About three o'clock on Saturday morning a heavy full of snow commenced, and continued till about daylight, when it turned to rain, and came down in torrents like a July shower. But it had not a shower's brevity, for it continued for twelve mortal hours without the intermission of a single minute. The snow that had fallen in the night, superadded to the accumulations of several previous storms, had left hillocks three and four feet high, everywhere, in the streets, and deep drifts in many places on the sidewalks. All the materials for a fine freshet were thus on hand, and a freshet we accordingly had. But we will not anticipate.

Immediately the rain began to fall, the wind-god Aeolus, not to be outdone, and seeing that January had accomplished all it could in the way of making our citizens uncomfortable, without so much as consulting him, opened that bag of his (vide The Classics) which confines the cold North-Easter, and let it forth to havoc as it would. And it was not particular what it did. It first compelled the rain to freeze as it fell, and such walking as there immediately was, elated all the surgeons in the City. They incontinently got their splints ready, and sat waiting for an impulsive dash at their door bells. Bones to set promised them and their little ones no stint of bones to pick. But besides freezing the rain, it almost froze pedestrians flesh, seemed to go straight through their bodies, them made a circuit of them, and upset them. Sometimes, meeting them full butt, it made them slide backward a yard or two, and half frightening them out of their wits, deprived hem of their hats, and left them with a laugh no, not a laugh__a howl of exultation. Happy was he who wore a Crimean cap, tightly strapped under his chin. Only the rain freezing on the seal-skin, made it as stiff as sheet-iron, and about as cold as an iceberg.

This continued for four hours, which we cannot but characterize as the worst, the very worst wintry hours ever experienced in the streets of a city. Getting tired of blowing down signs, ripping up window-shutters, and doing miscellaneous damage, the northeaster returned to Aeolus and reported progress. Master Aeolus instantly caught him and returned him to his bag.

The rain took fresh courage when the wind was gone, and descended with more force than ever. The thermometer rose considerably, the snow rapidly melted, culverts were, of course, everywhere stopped up, and soon the streets were converted into rivers, whose currents swept impetuously along at the rate of eight miles an hour. Vehicles, which four horses almost failed to move, were nearly immersed to the hub of their wheels. At the street-crossings, the rain and melted snow formed lakes varying from six inches to two feet deep. Along side streets the water rushed like a torrent, and getting to the lowlands of the City, which are generally the haunts of the poor, dashed into their basement habitations, floated their furniture, and half drowned their screaming offspring. The very rats got frightened, and ran about Washington street, South-street, the docks nod the markets, as the gushing thaw, like a landlord, weary of seeking arrears of rent, summarily ejected them.

Still, although the freezing had ceased, the half-melted snow was slippery enough, and not a few gentlemen took a sitz-bath during the day, their knees and shoulders being visible, but the rest of their bodies undergoing immersion. Diogenes would have smiled at their mishap, and who could blame urchins for laughing? The unkindest cut of all was when the Indies, especially the young and pretty ones, watching at their windows for such accidents, tittered their liveliest, and even clapped their hands in uncontrollable glee.

Of the miseries of drivers of vehicles; of the horses they attempted to guide, but which slipped and stumbled in every direction, throwing off steam like a boiler, sweating and straining in the almost hopeless task of moving at all; of all the ills which human flesh and horse flesh endured on the last memorable Saturday of January, we cannot pretend to give even any approximate account. Experience has written it in memory's page, and Experience declares it to be unparallel.

The Sixth and Eighth avenue Railroad Companies, shortly after the rain storm commenced on Saturday, had their tracks thickly scattered with salt. This, with the rain, effectually melted the snow, and the culverts having also been opened and channels cut from the tracks to them, the track was bared to the pavement by yesterday afternoon. Late on Saturday the cars presented a peculiar appearance. They were drawn through water a foot deep, and it required little imagination to think them paddle-wheel steamers. The splashing and turbulent waves they left in their wake kept up the delusion.

Broadway, and indeed the whole City, was in nearly as horrible a condition yesterday as on Saturday, and many ladies who started for church in the morning had to return home without hearing the sermon and displaying their fashionable attire, because they dared not attempt the passage. During the afternoon, however, enterprising boys with dilapidated brooms made a demonstration at divers crossings, and those who willed passed over nearly dry shod. It is fair to state that few failed to pay the accustomed penny-tax to Ebling's substitutes.

The bright sun, however, which shone yesterday, (it was as lovely a day overhead as we ever witnessed,) dried up most of the moisture on the sidewalks, and left them tolerably clean and comfortable. But the middle of the streets, as we have said, were nearly as bad as on Saturday. Towards evening it began to freeze, moderately, but there will be rare thawing work today, we opine.