Working with Professors James Alfred Ewing and Bertram Hopkinson, he made several important studies into the effects of vibration on structures and defects on the strength of plate steel.

Inglis sat on the board of inquiry investigating the loss of the airship R101 and was chair of a Ministry of War Transport railway modernisation committee in 1946.

[5][6] Inglis was 22nd wrangler[nb 1] when he received his Bachelor of Arts degree in 1897; he remained for a fourth year, achieving first class honours in Mechanical Sciences.

[2][5] He worked as a draughtsman in the drawing office for several months before being placed with Alexander Gibb, who was acting as resident engineer on an extension to the Metropolitan District Railway between Whitechapel and Bow.

[2] In 1901 Inglis was made a fellow of King's College after writing a thesis entitled The Balancing of Engines, the first general treatment of the subject – which was becoming increasingly important due to the growing speeds of locomotives.

[15] Inglis conducted research into the problem of fracture in the metal plates of ships' hulls and noticed that the rivet holes along the path of a crack were often deformed into an elliptical shape.

[16] This phenomenon led him to investigate the magnification of stress caused at the edges of an elliptical defect; in 1913 he published a paper of his theories that has been described as his most important contribution to engineering and the first serious modern work on the fracturing of materials.

[2][8] Upon the outbreak of the First World War in 1914, Inglis volunteered for active service in the British Army and was officially listed as an Assistant Instructor in the School of Military Engineering, with the temporary rank of lieutenant.

[29][30] He was promoted to the brevet rank of major as part of the King's Birthday Honours on 3 June 1918 and later that year worked with Giffard Le Quesne Martel to develop some of the earliest bridgelaying tanks.

[2][34] On 25 March 1919, he was selected to head the Cambridge University Engineering Department as the successor of Hopkinson, who had died in an air crash the previous year.

[2] He was responsible for expanding the department to meet the increased post-war demand for engineers and for the move from its traditional home at Free School Lane.

[35] Inglis acquired the 4-acre (1.6 ha) Scroope House on Trumpington Street for the department and constructed a 50,000-square-foot (4,600 m2) laboratory on the site by 1923, followed in 1931 by a structure containing lecture theatres and a drawing office.

[41] Undeterred, Inglis sought to give his students the broadest possible engineering education, covering all fields to prevent them becoming "cramped by premature specialisation".

[15] Inglis had close contacts with industry and was able to establish a professorship in aeronautical engineering and links with a nearby Air Ministry experimental flight station.

[42] From 1923, he was involved with the analysis of vibration and its effects on railway bridges, including a period spent working with Christopher Hinton during the latter's final year as a student at Cambridge.

[34][43] Inglis was appointed to a sub-committee of the British government's Department of Scientific and Industrial Research Bridge Stress Committee by Ewing, who was chairman, and became responsible for almost all of the mathematics of the investigation.

[34] He followed up the work by using a harmonic series and Macaulay's method to approximate the vibration of beams of non-uniform mass distribution or bending modulus.

[9] He received the ICE's Telford Medal in 1924 for a paper entitled The Theory of Transverse Oscillations in Girders and its Relation to Live Load and Impact Allowance.

[47] Inglis founded the Cambridge Engineers' Association to promote social activities at the University, and saw Sir Charles Parsons appointed as its first president in 1929.

[6][15] He was a member of the London, Midland and Scottish Railway's Advisory Committee on Scientific Research from 1931 to 1947 and conducted numerous experiments on their behalf in the laboratories at Cambridge.

[54] Testing of a prototype of the Mark III revealed a weakness in the top chord of the truss and the subsequent redesign complicated the production process.

[6][11][59] He gave the Parsons Memorial Lecture to the North-East Coast Institution of Engineers and Shipbuilders in 1945 in which he presented his Basic Function Method, an alternative to the use of Fourier series for the analysis of vibrations in beams.

[6] He received a knighthood in the 1945 King's Birthday Honours, and in 1946 was appointed as chair of the committee charged with advising the Minister of War Transport on railway modernisation.

[61] He published the textbook Applied Mechanics for Engineers in 1951, following which he spent three months as a visiting professor at the University of the Witwatersrand in South Africa.