Every one has read the treaty w which has just been concluded between the United States and China. Everyone has read it, but in it there are expressions which not every one understands. There are clauses which seem vague, other clauses which seem almost unnecessary, and still others which bear the flavor of ldquo;surplusage,rdquo; to speak in legal phrase. The most careful reading of the document will leave these impressionsmdash;that is, unless one comprehends the past and present condition of foreign intercourse with Chinamdash;in which case it will be seen at once that there is no word in the treaty without a meaning, and no clause in it but was dictated by a present need or a wise policy looking to the future. It will interest many of your readers to know why this, that, and the other provision was incorporated in the treaty; it will interest others to know in what manner and to what extent the treaty will affect our existing relations with China. Apart from its grave importance, the subject is really as entertaining as any I know of andmdash;asking pardon for the presumptionmdash;I desire to write a few paragraphs upon it. We made a treaty with China in 1858; Mr. Burlingames new treaty is an addition to that one, and an amplification of its powers.