The Mechanical Vibration of Atoms. 657 



(2) For the middle octaves of the pianoforte, when these 

 two halves have a natural pitch near the pitch of the strings 

 exciting them, a resonance takes place and a good musical 

 tone results. 



(3) For the two lower octaves the statement in (2) does 

 not apply. 



(4) Strong- 2nd and 3rd partials are detrimental to good 

 musical tone. 



14 City Road, London, E.G. 

 June 17, 1910. 



LXX. The Mechanical Vibration of Atoms. 

 By William Sutherland*. 



ON account of the electric origin of rigidity and of 

 cohesion, both within and without the atom, there is 

 no real distinction between the mechanical and the electrical 

 vibrations of atoms, but it is convenient to distinguish as 

 mechanical vibrations those which can be calculated without 

 directly considering the electrical properties of an atom. 



The experimental researches of Rubens and his collaborators, 

 Aschkinass, Nichols, and Ladenburg, have carried the mea- 

 surements of wave-lencrths into extreme regions of the infra-red 

 spectrum, where the period of vibration is getting quite 

 close to the order of magnitude to be expected from the 

 mechanical vibrations of atoms and molecules. The recent 

 measurements of wave-lengths by Rubens and Hollnagel 

 for NaCl, KC1, KBr, and KI down to the seventh octave 

 below the visible spectrum (Phil. Mag. [6] xix. May 1910, 

 p» 761) invite the following brief theoretical investigation. 

 {Suppose an atom to be replaced by the least cube of the same 

 mass and of uniform density that could circumscribe it. 

 Let N be the rigidity of the material of this cube, p its 

 density, in its mass, ?n/7i = M its ordinary atomic weight or 

 mass, and R the length of the edge of the cube, being equal 

 to the atomic diameter. Here h is the mass of an atom of 

 hydrogen, 1617 X 10" 27 gramme. The velocity of propaga- 

 tion of a shear or simple distortion without change of volume 

 through the cube is (N/p)s. The simplest type of vibration 

 of the cube would have two opposite faces as middles of 

 internodes so that within the atom the fundamental wave- 

 length = 2R and outside the atom it is \. = ct, where c is the 



* Communicated by the Author. 

 Phil. Maa. S. 6. Vol. 20. No. 118. Oct. 1910. 2 X 



