[ 392 J 



XLIII. 



ON TEXTUEE IN MEDIA, AND ON THE NON-EXISTENCE 

 OF DENSITY IN THE ELEMENTAL ETHEE. By G. 

 JOHNSTONE STONEY, a Vice-President of the Royal Dublin 

 Society, M.A., D. Sc, F.E.S. 



[Read February 19, 1890.] 



In the investigations of ordinary dynamics — the dynamics of se- 

 condary (a) motion — integrations have to be extended throughout 

 the bodies with which we are dealing, or over their surfaces. Now 

 whenever we employ this operation assumptions are tacitly made 

 which do not accord with what exists in real objective nature. 



Suppose that the problem is to obtain the pressure of water 

 against a sluice ; to ascertain the amount and distribution of the 



(a) In the computations of ordinary dynamics, we conceive the portion of space occu- 

 pied by the body with which we are dealing to be divided into elements of volume (the 

 dxdy «fe's), which elements of volume we regard as movable. Each of these we multi- 

 ply by a coefficient called the density, and call the product the element of mass 

 (dm — p . dxdydz). These elements of mass we picture to ourselves as acting on one 

 another, or as being acted upon by external forces ; and from the laws of these actions 

 we endeavour to deduce the motion of the element of volume, carrying its contents with 

 it, and in some cases changing its form or volume. 



In this process we take no notice of any motions which may be going on within the 

 element of volume, except so far as that some imperfect account may perhaps be indirectly 

 taken of them when we multiply the element of volume by a density. Nevertheless, in 

 all the real cases that occur in nature, there are, as a matter of fact, very active motions 

 of various kinds going on within the element of volume — motions of the molecules 

 which it contains, and still more deep-seated motions within the portion of the element 

 of volume occupied by those molecules, or in the interspaces between them. 



Accordingly, the motions with which we deal in our ordinary dynamical investiga- 

 tions are merely drifting motions — the drifting about of elements of volume, within 

 each of which, as events really occur in nature, there are elaborate subsidiary motions 

 going on. Now, secondary motion is to be defined as the motion which consists in the 

 drifting about, with or without changes of size and form, of elements of volume, 

 within each of which there are subsidiary motions. 



If the subsidiary motions consist exclusively of irrotational motions in an incom- 

 pressible and perfectly fluid medium, they cannot contribute to the density by which 

 the element of volume in which they occur is to be multiplied. It is, however, other- 

 wise if there are any rotational motions present. 



