There are really but seven notes in what is called the diatonic scale, the eighth note, C, being truly the first of seven other notes above, having relations to each other similar to those of the notes below, and constituting another octave. So we may have several octaves, one above another.

It is interesting to observe that the proportionate lengths of strings required to produce the eight notes of the scale have an exact numerical relation, but the reverse of that of the numbers of the vibrations. Thus if you have eight strings of the same size, their vibrating lengths required for the notes are as follows:

CDEFGABC
18/94/53/42/33/58/151/2.

For the notes of the octave above the lengths are thus:

CDEFGABC
1/24/92/53/81/33/104/151/4.

268. Unison.—In tuning instruments so as to make them harmonize the result is obtained when the corresponding parts of the instruments have the same number of vibrations. Thus the string in one violin that gives any particular note must vibrate just the same number of times in a second that the strings giving the same note in other violins do, or it will not be in perfect unison with them. The same is true of other strings for other notes, and also of the corresponding parts of all kinds of instruments which are to be played together. When, in tuning instruments together, it is said that a string of a violin, for example, is too flat, the difficulty is that it does not vibrate with sufficient rapidity, and it is therefore screwed up to make its note sharp enough, as it is expressed, to be in unison with the note of the corresponding strings or parts of other instruments.

269. Mysteries of Sound and Hearing.—There are many things of a mysterious character in relation both to sound and the manner in which it causes the sensation of hearing. I will barely notice but two of these. The effect, or rather the chain of effects, resulting in hearing is wholly mechanical, until we come to the nerve of hearing, which branches out with minute fibrils in the halls of audience of the internal ear. It is merely a series of vibrations. Now how it is that the mere agitation of a fluid inclosed in hard bone can communicate through fine white fibres to the brain, and through that to the mind, the idea that we have of all the various sounds that are produced, is a great mystery. All that we know is that the nerve is the medium of the communication, but of the manner in which it performs its office we know absolutely nothing. Again, while it is sufficiently mysterious that this information can thus be given to the mind when one sound after another communicates its vibration to the liquid in the ear, the mystery is greatly enhanced when various sounds come to the ear at one and the same time. To get a distinct idea of the very compound and wonderful character of the process of hearing in such a case we will suppose that a full band of music is playing, and at the same time mingled with its sounds there are various other sounds heard, some of them perhaps discordant. What a diversity of vibrations we have here! We have the slow vibrations produced in the grave notes, and the quick vibrations of the higher ones, all traveling together through the air to the ear, and each preserving its distinctive character. And more than this, after they arrive at the ear they are communicated unaltered through the drum, the chain of bones, the second drum, and the liquid where the nerve is, so that a correct report of each of all the notes is given through the nerve to the mind. Then, too, if there be any discord its vibration travels along with the rest, and so do the vibrations of other sounds, as the roaring of the wind, the report of cannon, and the noise of the people. And besides all this, in the multiplicity of the vibrations thus transmitted through so many different substances the mind gets a true report of the comparative loudness of the sounds, and even of their character, so that the sounds of drum, fife, trumpet, etc., are all accurately distinguished. In view of such wonders how significant is the question, "He that planted the ear, shall he not hear?"

[CHAPTER XIII.]
HEAT.

270. Heat and Cold.—In common language we speak of heat and cold as two distinct and opposite things. That this is not strictly correct may be shown by the following experiment: Take three vessels, and fill the first with ice-cold water, the second with hot water, and the third with tepid water. If you place your right hand in the first and the left in the second, and let them remain a little time, on taking them out and plunging them together into the third vessel, the water in it will feel warm to the right hand and cold to the left. So the air of a cellar seems warm to you in winter and cold in summer in contrast with the air outside. For the same reason water of a temperature that would ordinarily be refreshingly cool to us seems warm when drank after eating ice-cream. It is manifest, then, that there is no fixed dividing-line between heat and cold. There is, in fact, no such thing as cold. Substances are cold from being deprived of heat; and no substance ever has all its heat taken from it. Sir Humphrey Davy proved that there is heat in ice by rubbing two pieces together in a very cold room. They were gradually melted. Now this was not done by the air, for that was at a temperature below the freezing point. The heat which melted the ice came from the ice itself by means of the rubbing.