Dr. Charles J. B. Williams o?i Sound. 25 



the important considerations involved in the solution, are well 

 known to mathematicians. 



But it may not be useless for the student to bear in mind 

 the connexion between the form of the function in its integra- 

 tion and the principle of the superposition of small motions 

 arising from the circumstance of the linearity of the expression 

 (in which case alone the differential coefficient of a sum of 

 functions is the same as the sum of the differential coeffi- 

 cients). This point will be found illustrated in the particular 

 view which M. Cauchy takes of the subject. 



In his memoirs " On the Dispersion," &c., having esta- 

 blished the above equations of motion (12.), he pursues from 

 this point a different course to that adopted in his former me- 

 moirs ; and from certain considerations which he lays down 

 relative to the method of integration in this case, he is enabled 

 to deduce expressions, from which not only are all the laws of 

 the propagation of waves deducible as before, but also the other 

 important relations to which we have alluded established. 

 [To be continued.] 



IV. Observations on the Production and Propagation of Sound, 

 By Charles J. B. Williams, M.D,, SrC^ 



TT is rather singular that so simple and comparatively easy 

 -^ a science as acoustics should have been so tardily de- 

 veloped, and that much of its recent advancement should be 

 referrible rather to the illustrations which it affords to the 

 sister science, optics, than to its own intrinsic value. So 

 true is it that sight is our predominant sense, and that dark- 

 ness and ignorance have become synonymous terms. Can it 

 be a matter of wonder or of complaint that the organization 

 of the ear is still involved in mystery, when so much of the 

 laws of sound, to which it is doubtless adapted, is unap- 

 preciated or unexplained ? We would venture to hope that 

 some master-spirit will take up the subject of acoustics, not 

 only as an interesting and instructive link between the me- 

 chanical sciences and those subtler ones of light, heat, and 

 electricity, but also for its own sake, and for the support and 

 improvement of those useful and agreeable relations to social 

 happiness which depend on the perfect state of the sense of 

 hearing. In the mean time I venture to bring before the 



[* Communicated by the Author. — The substance of this paper was read 

 before the Section of Mathematics and General Physics of the British As- 

 sociation, at the Meeting at Edinburgh in September 1834 : see our last 

 volume, p. 387.] 



Third Series. Vol. 6. No. 31. Jan. 1835, E 



