NEW YORK, May 24, '79.—Perhaps no quarters of this city (I have return'd again for awhile,) make more brilliant, animated, crowded, spectacular human presentations these fine May afternoons than the two I am now going to describe from personal observation. First: that area comprising Fourteenth street (especially the short range between Broadway and Fifth avenue) with Union square, its adjacencies, and so retrostretching down Broadway for half a mile. All the walks here are wide, and the spaces ample and free—now flooded with liquid gold from the last two hours of powerful sunshine. The whole area at 5 o'clock, the days of my observations, must have contain'd from thirty to forty thousand finely-dress'd people, all in motion, plenty of them good-looking, many beautiful women, often youths and children, the latter in groups with their nurses—the trottoirs everywhere close-spread, thick-tangled, (yet no collision, no trouble,) with ma**es of bright color, action, and tasty toilets; (surely the women dress better than ever before, and the men do too.) As if New York would show these afternoons what it can do in its humanity, its choicest physique and physiognomy, and its countless prodigality of locomotion, dry goods, glitter, magnetism, and happiness. Second: also from 5 to 7 P.M. the stretch of Fifth avenue, all the way from the Central Park exits at Fifty-ninth street, down to Fourteenth, especially along the high grade by Fortieth street, and down the hill. A Mississippi of horses and rich vehicles, not by dozens and scores, but hundreds and thousands—the broad avenue filled and cramm'd with them—a moving, sparkling, hurrying crush, for more than two miles. (I wonder they don't get block'd, but I believe they never do.) Altogether it is to me the marvel sight of New York. I like to get in one of the Fifth avenue stages and ride up, stemming the swift-moving procession. I doubt if London or Paris or any city in the world can show such a carriage carnival as I have seen here five or six times these beautiful May afternoons.