He entered the army, obtaining a commission in the 12th Regiment of Foot, then stationed in India, where he assisted William Lambton in the Great Trigonometric Survey.

Failing health obliged him to return to England; and in 1808, then a lieutenant, he entered on a student career at the Senior Division of the new Royal Military College at High Wycombe.

[1] His first major contribution to science was the comparison of the merits of the Cassegrainian and Gregorian telescopes; Kater determined the latter to be an inferior design.

[1] His most substantial work was the invention of Kater's pendulum, enabling the strength of gravity to be determined, first at London[2] and subsequently at various stations throughout the country.

The treatise on "Mechanics" in Dionysius Lardner's Cabinet Cyclopedia was partly written by him; and his interest in more purely astronomical questions was shown by two papers in the Memoirs of the Royal Astronomical Society for 1831–1833 — one on an observation of Saturn's outer ring, the other on a method of determining longitude by means of lunar eclipses.