74 Royal Institution : — 



zling at the nodes. The vibrating chord is indeed better seen when 

 the light that falls upon it has been caused to pass through coloured 

 glass. We thus obtain at pleasure green, blue, and red spindles, 

 with nodes like fire shading off into the more subdued light of the 

 ventral segments. 



36. Substituting for the cotton rope a string of silvered beads 12 

 feet long, I send the beam from the electric lamp along the string. 

 On every bead rests a spot of light of sunlike brilliancy. When 

 the wheel is turned, each spot describes a circle, and every ventral 

 segment, of which we have now four, seems formed of a series of such 

 dazzling parallel rings, which diminish in size right and left from the 

 points of maximum amplitude till the diameters vanish at the nodes. 



37. So much for physical beauty; we have now to revert to 

 beauty of another kind. The experiments with tuning-forks above 

 described may be extended to the establishment of all the laws of 

 vibrating strings. I have here four forks/ a, b, c, d, whose vibra- 

 tions are in the proportion of the numbers 1, 2, 4, 8. Attaching a 

 string 8 feet long to the largest fork, I stretch it by a weight which 

 causes it to vibrate as a whole. Keeping the stretching weight or 

 tension the same, 1 attach pieces of the string to the other forks, and 

 determine in each case the length which swings as a whole. These 

 lengths are in the ratio of 8, 4, 2, 1. 



38. Hence the rapidity of vibration is inversely proportional to the 

 length of the string. 



39. Here the string 8 feet long vibrates as a whole when attached 

 to the fork a. I now transfer it to b, still keeping it stretched by 

 the same weight. It vibrates when b vibrates ; but how ? By di- 

 viding into two equal ventral segments. In this way alone can it 

 accommodate itself to the vibrating period of b. Attached to c, the 

 same string separates into four, while when attached to d it divides 

 into eight ventral segments. This may be deduced immediately 

 from the law enunciated in 38, and its experimental realization 

 reacts as a proof of that law. 



40. This result admits of extension. I have here two tuning- 

 forks separated from each other by the musical interval called a fifth. 

 Attaching a string to one of the forks I stretch until it divides into 

 two ventral segments ; attached to the other fork and stretched with 

 the same weight, the string divides instantly into three segments 

 when the fork is set in vibration. Now to form the interval of a fifth 

 the vibrations of the one fork must be to those of the other in the 

 ratio of 2 : 3. The division of the string therefore declares the in- 

 terval. Here also are two forks separated by an interval of a fourth. 

 With a certain tension one of the forks divides our string into three 

 ventral segments ; with the same tension the other fork divides it 

 into four, which two numbers express the ratio of the vibrations. In 

 the same way the division of the string in relation to all other musi- 

 cal intervals may be illustrated. 



41. Again. Here are two tuning-forks, a and b, one of which (a) 

 vibrates twice as rapidly as the other. I attach this string of silk to 

 a, and stretch the string until it synchronizes with the fork and 

 vibrates as a whole. I now form a second string of silk of the same 



