James Palladio Basevi was the son of the celebrated architect George Basevi, who designed buildings including the Fitz-William Museum at Cambridge. He attended Rugby School, Cheltenham College and the Honourable East India Company's Military Seminary at Addiscombe, before obtaining a commission in the Corps of Engineers, and went to India in 1853. In 1856 he was appointed to the Great Trigonometrical Survey of India, upon which he continued to serve until his death. He held a prominent role in each part of the operations, from the triangulations, linear measurements, topography and mathematical reductions; to completing two chains of principal triangulation of an aggregate length of nearly 300 miles; to supervising the measurement of a base-line at Cape Comorin and writing a paper on the errors of the measurement which was published in 'The Account of the Operations of the Great Trigonometrical Survey of India'.

In 1864 Basevi was selected to undertake the Pendulum Operations, determining the variations in gravity at certain points of the meridinal arc in India. The purpose of this was to obtain data to learn more about the hape of the earth and to understand more about the Earth's crust.

He died suddenly after a short illness at the age of 39.