There can be no question as to the extreme importance to science of the establishment and continued use of a seismographic instrument of unexceptionable construction at the Observatory upon Vesuvius; and it would be a valuable gift to science, were the Italian Government to enable Signor Palmieri to establish such an one. Its great value and the very first problem to set the instrument to solve should be, by _a rigid determination of the direction of propagation of the wave of shock_, of those slight or stronger pulsations which precede or accompany the Vesuvian like all other eruptions, on arriving at the Observatory, _to fix the depth, and the position vertically beneath the cone, whence these pulses are derived_. This would be, in fact, to fix the depth and position beneath the mountain at which the volcanic focus is situated for the time, or, at least, where the volcanic activity is at the time greatest. And the assured knowledge, even within moderate limits of accuracy, of this depth, and even for this single mountain, would be an immense accession to our positive knowledge, and a really new stage gained for future advances. At present, we know but little as to the actual depth below our globe's surface at which volcanic activity occurs, or to which it is limited, either upwards or downwards. I have, myself, established some data upon the flanks of Etna, not yet published, which may enable me to afford some information on the subject hereafter. Meanwhile, Professor Palmieri possesses unrivalled opportunities for such observations; and I trust health, life and means may be afforded him, to become the first who shall have made this great addition to our positive knowledge of Vulcanology. So far, popularly at least, the alleged chief uses and value of these seismographic instruments, at the Observatory of Vesuvius, have been made to depend upon their being presumed to afford means for foretelling eruptions, or affording precursory warnings of their probable progress and destructive course.