On his return to England, he qualified himself to serve on the general staff, and later in life retired on half-pay, from which period he devoted himself entirely to science. When Parliament, in the years 1818-19, determined on establishing an uniform system of weights and measures, Captain Kater, in conjunction with Sir Joseph Banks, Sir George Clerk, Davies Gilbert, and Drs. Wollaston and Young, was appointed to investigate this most important subject; and he instituted a series of experiments with a pendulum made of a bar of brass, 1½ inches wide and 1/8 of an inch thick, to which two knife-edges of a kind of steel prepared in India, and known by the name of wootz, were attached, playing upon agate plates. The knife-edges were placed in a parallel direction on the brass bar, facing opposite ways upon either of which it might be swung. They were so arranged, that when either was used as the point of suspension the other nearly represented the centre of oscillation, and by means of a small adjustable weight, this condition might be accurately fulfilled. These experiments were made in the house of Mr. H. Browne, F.R.S., which was situated in a part of Portland Place not likely to be disturbed by carriages. They occupied Captain Kater's close attention for several years; and he has permanently attached his name to the beautiful theorem of Huygens respecting the reciprocity of the centres of oscillation and suspension, and their consequent quality of convertibility. Although this was a property already known to belong to the centre of oscillation, it had never hitherto been practically applied to determine the exact length of a pendulum vibrating seconds; it was, therefore, highly creditable to his ingenuity, and claims the same order of merit as an original invention. In this, as well as in Kater's laborious inquiries respecting a standard of weights and measures, even where his conclusions have not escaped all the chances of error, he has led the way to the still more delicate researches which have followed.