His first important contribution to scientific knowledge was the comparison of the merits of the Cassegrainian and Gregorian telescopes, from which {Philosophical Transactions, 1813 and 1814) he deduced that the illuminating power of the former exceeded that of the latter in the proportion of 5: 2. This inferiority of the Gregorian he explained as being probably due to the mutual interference of the rays as they crossed at the principal focus before reflexion at the second mirror. His most valuable work, however, was the determination of the length of the second’s pendulum, first at London and subsequently at various stations throughout the country {Phil. Trans., 1818,1819). In these researches he skilfully took advantage of the well-known property of reciprocity between the centres of suspension and oscillation of an oscillating body, so as to determine experimentally the precise position of the centre of oscillation; the distance between these centres was then the length of the ideal simple pendulum having the same time of oscillation. As the inventor of the floating collimator, Captain Kater rendered a great service to practical astronomy {Phil. Trans., 1825, 1828). He also published memoirs {Phil, Trans., 1821, 1831) on British standards of length and mass; and in 1832 he published an account of his labours in verifying the Russian standards of length. For his services to Russia in this respect he received in 1814 the decoration of the order of St Anne; and the same year he was elected a fellow of the Royal Society. His attention was also turned to the subject of compass needles, his Bakerian lecture “On the Best Kind of Steel and Form for a Compass Needle” {Phil. Trans., 1821) containing the results of many interesting and valuable experiments. The treatise on “Mechanics” in Lardner’s Cyclopaedia was partly written by him and partly by Dr Lardner; and his interest in more purely astronomical questions was evidenced by two communications to the Astronomical Society’s Memoirs for 1831-33—the one on an observation of Saturn’s outer ring, the other on a method of determining longitude by means of lunar eclipses.

It is divided into one hundred and eighty-eight separate states, large and small, of which thirteen pay no tribute, ninety-six are tributary to the British Government, and seventy to the gâekwâr as the representative of the Marhattâs, while of these three classes of states one hundred and thirty-two pay a tax called zortalabi to the nawâb of Junâgarh. The states are arranged in seven classes: the chiefs of the first and second classes exercise plenary jurisdiction, both civil and criminal; the judicial powers of the lesser chiefs are graded in a diminishing scale, the residuary jurisdiction being vested in four British officers, each superintending a group of states. The political agent controls the whole. As a rule, no appeal lies from the decision of a chief; but on presumption of maladministration his proceedings may be called for and reviewed. During the past twenty years the states have established civil and criminal courts and written codes. Justice is administered by the political officers on the non-regulation system over 2058 square miles, or about one-tenth of the whole area. Outlawry, political and predatory, has been suppressed, and life and property are as safe as in British districts. A village police has been established, and municipal funds are voted by the states. In 1878 there were 488 schools, with 28,171 scholars; while at the Râjkumar College, and three high schools many of the chiefs receive a liberal education during their minority. There is railway communication with Wadhwân, and an extension is in progress to Dhorâji and Bhaunagar, while a network of good roads extend from Râjkot, the headquarters of the agency, over the greater part of the province. Kâthiâwâr is divided for administrative purposes into four prants or districts,—Jhalâwâr, Hâllâr, Sorâth, and Gohelwâr; but the old territorial prants are ten, viz., Jhalâwâr in the north, containing about fifty states; Machhukântâ; Hâllâr, with twenty-sixty states; Okhamandal, belonging to Baroda; Baradâ or Jaitwâr, also known as Porbandar; Sorâth; Babriâwâr; Kâthiâwâr; Und-Sarviya; and Gohelwâr. The last-named comprises the Gogo district, belonging to the Ahmedâbâd collectorate; Bhaunagar, probably the foremost state in Kâthiâwâr; and many others.

Generally speaking, the surface of the country is undulating, with low ranges running in very irregular directions; with the exception of the Tânghâ and Mândhav hills, in the west of Jhalâwâr, and some unimportant hills in Hâllâr, the northern portion of the country is flat; but in the south, from near Gogo, the Gir range runs nearly parallel with the coast, and at a distance of about 20 miles from it, along the north of Babriâwâr and Sorâth, to the neighbourhood of Gïrnâr. Opposite this latter mountain is the solitary 0sam hill, and then still farther west is the Baradâ group, between Hâllâr and Baradâ, running about 20 miles north and south from Gumti to Rânâwan. The Girnâr clump of mountains is an important granitic mass, the highest peak of which rises to 3500 feet. The principal river is the Bhâdar, which rises in the Mândhav hills, and flowing south-west falls into the sea at Navi-Bandar, in Baradâ; it is everywhere marked by highly cultivated lands adjoining its course of about 115 miles. Other rivers are the Aji, Machhu, and Satπinji—the last remarkable for wild and romantic scenery. Four of the old races, the Jâitwas, Churâsamas, Solunkis, and Wâlâs are now existing as proprietors of the soil who exercised sovereignty in the country prior to the immigration of the Jhalâs, Jârejas, Purmars, Kathis, Gohels, Jâts, Mohammedans, and Marhattâs, between whom the country is now chiefly portioned out.

The principal agricultural products consist of cotton, bàjrd, and jοdr, and in some parts sugar-cane, turmeric, and indigo. Horse and sheep breeding is carried on to a great extent—these animals, together with food grains, rawcotton,and wool, forming the chief exports. The principal imports are cotton manufactures, metals, and sugar. Iron is found in many parts of Barada and Hâllâr. Many iron-mines have, however, had to be abandoned of late years owing to the scarcity of fuel for smelting the ore. The principal towns are Jamnagar, Bhaunagar, Junâgarh, Rajkot, Porbandar, and Mangrol. The last two, as also Verâwal, are thriving seaport towns. Kâthiâwâr has many notable antiquities, comprising rock inscriptions of Asoka, Buddhist caves, and. fine Jain temples on the sacred hill of Girnâr, and at Pâlitana.