100 Mr. J. LeConte on 



locomotive is very loud at a distance of ten yards. At a mile 

 off the intensity must be 30,000 times less ; but the sound 

 still appears rather loud, and would probably be audible, under 

 favourable circumstances, even when enfeebled in the ratio of 

 a million to one. For this reason, it is not easy to obtain 

 complete shadows "*. In other terms, the range of audition 

 is so extensive, that the diffractive secondary waves originating 

 at the boundaries of the obstacle and propagated into the 

 geometrical shadow, though comparatively feeble, produce 

 decided sensuous impressions upon the auditory apparatus of 

 the ear. 



5. The mathematical theory of undulations indicates that 

 acoustical shadows should be more distinct for short waves 

 than for long waves. This prevision has been verified by the 

 experiments of Lord Kayleighf, who found that the sound- 

 shadows cast by acute sounds were more distinct than those 

 produced by grave sounds. 



6. Another prevision of theory has been experimentally 

 verified both in the case of light and of sound. It is well 

 known that the great geometer Poisson, in applying Fresnel's 

 integrals to the case of the diffraction of light produced by a 

 small opaque circular disk, was led to the startling result 

 that the illumination of the centre of the shadow was precisely 

 the same as if the disk had been altogether removed. This 

 deduction from theory was experimentally verified by the 

 illustrious Arago, by means of an opaque circular disk 2 mil- 

 lim. in diameter; for he observed a bright point in the centre 

 of the shadow of the disk on which waves of light were directly 

 incident. In this case the secondary waves originating at 

 the disk find the conditions of complete concurrence at a 

 definite point in the axis of the geometrical shadow. 



7. The difficulties to be overcome, in the experimental 

 verification of the acoustical analogue of this beautiful pheno- 

 menon, are entirely different from those of optics, on account 

 of the immense disproportion of wave-lengths. In light, the 

 disk must be small, and the luminous source must have a 

 very small angular magnitude. In sound, the disk must be 

 comparatively large, and the sounds must be acute. Lord 

 Eayleigh has recently succeeded in experimentally verifying 

 this prevision of theory in the case of sound, by means of a 

 circular disk about fifteen inches in diameter, with a bird-call 

 as the source of sound, placed at a distance of twenty inches 

 from the centre of the plane of the disk. At twenty-four 



* Phil. Mag. 5th series, vol. iii. p. 458 (1877). 

 t Ibid. pp. 458, 459 (1877). 



