Arthur Tyndall was born on 12 April 1891 in Dunedin, the eldest of five children of Arthur William Tyndall and his wife, Frances Lawson. He attended Bluespur School (where his father was headmaster), Lawrence District High School and Otago Boys' High School.
At the beginning of 1909 Tyndall (generally known as Bay) started work as an engineering cadet in the Dunedin district office of the Public Works Department under F. W. Furkert. He was involved with railway surveys and irrigation projects. From April 1914 to May 1915 Tyndall was assistant engineer to the Dunedin City Council. He then rejoined the Public Works Department, where his driving ambition was noted by his superiors. In October 1915 he was sent to take charge of construction of the new military camp at Featherston, a major job which he completed in three months. In 1917, commissioned as a lieutenant, he was posted as works engineer officer to Trentham Military Camp.
Tyndall married Gladys Muriel Stoneham, a music teacher, at Dunedin on 5 July 1916; they had no children. In September 1917 he was granted associate membership of the British Institution of Civil Engineers, winning its Bayliss prize by coming first in the examination. In June 1920 he was appointed engineer in charge of public works in Western Samoa. He spent three years there, constructing small water supplies, sanitation works, a hospital, housing and public buildings, and making roads.
Tyndall then spent nearly a year in the United States, where he took a series of specialist engineering courses at the Massachusetts Institute of Technology (MIT). On his return to New Zealand in mid 1924 he was given the post of engineer to the newly formed Main Highways Board, of which Furkert was chairman. He had to secure the co-operation of 236 local authorities who were to provide a proportion of the cost of construction and maintenance of main highways.
In 1925, in a widely distributed leaflet, Tyndall urged the importance of improved roading maintenance, and argued that construction should be concentrated on closing important gaps in the system of hard-surfaced roads. In 1926 the first hard-surfaced highway between Wellington and Auckland was completed. In 1930 he represented New Zealand at an international roading conference in Washington DC and studied highways in the United States, Canada and Mexico. During his time at the highways board, he oversaw the transformation of New Zealand's roads from an inheritance from the horse-and-cart era to a system more suited to the increasing numbers of motor vehicles.
To fit himself for administrative posts Tyndall had, between 1925 and 1928, passed all subjects for the law professional examination, and on 16 May 1929 he was admitted as a solicitor of the Supreme Court of New Zealand. By this time he had also passed all but two of the subjects for the professional accountants' examination. (He was eventually admitted as a professional accountant in 1959.)
To the regret of local authorities and motoring organisations Tyndall left the Main Highways Board in February 1934 to become secretary of mines. His department operated two coalmines and he took immediate and successful steps to improve coal sales, personally visiting all the country's gasworks. He also negotiated with overseas companies interested in drilling for oil. In 1935 he suggested legislation vesting all oil in the Crown; this was achieved with the passing of the Petroleum Act 1937.
In September 1936 Tyndall acceded to a request from the new Labour government to become director of housing construction, though he remained secretary of mines until 1940. He set out from the first to secure the co-operation of the building trade and the support of the New Zealand Institute of Architects. James Fletcher's firm had already been involved with preparing tenders for contracts to build state houses and taken steps which pre-empted decisions Tyndall had been appointed to make; Tyndall had these set aside.
Working closely with the under-secretary of housing, John A. Lee, he engaged talented staff such as town planner R. B. Hammond and architect F. Gordon Wilson. He also persuaded the government to import skilled tradesmen to build the number of houses required. Such was his drive and organising ability that when he left in March 1940, 6,459 houses had been built and the foundations of the 10,000th house had been laid. He was awarded the CMG for his services in 1939.
After considerable thought Tyndall accepted an offer of appointment as judge of the Court of Arbitration, which he took up on 9 March 1940. He correctly anticipated that his appointment would be attacked: the New Zealand Law Society questioned his right to use the terms 'Right Honourable' and 'Mr Justice', and the chief justice of New Zealand, Sir Michael Myers, refused to swear him because he had never practised as a solicitor. Tyndall simply saw his position as 'a real challenge'.
The court's main functions were to make awards, settle disputes and make standard and general wage orders. Tyndall quickly developed his personal approach with the firm view that a minimum of legalism would 'maintain the confidence of litigants'. He became noted for his capacious memory, his detailed knowledge of the statistics that were the basis for submissions put to the court, and the wit, intellect and humanity he brought to the proceedings. He firmly maintained the court's independence, although not all its decisions satisfied parties. Its refusal to issue a general wage order in 1952 led the New Zealand Federation of Labour to call for unions to boycott the court. When he retired in 1965 his work had ensured a large degree of industrial peace and social stability. He was knighted in 1955.
In addition to his work on the Arbitration Court, Tyndall chaired four commissions of inquiry, a court of inquiry and a royal commission: in 1955–56 on monetary, banking and credit systems. He was appointed in 1950 to the International Labour Organisation's commission on freedom of association. In 1952–53 he investigated labour problems in Pakistan; in 1957 he led a mission to Bolivia to report on an economic stabilisation programme (finding a moment on the way to indulge his lifelong hobby and go fishing for trout on Lake Titicaca). His last commission, in 1964–65, inquired into the trade union rights of public employees in Japan.
Tyndall enjoyed a continuing association with American institutions. He had been a member of the American Society of Civil Engineers since 1919, and became a life member. In 1953 he gave a series of lectures at North American universities on industrial relations and arbitration. From 1955 to 1976 he was president of the New Zealand section of the British American Co-operation Movement for World Peace (later the New Zealand–American Association).
Tyndall's concerns for others were evident in his election as president of the Wellington Social Club for the Blind in 1960 and of the Wellington Boys' Institute in 1961. He was a fellow of the New Zealand Institution of Engineers. His later achievements were recognised in 1973 when Victoria University of Wellington conferred on him the honorary degree of doctor of laws. That same year his wife died; Tyndall died at Wellington on 27 June 1979.