geology. We may, indeed, readily believe that we have much to do in both these departments. While so large a portion of the globe is geologically unexplored;-while all the general views which are to extend our classifications satisfactorily from one hemisphere to another. from one zone to another, are still unformed; while the organic fossils of the tropics are almost unknown, and their general relation to the existing state of things has not even been conjectured;-how can we expect to speculate rightly and securely, respecting the history of the whole of our globe? And if Geological Classification and Description are thus imperfect, the knowledge of Geological Causes is still more so. As we have seen, the necessity and the method of constructing a science of such causes, are only just beginning to be perceived. Here, then, is the point where the labors of geologists may be usefully applied; and not in premature attempts to decide the widest and abstrusest questions which the human mind can propose to itself.

It has been stated," that when the Geological Society of London was formed, their professed object was to multiply and record observations, and patiently to await the result at some future time; and their favorite maxim was, it is added, that the time was not yet come for a General System of Geology. This was a wise and philosophical temper, and a due appreciation of their position. And even now, their task is not yet finished; their mission is not yet accomplished. They have still much to do, in the way of collecting Facts; and in entering upon the exact estimation of Causes, they have only just thrown open the door of a vast Labyrinth, which it may employ many generations to traverse, but which they must needs explore, before they can penetrate to the Oracular Chamber of Truth.

I REJOICE, on many accounts, to find myself arriving at the termination of the task which I have attempted. One reason why I am glad to close my history is, that in it I have been compelled, especially in the latter part of my labors, to speak as a judge respecting eminent philosophers whom I reverence as my Teachers in those very sciences on which I have had to pronounce a judgment;-if, indeed, even the appellation of Pupil be not too presumptuous. But I doubt not that such men are as full of candor and tolerance, as they are of knowledge and thought. And if they deem, as I did, that such a history of

science ought to be attempted, they will know that it was not only the historian's privilege, but his duty, to estimate the import and amount of the advances which he had to narrate; and if they judge, as I trust they will, that the attempt has been made with full integrity of intention and no want of labor, they will look upon the inevitable imperfections of the execution of my work with indulgence and hope.

There is another source of satisfaction in arriving at this point of my labors. If, after our long wandering through the region of physical science, we were left with minds unsatisfied and unraised, to ask, "Whether this be all?"-our employment might well be deemed weary and idle. If it appeared that all the vast labor and intense thought which has passed under our review had produced nothing but a barren Knowledge of the external world, or a few Arts ministering merely to our gratification; or if it seemed that the methods of arriving at truth, so successfully applied in these cases, aid us not when we come to the higher aims and prospects of our being;—this History might well be estimated as no less melancholy and unprofitable than those which narrate the wars of states and the wiles of statesmen. But such, I trust, is not the impression which our survey has tended to produce. At various points, the researches which we have followed out, have offered to lead us from matter to mind, from the external to the internal world; and it was not because the thread of investigation snapped in our hands, but rather because we were resolved to confine ourselves, for the present, to the material sciences, that we did not proceed onwards to subjects of a closer interest. It will appear, also, I trust, that the most perfect method of obtaining speculative truth,-that of which I have had to relate the result,-is by no means confined to the least worthy subjects; but that the Methods of learning what is really true, though they must assume different aspects in cases where a mere contemplation of external objects is concerned, and where our own internal world of thought, feeling, and will, supplies the matter of our speculations, have yet a unity and harmony throughout all the possible employments of our minds. To be able to trace such connexions as this, is the proper sequel, and would be the high reward, of the labor which has been bestowed on the present work. And if a persuasion of the reality of such connexions, and a preparation for studying them, have been conveyed to the reader's mind while he has been accompanying me through our long survey, his time may not have been employed on

these pages in vain. However vague and hesitating and obscure may be such a persuasion, it belongs, I doubt not, to the dawning of a better Philosophy, which it may be my lot, perhaps, to develop more fully hereafter, if permitted by that Superior Power to whom all sound philosophy directs our thoughts.

ADDITIONS TO THE THIRD EDITION.

BOOK VIII.

ACOUSTICS.

CHAPTER III.

SOUND.

The Velocity of Sound in Water.

HE Science of which the history is narrated in this Book has for

THE

its objects, the minute Vibrations of the parts of bodies such as those by which Sounds are produced, and the properties of Sounds. The Vibrations of bodies are the result of a certain tension of their structure which we term Elasticity. The Elasticity determines the rate of Vibration the rate of Vibration determines the audible note: the Elasticity determines also the velocity with which the vibration travels through the substance. These points of the subject, Elasticity, Rate of Vibration, Velocity of Propagation, Audible Note, are connected in each substance, and are different in different substances.

In the history of this Science, considered as tending to a satisfactory general theory, the Problems which have obviously offered themselves were, to explain the properties of Sounds by the relations of their constituent vibrations; and to explain the existence of vibrations by the elasticity of the substances in which they occurred: as in Optics, philosophers have explained the phenomenon of light and colors by the Undulatory Theory, and are still engaged in explaining the requisite modulations by means of the elasticity of the Ether. But the Undulatory Theory of Sound was seen to be true at an early period of the Science and the explanation, in a general way at least, of all kinds of such undulations by means of the elasticity of the vibrating substances has been performed by a series of mathematicians of whom I have given an account in this Book. Hence the points of the subject already mentioned (Elasticity, Vibrations and their Propagations,

and Note), have a known material dependence, and each may be employed in determining the other: for instance, the Note may be employed in determining the velocity of sound and the elasticity of the vibrating substance.

Chladni,' and the Webers, had made valuable experimental inquiries on such subjects. But more complete investigations of this kind have been conducted with care and skill by M. Wertheim. For instance, he has determined the velocity with which sound travels in water, by making an organ-pipe to sound by the passage of water through it. This is a matter of some difficulty; for the mouthpiece of an organ-pipe, if it be not properly and carefully constructed, produces sounds of its own, which are not the genuine musical note of the pipe. And though the note depends mainly upon the length of the pipe, it depends also, in a small degree, on the breadth of the pipe and the size of the mouthpiece.

If the pipe were a mere line, the time of a vibration would be the time in which a vibration travels from one end of the pipe to the other; and thus the note for a given length (which is determined by the time of vibration), is connected with the velocity of vibration. He thus found that the velocity of a vibration along the pipe in seawater is 1157 mètres per second.

But M. Wertheim conceived that he had previously shown, by general mathematical reasoning, that the velocity with which sound travels in an unlimited expanse of any substance, is to the velocity with which it travels along a pipe or linear strip of the same substance as the square root of 3 to the square root of 2. Hence the velocity of sound in sea-water would be 1454 mètres a second. The velocity of sound in air is 332 mètres.

M. Wertheim also employed the vibrations of rods of steel and other metals in order to determine their modulus of elasticity—that is, the quantity which determines for each substance, the extent to which, in virtue of its elasticity, it is compressed and expanded by given pressures or tensions. For this purpose he caused the rod to vibrate near to a tuning-fork of given pitch, so that both the rod and the tuningfork by their vibrations traced undulating curves on a revolving disk. The curves traced by the two could be compared so as to give their relative rate, and thus to determine the elasticity of the substance.

1 Traité d'Acoustique, 1809.

3 Mémoires de Physique Mécanique. Paris, 1848.

2 Wellenlehre, 1852.