ing with phenomena about which Science says she does know something: from a consideration of these known facts we shall be able, slowly but surely, to grasp some of the much less familiar phenomena with which spectrum analysis is especially concerned.
We all know that some sounds are what is termed high and others low, a difference which in scientific language is expressed by saying that sounds have a difference in pitch. We know that the difference between a sound which is pitched high and a sound which is pitched low is simply this—that the pulses or waves, as we may call them for simplicity's sake, which go from the sender-forth of the sound (which may be a cannon, a piano, or anything else) to the receiver, which is generally the human ear, are of different lengths. What in physics is called a sound-wave is constructed as follows: We have a line A X, which represents the normal condition of the air through which the sound is traveling, and curves which represent to the eye—first, the relative amounts of compression (+) and rarefaction (—) brought about by the sound in the case of each pulse, and secondly the relationship of this to the actual length of the wave, or, what is the same thing, the time taken for the pulse to travel. Thus we may have long waves and short waves independently of the amount of compression or rarefaction, and much or little compression or rarefaction independently of the length of the wave. We know that the difference between a high note and a low note, whether of the voice or of a musical instrument, is, that the high note we can prove to be produced by a succession of short