as consultants. The Christchurch City Council commissioned a report from them in 1882 on providing a public water supply for the city. Artesian wells were plentiful but many private shallow wells were contaminated, and the Avon River was an open drain. Christchurch's figures for typhoid, diphtheria, dysentery and fevers were the worst in New Zealand in the nineteenth century because of the swampy nature of the soil and inadequate sanitation. Fire-fighting was badly hampered with no high pressure supply. Some favoured drawing water from the Waimakariri River, but the Dobsons calculated there was ample artesian water under the city for all requirements. The council approved their scheme, but the ratepayers kept refusing, fearing a rise in rates.
The Dobson partnership dissolved in 1885. Edward Dobson pursued his interest in education. In the 1860s he had participated in lectures to the Christchurch High School which were judged 'the first attempt to make Physical Science a branch of regular instruction in this colony.' He wrote papers for the Philosophical Institute of Canterbury, and the Institute of Civil Engineering, Westminster, London, which awarded him the Telford Medal for his paper 'The public works of the province of Canterbury, New Zealand'. He helped establish the Canterbury College School of Engineering in 1887, submitting ambitious proposals. He lectured part-time in civil engineering until 1892. He was elected a member of the Institute of Civil Engineers in 1881, and wrote many books on engineering. He died in Christchurch on 19 September 1908.
Arthur Dobson moved to Australia in 1885 as the 1880s depression had curtailed Canterbury public works, and for the rest of the century pursued a successful career in engineering. In 1886 he won the contract for the Warrnambool breakwater in Victoria. Designed by the British expert Sir John Coode, Dobson's breakwater remains in place today, although siltation has made the port too shallow for shipping. He then built the Wollaston cable suspension bridge, spanning the Merri River. Although strong enough when first built to carry traction engines, today it is a footbridge, protected by the National Trust of Australia.
Bank failures in Victoria almost ruined Arthur, and he returned to Canterbury in 1898. In 1901 he was appointed city engineer, Christchurch. At last he could perhaps achieve a healthy public water supply for the city. In 1907 the drainage board announced it would proceed with its sewerage scheme whether Christchurch's public water supply was operating or not. Those citizens not on high pressure would be compelled to pay much more for connection with the sewer and to provide their own water for it. The ratepayers capitulated, the water supply loan was passed, and reticulation commenced.
The advent of the motor car meant smoother road surfaces were desirable in Christchurch. Arthur experimented with tar macadam and resurfaced many of the city's streets. His plans to supply hydro-electricity from the Waimakariri River were blocked by legal difficulties with the Waimak–Ashley Water Supply Board.
Arthur Dobson became a member of the Geological Society of London on 30 December 1874, and of the Institute of Civil Engineers on 8 March 1882. He was a member of the Royal Society of Victoria and twice president of the Philosophical Institute of Canterbury. In 1925 he became president of the New Zealand Society of Civil Engineers; knighted in 1931, he died at Christchurch on 5 March 1934.