From the Washington Union. General Cazneau's letter on the Dominican Republic.

It was hardly worth the trouble to deny, in a formal manner, the ridiculous stories put in circulation by the New York Evening Post respecting Gen. Cazneau's business last winter in St. Domingo. His honorable career as a [illegible] of their people. It is our interest to cherish the power, production, and general welfare of all these American States, and build up a strength to contribute to our own. It is so much strength added to the American force, in opposition to the present and future pretensions of European dictation. This is the principle of the American system, or it has none. In accordance with that principle, I have been urging upon my friends the propriety of giving to the Dominican republic the encouragement of a friendly recognition, as long and as earnestly as I have opposed it in the service of the black Emperor Faustin Soulouque.

The only plan I have ever heard of, or advocated, in connection with Gen. Cazneau, or any successor of his in office, was to strengthen the country relation with all the Spanish American States, and to establish them where they did not exist, as in the case of Dominica. It was only on this principle of American policy, that the recognition of Dominica was discussed with Senators Rusk, Douglas, Mason, Slidell, and many other distinguished members of the Senate, prior to Gen. Cazneau's connection with them; and those gentlemen should be as little suspected of a scheme of "filibustering" as the allies of Faustin.

We infer, says the Post, coming at last to the real question, "that it is the intention of the Post's editorial friends to show that Dominica and Hayti are under the control of different races, and that it is the interest of the whites for which they show such an anxiety."

This is precisely the issue; they are different races. Dominica is governed by civilized white manners, with a democratic constitution, and, obedient to the laws of nations. There is not, to name one man, either in the cabinet, Congress, or the Dominican forces, that has a drop of African blood in his veins. Hayti is an ignorant, barbarous, stubborn negro despotism, without a legal code, and obedient to no laws, unanalogous to the French.

They are governed throughout by men of negro blood and negro ideas. In their wars, they are as merciless enemies to quadroons as to whites, for they audaciously proclaim their intention to wholly annihilate the white and mixed race on the island. This creed of extermination is the leading point in those "rights of Hayti," which the Post's editorials maintain in terms so remarkably like the official bulletins of Soulouque.

The Dominican people, on the contrary, are from Spanish stock, and their character is not "without character and courage," as the Post says. As a matter of history, having sustained themselves since the establishment of their republic, they have been victorious in every battle with the Haytians. Under Santana, as well as under Santana's predecessors—at the battle of Las Carreras, Faustin had five times their force, and yet victory was with the Dominicans. Have the Dominicans had the "character and courage" to put him to flight, with the loss of thousands of his troops? He escaped, and the frontier was characteristic of Haytian warfare, and marked by blood and ashes, by the destruction of property and the cruel slaughter of women and children.

Haytian emissaries came among the colored population in Dominica, and tried to set the country on fire, to incite them to rise and murder the whites in the interior districts. They asserted that the Americans were coming to make slaves of them—in the style of the Post's phraseology about "the extension of slavery;" but the Dominican blacks were not ignorant enough to believe these monstrous absurdities. Their prudence does not excuse, and should put to shame an American journal in continually presenting the case in a shape to alarm and excite the blacks into insurrection, while it defends the "rights of Hayti" to make a general destruction of the white race.