On the arrival of the first of the American steamers bound to Bremen at Southampton, in the month of June last, the British post-office directed the collection of discriminating postages on all letters and other mailable matter which she took out to Great Britain or which went into the British post-office on their way to France and other parts of Europe. The effect of the order of the British, post-office is to subject all letters and other matter transported by American steamers to double postage, one postage having been previously paid on them to the United States, while letters transported in British steamers are subject to pay but a single postage. This measure was adopted with the avowed object of protecting the British line of mail steamers now running between Boston and Liverpool, and if permitted to Continue must speedily put an end to the transportation of all letters and other matter by American steamers and give to British steamers a monopoly of the business. A just and fair reciprocity is all that we desire, and on this we must insist. By our laws no such discrimination is made against British steamers bringing letters into our ports, but all letters arriving in the United States are subject to the same rate of postage, whether brought in British or American vessels. I refer you to the report of the Postmaster-General for a full statement of the facts of the case and of the steps taken by him to correct this inequality. He has exerted all the power conferred upon him by the existing laws. The minister of the United States at London has brought the subject to the attention of the British Government, and is now engaged in negotiations for the purpose of adjusting reciprocal postal arrangements which shall be equally just to both countries. Should he fail in concluding such arrangements, and should Great Britain insist on enforcing the unequal and unjust measure she has adopted, it will become necessary to confer additional powers on the Postmaster-General in order to enable him to meet the emergency and to put our own steamers on an equal footing with British steamers engaged in transporting the mails between the two countries, and I recommend that such powers be conferred. In view of the existing state of our country, I trust it may not be inappropriate, in closing this communication, to call to mind the words of wisdom and admonition of the first and most illustrious of my predecessors in his Farewell Address to his countrymen. That greatest and best of men, who served his country so long and loved it so much, foresaw with "serious concern" the danger to our Union of "characterizing parties by geographical discriminations--Northern and Southern, Atlantic and Western--whence designing men may endeavor to excite a belief that there is a real difference of local interests and views," and warned his countrymen against it.