the Propagation of Motions in Elastic Mediums. 329 



tarcling force P, according to this view, will result from the 

 mean effect of the reflections of the undulations from the ma- 

 terial particles of the medium. Its ratio, k-, to the accelerative 

 force which under the same state of density would exist out of 

 the median), might be shown to vary as the number of the 

 material particles in a given space, and the velocity of propa- 

 gation conjointly ; but the reasoning for this purpose is too 

 long to be inserted here. Admitting this, which of itself is 

 probable, to be the case, if 8 = the density of the medium, 



1 H 5 to2 - 1 T T 



1 = — , or r— = H. 



m- m m d 



The quantity H will be the same in different slates of the 

 same medium, but different in different mediums. If the states 

 of the medium be as different as the aeriform and fluid or 

 solid, H will probably not retain the same value, because this 

 quantity must be a function depending on the arrangement of 



the atoms. If the medium be a gas, ?« = I nearly, and — r — 



is nearly constant for different states of compression. This 

 M. Biot has found by experiment to be the case in atmo- 

 spheric air. The constancy of the value of — r — for different 



states of the same medium is a result which has been deduced 

 from the corpuscular theory of light; and in this respect (per- 

 haps, in this alone) the corpuscular seemed to have the ad- 

 vantage over the rival theory. 



I take this opportunity of adverting to a communication 

 I made to the Phil. Mag. and Annals of Philosophy for August 

 1829, in which it was stated that the integral of the equation, 



-j-r + —j-T + "rfTT — ^> obtained on the supposition that <p 



is a function of x- + j/^ + ^-, or r® and t, is not necessarily re- 

 stricted to a particular case, in its application to the motion 

 of incompressible fluids, but points to a general law of the mo- 

 tion. The reason of this is, that the equation d<^ = udx + 

 vdy -\- wdz, on which the integral is dependent, implies that 

 when the parts of the fluid move inter se, and not in such a 

 manner that it may be considered solid, the motion in every 

 individual portion is directed to a fixed or moveable centre; in 

 the same manner as the equation c/ V = X d x + \ dy + 7jd z 

 implies, that the impressed forces are directed to fixed or 

 moveable centres, 'riiis remark, which is important to the 

 theory of fluid motion, was verified in the instance in which 

 the motion is in space t)f two cUmensions, by showing that (lie 

 same result is arrived at wlielhcr ;fi be supposed a funttion of 

 N. S. Vol. 7. No. 11. May IBfiO. '2 U ,• ancl 



