TRANSACTIONS OF SECTION A. 691 



be the equation of the surface, the problem of reflection is readily solved so 

 long as ^ in (1) is small relatively to k or Stt/X ; that is, so long as the wave- 

 length of the corrugation is large in comparison with that of the vibrations. The 

 solution assumes a specially simple form when the second medium is impenetrable, 

 so that the whole energy is thrown back either in the perpendicularly reflected 

 wave or in the lateral spectra. Of this two cases are notable : (a) when — in the 

 application to sound — the second medium is gaseous and devoid of inertia, as in 

 the theory of the ' open ends ' of organ-pipes. The amplitude A,, of the perpen- 

 dicularly reflected wave, so far as' the fourth power of pjk inclusive, is then 

 given by 



- Ao = Jo {2kc) + |J . Ike J, {2kc) + l' J^^kc J, {2kc) - Wc'J,(2kc) \ . (2) 



in which there is no limitation upon the value of kc, so that the corrugation 

 may be as deep as we please in relation to X. If p be very small, the result — 

 viz., -J^, (2Ae) — is the same as would be obtained by the methods usual in 

 Optics ; and it appears that these methods cease to be available when p cannot be 

 neglected. 



The second case (/3) arises when sound is reflected from a rigid and fixed wall. 

 We find, as far as p'^lK^, 



A, = J,{2kc) - £L .kc.J, (2kc) (3) 



If p, instead of being relatively small, exceeds k in magnitude, there are no 

 lateral spectra in the reflected vibrations ; and if the second medium is impene- 

 trable, the regular reflection is necessarily total. It thus appears that an 

 extremely rough wall reflects sounds of medium pitch as well as if it were mathe- 

 matically smooth. 



The question arises whether, when the second medium is not impenetrable, the 

 regular reflection from a rough wall {p>k) is the same as if c = 0. Eeasons are 

 given for concluding that the answer should be in the negative. 



6. On the Piezo-electric Property of Qxiartz. By Lord Kelvin, Pres.B.S} 



7. On a Piezo-electric Pile. By Lord Kelvin, Pres.E.S. 



The application of pressure to a voltaic pile, dry or wet, has been suggested as 

 an illustration of the piezo-electric properties of crystals, but no very satisfactory 

 resultshave hitherto been obtained, whether by experiment or by theoretical con- 

 siderations, so far as I know. Whatever effects of pressure have been observed 

 have depended upon complex actions on the moist, or semi-moist, substances be- 

 tween the metals and electrolytic or semi-electrolytic and semi-metallic conduct- 

 ances of the substances. Clearing away everything but air from between the 

 opposed metallic surfaces of different quality, I have made the piezo-electric pile 

 which accompanies this communication. It consists of twenty-four double plates, 

 each 8 centimetres square, of zinc and copper soldered together, zinc on one side 

 and copper on the other. Half a square centimetre is cut from each comer of each 

 zinc plate, so that the copper square is left uncovered by the zinc at each of its 

 four corners. Thus each plate presents on one side an uninterrupted copper sur- 

 face, and on the other side a zinc surface, except the four uncovered half square 

 centimetres of copper. A pile of these plates is made, resting one over the other 

 on four small pieces of indiarubber at the four copper corners. The air-space 

 between the opposed zinc and copper surfaces may be of any thickness from half a 

 millimetre to 3 or 4 millimetres. Care must be taken that there are no minute 

 shreds of fibre or dust bridging the air-space. In this respect so small an air-space 

 as half a millimetre gives trouble, but with 3 or 4 millimetres no trouble is found. 



" Published in the PliUosophical Magazine, October 1893, pp. 331-542. 



T T 2 



