Washington, July 11- The following is the eorrespondence between the President and Queeu Victoria, relative to the visit of the Princo of Wales: "To her Majesty Queex Victoria : I have learned from the public journals that the Prince of Wales is about to visit your Majesty's North American dominions. Should it be the intcntiou of his Iloyal Highness to extend bis visit to the United States I need not say how happy I should be to give hiin a cordial weieome to Washington. " You may be well assured that everywhere in this country he will be greeted by the American people in such a manner as caunot fail to prove gratifying to your Majesty. In this they will manifest their deep sense of your doniestic virtues, as ■well as their couvietions of your merits as a wise patriotic, and coustiutional Sovereign. "Your Majesty's mostobedient servant, ''James Büohanam, "WashhjntÓH, June 4, 1860." "BccKiNGiiAM Palace, June 22, 1860. "Mï (jood Fiuen'd : I have been much gratified at the feeliugs which prompted you to write to me inviting tho Prince of Wales to come to Washington. He intends to return frora Canada through the United States, and it will give him great pleasure to have an opportunity of testifying to you in person that theso feelin's are fully reeiprocatcd by hiin. He will thus be able, at the same time, to mark the respect which he entertains for the Ohief Magistrate of a great and friendly State and honored nation. The Prince will drop all royal state on leaving ïny dominions, and travel under the name of Lord Renfrew, as he has dono when traveling on the continent of Europe. "The Prince Consort wishes to be kiudly remeinbercd to you. "I remain, ever your good friond, "VaïORiA 11."