From tho Londoa Time, Oct. 7. Every succeeding report of the American battlo, by some invariable rule, seems to be nearer the truth than the h'is't. Three steamers have arrived since the earliest intelligence of the two daye' engagement on the soutbern frontier of Tennessee reached Mew York, and it is only from the third series oi telegram that we begin to learn the facts with certainty. The Damuscus brings a brief abstract of Gen. Bragg's offioial report of the battle, and some further details from an eye-witnesa of the conflict, that have been published in New York. There is no " danger," it is stated in the present position of Bosecrans.- Again a Federal army has placed itelf in " safety." But to the side that nist completely conquer to effect anyling the use of such a word implies 11 that can be underatood as failure. - An army of invasión or occupation reuced to the " defensive" is buffled in very purpose of the hoatilitiea, and all ho expenditure of money and livss is made in vain. The invasión on both ides have failed, only serving to provo he hopeless nature -of the conflict.- Mie questions in dispute appear to opeans of the kind that cannot be deeVrrtined by arrns. The greatest c les ure becoming only repetitions of ghting. The loss or gsio, more or bk8 decisive, brings tbe hostile parties o nearer the reault, which must be a jolitical supremacy to be oi any effect. n whatever part of the immense inent the strife rages, it is, in relation 5 o the vvhole country, but an isoiated xnnt. An engagement adds auother ale of sianghter to the nlready i ng list, but it is not followed by any i resalta to place it among the " deciwive ■ lattles of the world." By do fluctuation of military Bucoees is a government irèntratöd, a dynasty changed, or the jcmmand of a wholo realm secured by the possession of its capitals as in Europe. Everything short of the entire conquest of the South is to the North a laiiui-e. To the Oonfedacaoy, to main tain their defense 3 succes.. If the ighting is continued for years to come, it is difficult to conceive how it can ehange these conditions. The retreat of anotber Federal army with safety, congratulating itself on something gained when reaching it, ought to ariso grave misgivings as to the principie of such a war. A result that seem9 unvarying must arise frorn the operation of 8 ome gonoral law. - Hitherto invasión has always broken its wing, and been compelled to retire to take to some perob of safety and remnin inactive, incapable for a time of any fresh fligbt. In the Chattanooga mountains the Federal ar.ny of tbe West is now driven to a refuge. The incidenfï of the war repeat themselves aimost in monotony.