108 Mr. J. LeConte on 



moderate distances from the sonorous centre only the short 

 and sharp sound due to the shock of the striking hammer was 

 transmitted to distant points through the water. It is obvious 

 that the wave-lengths of sounds of this character must be 

 determined by other considerations than those relating to the 

 musical pitch. 



In relation to solitary waves generated by sudden blows 

 and explosions*, it may be more difficult to form a just estimate 

 of the wave-length than in the case of musical sounds. Never- 

 theless it is evident that the wave-length must be directly pro- 

 portional to the time occupied by the displacing impulse, mul- 

 tiplied by the velocity of transmission of the elastic pulse. 

 In algebraic terms, if L = wave-length, £ = time of the genera- 

 ting impulse, and v = velocity of sound in the elastic medium; 

 we have, L varies as txv, or Jj = txv. Consequently, in a 

 given medium, in which v remains constant, L will be a func- 

 tion of t, or the duration of the generative impulse ; so that 

 when the factor t is indefinitely small, the value of L will be 



* It may be questionable wbetber the elastic waves generated by 

 momentary explosions or detonations can be properly regarded as strictly 

 solitary. It is possible that, in such cases, groups of waves are generated 

 similar to those discussed by Lord Rayleigh in the Appendix to his work 

 on the Theory of Sound, vol. ii. pp. 297-302. 



Furthermore, the admirable and exquisitely refined arrangements de- 

 vised by Regnault for investigating the phenomena of sound enabled him 

 to submit this question to a more or less satisfactory experimental test, so 

 far as aerial waves are concerned (Memoires de VAcad. des Sciences, 

 vol. xxxvii. pp. 45-49 et pp. 278-282: Paris, 1868). He found that 

 the explosion of a pistol charged with ordinary powder does not produce 

 only a single wave, since it gave rise to a recognizable musical tone of very 

 brief duration (p. 45) ; and the same was the case with the sound pro- 

 duced by the detonation of a mixture of oxygen and hydrogen gases 

 (p. 48). But the explosion of a small charge of fulminate of mercury was 

 so sudden that the wave generated in the air was much shorter, and the 

 " coup " was much more " sec," than that which was produced by a 

 pistol charged with ordinary powder (pp. 47, 48, and pp. 278-281). 

 He adds, " 11 est encore difficile de decider si l'on a produit ainsi une onde 

 unique, mais il est certain que si plusieurs ondes prennent naissance, elles 

 doivent se suivre de tres pres'' (p. 48). 



Again, the observations of General H. L. Abbot (U. S. Engineers), incident 

 to the heavy blastings at Hallet's Point, Hell Gate, in the harbour of New 

 York, seem to render it at least probable that the waves transmitted by the 

 earth reached the distant observers in groups, or as a train of waves 

 (Silliman's Journal, vol. xv. (1878), p. 178 et seq.). 



Sir G. B. Airy maintains that " there is reason to think that a single 

 wave in air or in the medium of light would not produce the sensation of 

 sound or colour" (Undulatory Theory of Optics, p. 15, art. 18, 1866). 

 No reason is assigned for this somewhat extraordinary assertion. In the 

 case of light, it is obviously impossible to experimentally test the validity 

 of this idea of the former Astronomer Royal ; and it does not appear to 

 be sustained by the results of acoustical experiments. 



