The crimes of robbery and murder becoming of so frequent occurrence in San Francisco that all security of person and property was threatened with destruction, a meeting of citizens was called, and it was resolved to organize a Vigilance Committee, for the summary trial and execution of offenders. This was an open manifestation of contempt for the constituted authorities, and they protested against it. But a majority of the citizens of San Francisco, feeling that extraordinary measures were necessary, supported those persons who were appointed upon the Committee. Such officers generally abuse the extensive authority conferred upon them; but justice requires that we should say, that the members of the San Francisco Vigilance Committee acted throughout with a due appreciation of an awful responsibility. Several persons were arrested, tried, convicted and hung. One or two were notorious criminals, who had often been up before the regular courts, and always contrived to elude justice. By the certain and summary measures of the Committee, security was in a great measure restored, and the members then surrendered their authority--acknowledging the entire supremacy of the courts. In October, 1851, the State elections occurred. The contest was spirited. The Democrats were generally successful. John Bigler, their gubernatorial candidate, was elected by about thirteen hundred majority over Mr. Reading, the candidate of the Whigs. At the succeeding session of the Legislature, John B. Weller, formerly of Ohio, was elected to the Senate of the United States, to succeed John C. Fremont, who had resigned his seat. Mr. Weller had long been a prominent member of the Democratic party. He commanded the Ohio regiment in the Mexican war. It was believed that he would be an efficient colleague of the industrious and practical Senator Gwin. The Chinese portion of the population of California has gradually become quite numerous. They have proved themselves steady, energetic and useful citizens. Gov. Bigler, however, had a different estimation of them. As they do not respect the oaths and forms established by law for the regulation of business in California, he thought they could not be bound sufficiently in their bargains to suit the business community; and accordingly he recommended to the Legislature, that some measures should be adopted for checking Chinese immigration. This called forth a spirited remonstrance from the Chinese citizens of San Francisco. They argued with much reason, that they had conducted themselves properly ever since they had entered California, and that there was no real ground of complaint against them. The methods of binding them were explained, it is believed, to the general satisfaction of the business community. We should think that Chinese labor would be in great demand in California, as the "Celestials" not only work for less than the Americans, but can endure more toil and exposure.