274 



SCIENCE-GOSSIP. 



Absolute truth must not be looked for here. The 

 subject is essentially a matter of comparison, and 

 the facts to be described may, quite correctly, be 

 presented in very different aspects ; for any 

 vibration may be the resultant, and therefore the 

 equivalent, of any number of other vibrations. 

 Any description of any curve is, therefore, but one 

 view out of a possibly unlimited number. 



Consider two similar simple pendulums, each 

 capable of free vibration in one plane. Their 

 ratio (comparative rates of vibration) will be the 

 simplest possible, because their lengths are equal. 

 Set them going with equal amplitudes (equal 

 lengths of swing), and let their directions be at 

 right angles to each other. Now, in order to clear 

 away unnecessary difficulties, we may overlook 

 inessential points, such as the slight vertical 

 curvature of the pendulum paths, and the impossi- 

 bility of constructing perfect pendulum. 



If both pendulums start at the same instant, the 

 respective movements will meet at the centre of 

 their paths ; then, what will happen ? That which 

 must happen ; for if the laws of nature are not 

 identical with the laws of necessity, there certainly 

 can be no antagonism between them. But the laws 

 of necessity are no other than the law T s of mathe- 

 matics — whether written or unwritten. 



The pendulum movements, at right angles to 

 each other, being both started at the same instant, 

 and having met at the centre of their paths, 

 will, from that point, continue to vibrate in a 

 straight line equi-distant between their original 

 courses. 



The straight line is therefore one of the vibra- 

 tion paths or vibration figures of the unison. 

 For the unison, in respect to its audibility, is 

 merely the motion form assumed by the sonorous 

 molecule conveying to the ear its own peculiar 

 combination of virbrations ; and the laws of 

 morion are the same whether applied to pendu- 

 lums, points, or planets. 



In the foregoing experiment the second pendulum 

 is simply a convenient vehicle of motion. What- 

 ever means are employed for conveying the 

 second impulse to the first pendulum, the same 

 result must follow : the second vehicle may there- 

 fore be disregarded. 



Now suppose the second impulse to hit the 

 pendulum at the end of its path. At the moment 

 of collision the mass will be acted upon by two 

 equal forces at right angles ; one entirely potential, 

 the other entirely kinetic ; both alternating in equal 

 periods from one condition to the other. The 

 result will be that the pendulum will move in a 

 circle, and will continue so to move as long as it is 

 not interfered with ; but if there be any wasting 

 of the original forces through friction, the ampli- 

 tude of the circle will be promptly and propor- 

 tionately diminished. Whilst the wasting process 



continues to act evenly, the motion will remain 

 circular (or, more strictly, spiral). Irregularities in 

 the wasting process must produce corresponding 

 changes in the figure. Generally, the circle 

 approximates to a straight line ; sometimes in one 

 direction, sometimes alternating. 



There is no room for question as to the identity 

 of pendulum-figures with the actual paths of 

 sonorous molecules. We assume the truth of the 

 laws of motion and the elasticity of matter ; all 

 the rest is plain arithmetic. We may, therefore, 

 correctly refer to the various figures as being 

 synonymous with corresponding musical intervals. 



The unison — as we have just seen — has two 

 principal phases, the circle and the straight line ; 

 it may also have any possible phase of the ellipse 

 between these two limits. 



The ellipse is thus the comprehensive mechanical 

 equivalent of the unison ; but the unison has one 

 other remarkable phase, in respect to which there 

 exists no parallel amongst other intervals — the phase 

 of dead antagonism. If two unison-pendulums meet 

 each other in direct opposition at the centre of 

 their course, the whole of their visible motion will 

 disappear ; molar will be transformed into molecu- 

 lar motion — that is, into heat. The acoustic equiva- 

 lent of this phenomenon becomes apparent to us 

 in the form of "beats"; but its practical effect 

 consists rather in the actual loss of sound, which 

 occurs when many voices are heard together. 



Due consideration of the facts here stated will 

 lead to the conclusion that musical intervals 

 generally are correctly represented by combina- 

 tions of two ellipses, rather than by com- 

 binations of two straight lines. Let anyone who 

 doubts this statement refer to the sound-diagrams 

 in Tyndall's book on "Sound," copied by Young 

 from the actual vibrations of pianoforte wires. 



I have no space for the history of the subject, 

 except to mention the names of some of its chief 

 investigators. Chladni, Young, Wheatstone, Strohe, 

 Blackburn, Lissajous, Airey, Tisley, Melde and 

 others have done much to extend our knowledge of 

 the mysteries of vibration, but the apparent 

 magnitude of the task increases with every new 

 accession of light. 



Much important information respecting the 

 varieties and typical forms of vibration curves has 

 also been accumulated by worth}- labourers in 

 other fields of knowledge, who have had no 

 suspicion of its relationship in this direction. 

 Such are Bazley's " Index to the Geometric 

 Chuck," Perigal's " Contributions to Kinetics," 

 and the many excellent works on ornamental 

 turning. Even Young and Tyndall and other 

 eminent philosophers have missed the meaning of 

 phenomena, which their labours have brought to 

 light. 



68, Shakespeare Street, Nottingham ; December, 1894. 



