From _California_ our dates are to May 31. On the night of the 3d of May, the anniversary of a great fire of last year, a destructive conflagration took place in San Francisco, by which a large portion of the business part of the city was destroyed. The number of buildings burned is set down at 1500; the loss was at first stated at from ten to twelve millions, which is probably three or four times the actual amount. A number of lives were also lost. In one case six persons undertook the care of a store supposed to be fire-proof; the iron doors and window-shutters became expanded by the heat to such a degree that it was impossible to open them, and the inmates were all burned to death. The work of rebuilding was commenced and carried forward with such characteristic rapidity, that within ten days after the fire 357 buildings were in process of erection, of which the greater part were already occupied. At the close of the month it is stated on reliable authority, that the number of buildings actually tenantable was greater than before the conflagration. The city of Stockton suffered severely by a fire on the 12th of May. The amount of gold produced continues to be very great. The gold bluffs of the Trinity River, the reported discovery of which caused such an excitement a few months since, prove to be of little or no value; but the extraction of gold from the auriferous quartz is rapidly developing itself as experience points out new and improved methods of procedure. This promises to become the most productive of all the mining operations in California. It is evident that the market is altogether overglutted with goods, the large amount destroyed at the fires, apparently producing no effect upon prices in general. Political excitement runs high: party lines beginning to be strictly drawn. The nominations for State officers of both parties have been made. The depredations and outrages of the Indians have not altogether ceased. The severe code of Lynch law still continues in practical force, though instances of its execution are somewhat less frequently given. Large numbers of emigrants from China are arriving; a British vessel from Hong Kong lately brought 381 Celestials to San Francisco. They promise to out-number the emigrants from any other foreign people, and manifest a most unexpected facility in acquiring the language, manners, and modes of thought and life of their new homes. An expedition raised in the southern part of the State, for the purpose of invading the Mexican province of Lower California, appears to have miscarried.