The correspondent of the Sydney Morning Herald writes on April 25th a 3 folio v;s, concerning the influx of Chinese into Cook town: — The last few weeks in Cooktown have been pregnant with events. The most important of any incident in the history of this port— the arrival of the Chinese immigrants direct from China in swarms —stands out promi nently as the chief item of interest, and the possible cause of much future good or evil to the colony. This immigration has many special features which distinguish it from any previous Mon golian rush in colonial history. Cooktown is situated so near the great ports that empty out their surplus coolies into neighboring coun tries, the facilities for reaching the gold-field are so unusual, the expense is so compara tively slight, that, apait from other considera tions, it is small wonder that John Chinaman is hurrying here, with his stick and baskets filled with pots and pans, as fast as he can. The whole secret of the matter is that cer tain Chinese merchants in Hong Kong and Canton have excited the cupidity of their countrymen by the most extravagant ac counts of the riches of the Palmer. Pla cards announcing the astounding fact that gold paved the highways of Cooktown—that men picked up nuggets of fabulous size at the diggings as easily as a schoolboy picks up shells on the beach—were paraded in the streets ; a fever seized on the swarming population who daily tread each other down for a bare subsistence in these great Eastern ports ; the required excitement was obtained, and then step in the Chinese merchants— charterers of steamers to the El Dorado, and shippers of produce sufficient to feed all they could induce to emigrate. The arrival of the mail steamer Singapore, with 470 pas sengers, followed the same evening by the Adria, with about 600 more, was our first intimation of the new and certainly unexpected rush to our port. Since then we have had 1200 in the steamers Namoa and Egeria, and the Somerset brings tidings that we may very soon expect three steamships crowded with passengers, that were laid on for Cooktown prior to the departure of the mail from Hong Kong. 