series of particles situated along the line are solicited in opposite directions at the same instant, by one wave in one direction, and by the other in the contrary direction; the wave then which the combined motion would transmit will undergo considerable modification from this action. And it may even happen that the motions of the particles are absolutely destroyed, and consequently, that no wave will be propagated, or no sound come to the ear. Of this several remarkable instances occur in the vibration of musical strings, and in other cases.

Suppose two strings to be so nearly in unison that one performs 100 vibrations while the other performs 101. Their first few vibrations will conspire and produce a sound wave, such that the effect on the ear will be double. But at the 50th vibration one string will be half a vibration in advance of the other, that is, the motions of the strings will be at this instant in exactly opposite directions, and consequently the motion of the aerial particles in the two waves, one of which is produced by each string, will not be in the same, but in opposite directions; and the two waves being supposed exactly equal, they will interfere and exactly destroy each other. At this instant then the ear can receive no sound. The same will be partially the case for many vibrations on each side of the 50th; there will then be a general decay of sound up to this point, and it will gradually increase up to the 100th, when one string having gained one vibration on the other, the motions of the particles will be exactly in the same direction, and the sound wave will consequently be double.

The general effect on the ear then resulting from two such strings will be an intermitting sound, alternately loud and faint. These alternate subsidences and augmentations of sound are termed by musicians beats. The nearer the strings are in unison the longer will be the interval between the beats; and perfect harmony consists in the complete destruction of beats by tuning the strings to unison. If the notes differ much from each other, or

the unison be very defective, these alternations cause a disagreeable rattle, which is only removed by preventing the interference of opposite waves.

138. Musical Instruments.—The laws which have just been so fully stated with respect to musical sounds and strings will be at once recognised in all musical sounds in whatever manner produced. In the bell, for instance, or whenever the sound originates from a similar cause, the vibration of a metallic mass, the tone depends on the rapidity with which the vibrations are executed, and on its mass. The large church bell gives us a very deep low sound, because of the slowness of the vibrations. The mass of metal which is here set in motion may be considered as composed of circular rings of different diameters, which, when separate, would perform their vibrations in different times, but which, owing to their connexion, take a mean undulation or motion of vibration; the size of the rings enables them to make extended excursions, which being executed with a certain slowness, give deepness to the resulting tone. But in a small bell the circular zones are incomparably less; their vibrations being then much less extended are performed in less time. For a very

deep tone there must be a mass of metal and a consequent slowness of vibration; and the tone will be higher as the metal is less, and the rapidity of vibration greater. Bells may be combined so as to have the natural musical relations, and thus produce harmonious sounds.

In wind instruments the sound is produced by the vibrations of a column of air contained in a straight or crooked pipe, and having openings by which the sound waves can diverge. The simplest method of producing a musical note from a column of air is by blowing across the end of a reed or pipe; the edge will catch some of the current, and diverting it downwards will produce a series of alternate condensations and rarefactions, which being reflected at the closed end will produce a musical note. The tone emitted by a pipe depends on the dimensions of

the contained column, as well as on the magnitude and form of the orifice, by which the communication is effected. The tone is deeper or more grave when the column of air is large and long, and becomes higher in proportion as it is shortened. Thus in an organ there are pipes of very different lengths. In a flute the column is lengthened or shortened, by closing or opening the holes, and it appears both from theory and experiment that a tube open at both ends gives the same note as one of half the length whose end is closed. The lowest or fundamental note being sounded by blowing steadily across a pipe, if the blast be increased the note will start up an octave higher; and there are here, as well as in vibrating strings, limits to the powers of the ear; or vibrations which, so far as we are concerned, are as if they did not exist.

Nearly all solid bodies have a note peculiar to themselves; particular panes in the window will rattle to particular notes of an organ; the glasses in a room may be set in vibration, and sometimes broken, by singing into them; each portion of inanimate matter appears to have some note to which it responds. It is from a principle analogous to this that the sounding boards and cases of instruments are so essential; the vibrations transmitted directly or through the air to these substances strengthen the sound of the instrument, since they cause larger sound waves than could be generated by the single strings. The co-existence of vibrations, their isochronism and sympathy, and all the phenomena of nodal sections, are questions into which we cannot possibly enter; but enough we hope has been said to place the principal phenomena of sound in a distinct point of view, and to establish the general laws of its propagation.

CHAPTER IX.

ON HEAT.

SECTION I.

PRELIMINARY REMARKS-TEMPERATURE-THERMOMETERS-EXPANSION OF SOLIDS-COMPENSATION PENDULUM-ILLUSTRATIONS.

139. THE phenomena and laws of gravity having been considered, those of heat are unquestionably the most universal. Its agency is to be recognised every where, and has been already alluded to as the probable cause of the three different states, as solid, liquid, or gaseous, in which matter may exist. Of this important agent we propose to treat in the present chapter; and that the student may not be embarrassed by any unnecessary difficulties, we shall defer for the present all hypothesis respecting the nature of heat, and commence with the phenomena which present themselves naturally for every one's consideration.

Every substance in nature is capable of exciting or producing in us those peculiar sensations to which the terms heat and cold have been applied. These sensations may be produced either by what we consider immediate contact, or at great distances, and their peculiar character forbids our considering the particles of mere matter as the cause. We readily admit that it is not the material particles of the coals composing the fire which reach and warm us, or the constituent matter of the sun, which by its action on

Ji

our bodies produces the sensation of heat, and on our eyes the sensations referred to light. There is then an agent, distinct from the peculiar substance of the body, residing in their masses, transmitting itself to great distances, and establishing betwixt us and it a continual communication; which agent is the cause of the sensations we experience. This unknown agent has received different names; it is sometimes called heat, thereby confounding cause and effect. This, however, in general, leads to no confusion; but the term caloric may be used specifically for the agent, while the term heat is confined to designate the science which treats of the properties, the effects, and the laws, of caloric. It is not necessary rigidly to observe these distinctions; and in the following pages we shall, in conformity to the more established usage, continue to employ the word heat, both with reference to the cause and the effect; the preceding explanation will preclude any misapprehension which might arise in the mind of the student from this apparent confusion in terms.

Of the effect and influence of heat on our own organized bodies we are perfectly sensible; but it likewise acts on all inorganic substances. Ice melts, water boils, iron becomes red hot and passes into a fluid state; these and many other phenomena have necessarily a cause, and our senses inform us that this cause is caloric. There exists such a correspondence, such a simultaneous action, between the modifications of these substances and the changes in our sensations, that we feel no hesitation in forming this opinion. These considerations enable us at once to class the phenomena, and they may be referred to the following heads: the physical effects of heat, as shewn in the dilatation and change of state of substances; the propagation of heat; the quantity of heat which substances contain; and the production of heat and cold.

140. Temperature.-All bodies can produce in us the sensation of heat or cold, and the degree of heat or of cold produced is to a certain extent an indication of the state of