The establishment of a firm government in Arizona will extend the protection of the United States over American citizens resident in the adjoining Mexican provinces. This protection is most urgently demanded. Englishmen in Sonora enjoy not only perfect immunity in the pursuit of business, but also encouragement. Americans are robbed openly by Mexican officials, insulted, thrown into prison, and sometimes put to death. No redress is ever demanded or received. This state of things has so long existed that the name of American has become a byword and a reproach in northern Mexico, and the people of that frontier believe that we have neither the power nor the inclination to protect our own citizens. The influence of a Territorial government, with the tide of American emigration which will surely follow it, must entirely change the tone and temper of these Mexican States. The population of Arizona to-day, exceeds that of Washington Territory, and is far greater than was that of Minnesota, Kansas or Nebraska, at the time of their organization. An election for a Delegate has been held, at which several hundred votes were polled, and the writer returned without opposition. The unsettled and dangerous condition of the country prevented a convention being held, but letters have been received from all parts of the Territory, expressing a hearty concurrence in the election on the part of those unable to vote, and an earnest desire for the Territorial organization. A number of gentlemen at present in Washington, can testify from actual observation, to the truth of the statements here made in reference to Arizona--among them I am permitted to name General Anderson, late U. S. Senator from Tennessee, who almost alone, with rare perseverance and courage, explored, in 1850, the whole length of the Territory, Major Heintzelman, U. S. A., whose long station at Fort Yuma made him acquainted with the resources of the country, and who has shown at once his intelligence and foresight and his faith in the prospective wealth of the silver region, by large investments of capital, Col. A. B. Gray, late U. S. Surveyor of the Mexican Boundary line, I. Smith McMicken, Esq., whose residence for many years on the Mexican frontier has entitled his opinion to some weight, and A. H. Campbell, Esq., Superintendent of Wagon Roads, whose information is full and reliable. To these names it may not be improper to add that of the writer, who has for two years past, while residing at the junction of the Gila and Colorado Rivers, made the new Territory and its resources, an object of constant observation and study, and whose experience on the Pacific coast, and in the frontier Territories, and on the route across the continent, during the past five years, has enabled him to speak understandingly of the capabilities and necessities of a new country, and of a frontier people.