In the 1890s, Erskine worked at Canterbury College with Ernest Rutherford on a number of electrical experiments and was awarded the Exhibition of 1851 Scholarship as an engineer of exceptional promise.
After working in Germany and London, he returned to the College to obtain first class certificates in strengths of materials, advanced steam, mechanics and machinery. He then worked for the General Electric Company in the US followed by the Sulphide Corporation at the Broken Hill mines in Australia, and again for General Electric in Australia.
In the 1920s, Erskine worked as a private consultant, applying his analytical skills to the stock market which he played with great success.
When he died in 1960, his will established the Erskine Programme, a trust fund to support teaching staff overseas to increase their knowledge of any subject taught in the science, engineering or commerce faculties and better enable them to teach those subjects.
This legacy, known today as the Erskine Programme, still supports academics travelling to and from UC, and the building that houses mathematics and statistics at the University is named for him.