In the correspondence that has recently taken place respecting the origin of Gompertz's formula expressive of the law of mortality, it has been stated, much to my surprise, that the investigation first given by that gentleman in the Philosophical Transactions of the Royal Society for the year 1825 was defective and inaccurate. I do not here propose to reopen the controversy on the subject of the originality of discovery, or to enter upon a renewed discussion of certain other allegations that have been so efficiently disposed of by Professor De Morgan and Mr. Sprague; but, after the statement to which I have more particularly alluded, it is only right that I should avail myself of the present opportunity to communicate the circumstance that Mr. Gompertz kindly presented me with a copy of his valuable Memoir in January, 1839, in which the various misprints had, in the most legible manner, been previously corrected by himself, and that the processes so corrected are perfectly accurate in every respect. In order that any one may be enabled to judge of this for himself, I shall here give a faithful transcription of that portion of the Memoir which contains the mathematical investigation of the formula, as it will occupy but little space.