FT '■ 



THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 





[SIXTH SERIES.] 



AUGUST 1911. 



XXIV. On the Calculation of Chladms Figures for a Square 

 Plate. By Lord Rayleigh, O.M., F.lt.S* 



IN my book on the Theory of Sound, eh. x. (1st ed. 1877, 

 2nd ed. 1894) I had "to speak of the problem of the 

 vibrations of a rectangular plate, whose edges are free, as 

 being one of great difficulty, which had for the most part 

 resisted attack. An exception could be made of the case in 

 which /a (the ratio of lateral contraction to longitudinal 

 elongation) might be regarded as evanescent". It was shown 

 that a rectangular plate could then vibrate after the same 

 law as obtains for a simple bar, and by superposition some 

 of the simpler Chladni's figures for a square plate were 

 deduced. For glass and metal the value of ft is about £, so 

 that for such plates as are usually experimented on the 

 results could be considered only as rather rough approxi- 

 mations. 



I wish to call attention to a remarkable memoir by W. Ritz f 

 in which, somewhat on the above lines, is developed with 

 great skill what may be regarded as a practically complete 

 solution of the problem of Ohladni's figures on square plates. 

 It is shown that to within a few per cent, all the proper 



* Communicated by the Author. 



f Theorie der Transversalschwingungen einer quadratischen Platte 

 mit freien Handera, Annalen des Physik, Bd. xxviii. S. 737 (1909). The 

 early death of the talented author must be accounted a severe loss to 

 Mathematical Physics. 



Phil Mag. S. 6. Vol. 22. No. 128. Aug. 1911. Q 



