8 Prof. J. Le Conte on the Discrepancy between the Computed 



sation are "suppressed by the ear;" and "that aerial rarefac- 

 tions are alone capable of stimulating that organ in man"*. 

 Assuredly it would have been more reasonable to suspect the 

 correctness of the approximate analysis by which such a result 

 had been attained, than to have attempted the solution of the 

 difficulty presented by its discordance with experience by making 

 a gratuitous physiological assumption which, from the very 

 nature of the case, is utterly incapable of being tested by obser- 

 vation. 



But conclusions of a still more extraordinary character in rela- 

 tion to the propagation of sound have been deduced by the Rev. 

 Samuel Earnshaw of Sheffield, from his recent and elaborate 

 mathematical researches on this subjectf. As they have an 

 important bearing on Laplace's explanation, I propose to notice 

 them somewhat in detail. Like Euler, he at first thought that 



it was not admissible to assume the factor l-f-) = lj but, to 



his astonishment, when he had succeeded in integrating the dif- 

 ferential equation without the use of approximative assumptions, 

 the theoretical velocity of sound remained the same as before. 

 This led him to examine the problem of the propagation of waves 

 in an elastic medium ab initio. He maintains that previous geo- 

 meters have erroneously assumed elastic media to be continuous, 

 whereas he looks upon them as consisting of " particles separated 

 by finite intervals" This is the fundamental peculiarity from 

 which his mathematical investigation starts, and from which the 

 anomalous results are presumed to flow as logical sequences. I 

 shall briefly indicate some of the extraordinary conclusions to 

 which his formulae conduct. 



a. " That the atmosphere is capable of transmitting sound-waves 

 with any degree of velocity from zero to infinity : . . . . that there 

 is no other limit to the velocity with which a violent sound is 

 transmitted through the atmosphere, than that which the possi- 

 bility of supplying a sufficient degree of force in its genesis may 

 impose." 



b. "That a musical note of any pitch is transmissible with two 

 different velocities ; and that there are two waves for every note." 



c. According to Mr. Earnshaw, the extreme range of velocity 

 indicated in «, divides itself into three distinct kinds of waves, 

 all propagated with different velocities — giving rise to what he 

 designates the " Triplicity of Sound" Assuming v to be the 

 observed velocity of sound, he makes the following classification 



* Phil. Mag. S. 4. vol. xvi. p. 528 et seq. (1858). 



t Ibid. S. 4. vol. xix. p. 449 et seq. ; also vol. xx. pp. 37 and 186 et seq. 

 (1860). 



