382 Dynamic Theory. 



motion in a particular way. Referring to our table of tonic vibrations, 

 in the last chapter, we find the Gr of the lowest octave is made by 49 

 and a half vibrations. If we call this the beginning of octave number 

 1, the Gr at the beginning of octave No. 2 has 99 vibrations, No. 3 is 

 produced by 198, No. 4 by 396, &c. The G at the beginning of the 

 10th octave is formed by 25,344, and the llth by 50,688. But this 

 rate is too rapid to make any impression on our ears, probably because 

 each succeeding vibration reaches the drum of the ear before the one 

 preceding it has had time to produce an effect. The result to the ear is 

 silence, but the vibrations may go on all the same, doubling in num- 

 ber for each octave. When the beginning of the 20th octave is reached, 

 the G- will be formed by 25,952,256 vibrations per second. The 30th 

 octave takes, in round numbers, 26,575,000,000 vibrations, the 40th 

 27,212,800,000,000, and the 44th requires 435 and a half trillions at 

 the beginning and 871,000,000,000,000 at the end, or the beginning of 

 the 45th octave. These are large figures and difficult to be conceived. In 

 order to count a million a day a man would have to count nearly 12 per 

 second for the whole twenty-four hours. Although no one can count more 

 than half so fast, even at that rate it would take over 2,384,000 }^ears 

 to count 871 trillions. Yet it is proved by satisfactory demonstration 

 that this number of vibrations actually takes place in a second. 



The G- at the beginning of the 44th octave makes its impression upon 

 us through the sense of sight, giving the sensation of that color which 

 a metal takes on when heated to redness. If the heat be increased the 

 color of the metal will change to bright red, then yellow, and with inti- 

 mations of greenish and bluish tinges finally become white. In passing 

 through these phases of color it has, in reality, passed through different 

 states of vibration, the final white color representing simultaneous vi- 

 brations of all the notes in the 44th octave, from Gr to Gr. These notes 

 represent all the colors that are visible to our eyes, and are designated 

 by the seven names, red, orange, yellow, green, blue, indigo, and violet. 

 In reality, the tones pass from one to another by imperceptible steps 

 representing a gradually increasing rate of vibration, so that there is no 

 definite boundary between the red and orange, for example, or between 

 the green and the blue, &c. These intermediate steps constitute the 

 tints and shades of color too numerous to be named. Sunlight and 

 the light of the electric arc contain all the vibrations of this 44th octave, 

 and some notes both above and below it. By means of a prism these 

 different tones can be separated from each other. A ray of sunlight 

 allowed to pass through a slit or hole into a dark chamber, and then 

 through a prism, and falling at last on a white screen, is analyzed by 

 the prism, the different parts of the ray being caused to diverge from 

 each other like the rays of a folding fan. And when the light reaches 



