The new matter of greatest importance which has been introduced into this edition is an account of an investigation which, during the past two years, I have had the honor of conducting in connection with the Elder Brethren of the Trinity House. Under the title “Researches on the Acoustic Transparency of the Atmosphere, in Relation to the Question of Fog-signalling,” the subject is treated in Chapter VII. of this volume. It was only by Governmental appliances that such an investigation could have been made; and it gives me pleasure to believe that not only have the practical objects of the inquiry been secured, but that a crowd of scientific errors, which for more than a century and a half have surrounded this subject, have been removed, their place being now taken by the sure and certain truth of Nature. In drawing up the account of this laborious inquiry, I aimed at linking the observations so together that they alone should offer a substantial demonstration of the principles involved. Further labors enabled me to bring the whole inquiry within the firm grasp of _experiment_; and thus to give it a certainty which, without this final guarantee, it could scarcely have enjoyed. Immediately after the publication of the first brief abstract of the investigation, it was subjected to criticism. To this I did not deem it necessary to reply, believing that the grounds of it would disappear in presence of the full account. The only opinion to which I thought it right to defer was to some extent a private one, communicated to me by Prof. Stokes. He considered that I had, in some cases, ascribed too exclusive an influence to the mixed currents of aqueous vapor and air, to the neglect of differences of temperature. That differences of temperature, when they come into play, are an efficient cause of acoustic opacity, I never doubted. In fact, aërial reflection arising from this cause is, in the present inquiry, for the first time made the subject of experimental demonstration. What the relative potency of differences of temperature and differences due to aqueous vapor, in the cases under consideration, may be, I do not venture to state; but as both are active, I have, in Chapter VII., referred to them jointly as concerned in the production of those “acoustic clouds” to which the stoppage of sound in the atmosphere is for the most part due.