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,1 and the Webers,2 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.3 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

1 Traité d'Acoustique, 1809.

3 Mémoires de Physique Mécanique. Paris, 1848.

2 Wellenlehre, 1852.

BOOK IX.

PHYSICAL OPTICS.

Photography.

HAVE, at the end of Chapter xi., stated that the theory of which I have endeavored to sketch the history professes to explain only the phenomena of radiant visible light; and that though we know that light has other properties-for instance, that it produces chemical effects-these are not contemplated as included within the domain of the theory. The chemical effects of light cannot as yet be included in exact and general truths, such as those which constitute the undulatory theory of radiant visible light. But though the present age has not yet attained to a Science of the chemistry of Light, it has been enriched with a most exquisite Art, which involves the principles of such a science, and may hereafter be made the instrument of bringing them into the view of the philosopher. I speak of the Art of Photography, in which chemistry has discovered the means of producing surfaces almost as sensitive to the modifications of light as the most sensitive of organic textures, the retina of the eye and has given permanence to images which in the eye are only momentary impressions. Hereafter, when the laws shall have been theoretically established, which connect the chemical constitution of bodies with the action of light upon them, the prominent names in the Prelude to such an Epoch must be those who by their insight, invention, and perseverance, discovered and carried to their present marvellous perfection the processes of photographic Art :-Niepce and Daguerre in France, and our own accomplished countryman, Mr. Fox Talbot.

Fluorescence.

As already remarked, it is not within the province of the undulatory theory to explain the phenomena of the absorption of light which take place in various ways when the light is transmitted through various