The publication of a number of letters by the wife of John Adams, which had been addressed to him as well as to others, is understood to have excited some curiosity to see his replies. Apart from the general and natural desire to read both parts of any interesting correspondence, a wish has been expressed by some persons to the Editor, that the mode and degree in which the affection and sensibility of the lady were returned should be shown. Intimations have even been made that she has been presented in a favorable light somewhat at the expense of her husband, and that something should be done to restore his reputation as well in his public as in his domestic relations.