SOME time in September last, a female black servant child, between three and four years of age, and belonging to Samuel Verplank, Esq; of Fishkill, in Dutchess county, by some means unperceived by the family, fell into a well, wherein the water was deeper than the height of the child. Although the exact time when the accident happened cannot be ascertained, yet, from a number of circumstances it was generally agreed, that she was at least an hour under water. Upon being taken out, her skin was discolored -- the joints rigid -- the abdomen inflated, and in short, the representation of death was complete. Notwithstanding this combination of unfavourable appearances, Mr. Verplank's philanthropy impelled him to endeavour to re-illume the lamp of life. His long residence in Europe had made him acquainted with some of the methods which had been practiced there with success. He ordered a blanket to be spread before a fire, on which the child was laid, stripped of its clothes, and directed it to be rubbed with warm flannel on every part, and at the same time, tobacco smoke to be injected up its nostrils; in which operation a full paper was consumed.