THERE has lately been much suffering here from heat; we have had it upon us now eleven days. I go around with an umbrella and a fan. I saw two cases of sun-stroke yesterday, one in Pennsylvania avenue, and another in Seventh street. The City railroad company loses some horses every day. Yet Washington is having a livelier August, and is probably putting in a more energetic and satisfactory summer, than ever before during its existence. There is probably more human electricity, more population to make it, more business, more light-heartedness, than ever before. The armies that swiftly circumambiated from Fredericksburghmarchd, struggled, fought, had out their mighty clinch and hurl at Gettysburgwheeld, circumambiated again, returnd to their ways, touching us not, either at their going or coming. And Washington feels that she has passd the worst; perhaps feels that she is henceforth mistress. So here she sits with her surrounding hills spotted with guns, and is conscious of a character and identity different from what it was five or six short weeks ago, and very considerably pleasanter and prouder.