Propagation of Waves in a Resisted Fluid. 329 



medium produces no resistance along the normal of the path 

 of the particle : in fact, in the case of a particle describing a 

 very small oval with a small velocity, the principal resistance, 

 it seems to me, would be along the normal. 



7. From the consideration of a particle moving in a resist- 

 ing medium, we may easily pass to the consideration of the re- 

 sistance experienced by a moving fluid in which a great 

 number of fixed particles are immersed at regular intervals 

 from each other. In such a case we must suppose that the 

 magnitude and direction of the resistance on any element of 

 the fluid depends upon the velocity of that element, the differ- 

 ential coefficients of the velocity with respect to the time, and 

 the curvature of the path described by the element. We 

 must also, 1 think, suppose that in general the resistance on 

 any element depends in some degree upon the state of motion 

 of the elements which surround it; but, in the particular case 

 where the state of motion varies very slowly in passing from 

 element to element (which will be the only case we shall have 

 to consider), it will not be necessary to take this into account. 

 There will also be a certain amount of internal agitation pro- 

 duced in each element, which will depend upon the magnitude 

 of the resisting particles and the distances between them. 

 When the particles are placed at very small intervals from 

 each other, and their magnitudes are very small compared 

 with these intervals, this internal agitation will be inconsider- 

 able compared with the motion of translation of the element. 

 We suppose, of course, that each element of the fluid (/. e. each 

 portion of it throughout which the state of motion may be re- 

 garded as sensibly the same) includes a great number of the 

 resisting particles within it, which amounts to supposing that 

 the variation of the state of motion is sensible only when we 

 pass over a distance considerably greater than the intervals 

 between the resisting particles ; or, in other words, that the 

 length of the wave (supposing the motion of the medium to be 

 undulatory) is extremely large compared with the intervals be- 

 tween the resisting particles. 



8. We shall now apply these considerations to the case of 

 plane transversal waves transmitted through the aether, sup- 

 posed to be resisted by the particles of an uncrystallized body. 



Let us choose three rectangular axes, and assume the axis 

 of sf so as to coincide with the direction of propagation. Con- 

 ceive the asthereal medium to be divided into a series of ele- 

 mentary slices by planes parallel to that of xy, the thickness 

 of each slice being very small compared with the length of the 

 wave, but very much larger than the intervals between the 

 particles of matter, which we shall suppose to be so many phy- 



