On the Propagation of Motion through Elastic Meditims. 325 



Huel Abraham 45 inches diameter of larger cylinder*. 



60 



Huel Alfred... 70 



I waited to see the remainder of Mr. Farcy's evidence, but 

 as you have not continued it in the March Number of your 

 valuable Journal, I am induced to trouble you on this subject 

 whilst that gentleman's statements are fresh in the minds of 

 your readers. I have the honour to be, yours, &c. 



Perran Wharf, near Truro, Wm. J, Henwood. 



March 16, 1830. 



XLVII. Some general Considerations respecting the Propa- 

 gation of Motion through Elastic Mediums ; with Remarks 

 on a former Communicatio?i. By J. Challis, Esq. Fellow of 

 Trinity College Cambridge^ and of the Cambridge Philoso- 

 phical Society-^. 



THE following mode of considering the transmission of 

 motion through elastic substances, which has not yet, 

 I believe, occurred to any one, may serve to throw some light 

 on a subject confessedly difficult, but which is nevertheless 

 interesting ; as it has direct reference to the manner in which 

 our organs of hearing and sight are acted upon by external 

 objects. 



The elastic substance to be considered may be either solid 

 or fluid. Suppose an indefinitely slender column of it, the 

 transverse section of which is every where the same, and the 

 parts of which are moving in any manner, to be divided into 

 an indefinite number of very small equal masses. Call «, ^, y, 

 three of these masses taken in order, of which « is nearest the 

 origin of x the abscissa : the density of each may be consi- 

 dered the same throughout, but their densities to vary from 

 one to another. Let z be the length of a, s' of /3, z" of y. 

 Then the distance between the centres of gravity of « and ^ is 



ii-^, and that between the centres of gravity of /3 and y, 

 l'^'^' , Let t/, t', be respectively the velocities of the centres 



of gravity of /3 and y, at a time t reckoned from a given in- 

 stant. Then •d — v = their relative velocity. At the end of 



a small additional time t, t/ becomes t^ + 77^'r+ TT''' 



• Subsequently removed to Unci Wcntworth. 

 \ Coniiininicatcd liy the Author. 



and 



