The accounts from India are from Bombay to October 3, and from Calcutta to September 21st. Great preparations were on foot for the great Industrial Exhibition at London. The Maharajah has ordered specimens of every kind of Cashmerian product to be got ready without delay. The shawls intended for the purpose are described as remarkably splendid. The heir to the throne, Rajah Runheer Singh, having heard of the distinguished "success" at London of the Nepaul Envoy, is anxious to visit England himself; but the prospect of a disputed succession, in the event of his father's death, will probably keep him at home. The whole of _British India_ was tranquil, but the petty civil war on the Nizam's borders still continued. The native state of _Oude_ seems inclined to rival the Nizam's territories in anarchy and misgovernment. Some months since an English officer was killed and two guns lost in an attack on the fort of a refractory vassal of the King of Oude. A second event of the same nature has occurred. The Rajah of Esanuggur had shown himself for some time unwilling to pay the portion of revenue due from him to the Oude government, and in endeavoring to obtain these dues from him, Lieut. P. Orr, with a small party, had a brisk fight, each side losing a considerable number. Lieut. Orr was forced to retreat, and took refuge in the districts of a rival Rajah. The present aspect of the _Punjaub_ is most encouraging; the population, now disarmed, have settled down into their former habits of industry. The breadth of land under cultivation this season is said to be unprecedented, and the crops are every where most promising. The most important piece of intelligence from _Hong-Kong_ is the continuation of the fearful mortality among the British troops. This mortality was chiefly in the 59th regiment, which had lost ninety men in about two months. This sickness, therefore, is ascribed to the unhealthiness of the barracks and the want of sufficient sanitary precautions. The mortality, however, had begun to abate. A formidable _insurrection_ against the Chinese government had broken out in the province of Kwang-si. The leader, who is named Li-ting-pang, is said to be at the head of 50,000 men. He has assumed the title borne by the highest Tartar generals, and threatens to exterminate the present, and restore the old Chinese dynasty. In Bombay, the culture of cotton is rapidly extending. Two years ago, the whole of the land under cultivation with American cotton in that Presidency, was under twenty thousand acres. At the present moment the quantity exceeds one hundred thousand acres, and there is every certainty of a rapid increase taking place.