312 Mr. stokes, on THE FRICTION OF FLUIDS IN MOTION, 



16. The conditions to be satisfied at the surface of the solid may be easily deduced from 

 the analogous conditions in the case of a fluid with a free surface, only it will be necessary 

 to replace the normal pressure FI by an oblique pressure, of which the components will be 

 denoted by X,, l', Z,. We have then, making the necessary changes in the quantities involved 

 in (14), 



,. „f da Ida d&. ida dy\\ 



( a,r \dy dxl \dz dwi ] 



for the case of equilibrium, and for the case of motion such as that just considered it will only be 

 necessary to replace A hy m A in these equations. If we measure the angles of which I, m, n are 

 the cosines from the external normal, the forces X^, 1\, Zj must be reckoned positive when /, m and 

 n being positive, the surface of the solid is urged in the negative directions of ,v, y, z, and in other 

 cases the signs must be taken conformably. 



If the solid considered is in a state of constraint when at rest, and is moreover put into a state 

 of vibration, the pressures and displacements due to these two causes must be calculated separately 

 and added together. If m were equal to 1, they could be calculated together from the same 

 equations. 



SECTION IV. 



Principles of Poissotfs theory of elastic solids, and of the oblique pressures existing in 

 fluids in motion. Objections to one of his hypotheses. Reflections on the constitution, 

 and equations of motion of the luminiferous ether in vacuum. 



17- In the twentieth Cahier of the Jvurnal de PEcole Polytechnique may be found a memoir 

 by Poisson, entitled Memnire sitr les Equations generates de FEquilibre et du Mottvement des 

 Corps solides elastiques et des Fluides, which contains the substance of two memoirs presented 

 by him to the Academy, brought together with some additions. In this memoir the author 

 treats principally of the equations of equilibrium and motion of elastic solids, of the equations 

 of equilibrium of fluids, with reference especially to capillary attraction, and of the equations 

 of motion of fluids supposing the pressure not to be equal in all directions. 



It is supposed by Poisson that all bodies, whether solid or fluid, are composed of ultimate 

 molecules, separated from each other by vacant spaces. In the cases of an uncrystallized solid 

 in its natural state, and of a fluid in equilibrium, he supposes that the molecules are arranged 

 irregularly, and that the average arrangement is the same in all directions. These molecules 

 he supposes to act on each other with forces, of which the main part is a force in the direction of the 

 line joining the centres of gravity, and varying as some function of the distance of these points, 

 and the remainder a secondary force, or it may be two secondary forces, depending on the 

 molecules not being mathematical points. He supposes that it is on these secondary forces that the 

 solidity of solid bodies depends. He supposes however that in calculating the pressures these 

 secondary forces may be neglected, partly because they become insensible at much smaller distances 

 than the main part of the forces, and partly because they act, on the average, alike in all 

 directions. He suppo.ses that the molecular force decreases very rapidly as the distance increases, 

 yet not so rapidly but that the sphere in which the molecular action is sensible contains an immense 

 number of molecules. He supposes consequently that in estimating the resultant force of a 

 hemisphere of the medium on a molecule in the centre of its base the action of the neighbouring 

 molecules, which are situated irregularly, may be neglected compared with the action of those 



