MUTUAL CHANGES COMMON TO ALL MATTER 63 



to resist the stress between the earth and the imaginary 

 column x Y. 



3. That the pressure in a vessel of the shape shown in 

 No. 4 is found to be the same as it would be if the sides were 

 perpendicular, as c E, D F. 



The pressure in the part A K L B (No. 4) is evidently due to 

 the stress between the liquid and the earth, and no difficulty 

 arises in this case. But we need now to explain why the 

 pressure on the areas c K and L D is the same as if the sides c A 

 and D B were vertical as c E and D F. In order to do this we 

 must make the following assumption : ' that the stresses be- 

 tween the parts of a liquid at rest are always perpendicular to 

 the surfaces of separation between those parts.' From this 

 assumption we can deduce the following facts : In the portion 

 A c K are pressures perpendicular to A c and A K from the side 

 A c and the column of liquid A B K L respectively, which pro- 

 duce a resultant pressure downwards, as shown in the figure. 

 The pressure from A c, due to the narrowing of the vessel at 

 the top, is found from the observation to be exactly equal to the 

 pressure which the side A c would bear from the presence of 

 the same liquid in a vessel of the shape and dimensions ACE. 



From this it is evident that the whole pressure from the 

 part A c K is due to two causes : the first is the pressure 

 due to gravity, and the second is the resultant of the per- 

 pendicular pressures from A c and A K. These two pressures 

 are together equal to the pressure which a column of liquid 

 represented by E K would exert on the bottom of the vessel in 

 virtue of the stress existing between it and the earth. 



The fact that the pressure on the sides of a vessel varies 

 with the depth also requires to be observed and explained. 

 If we consider the liquid to be made of very small particles, it 

 is evident the top particles press on the next, and so on until 

 the pressure on the lowest particles is due to the sum of the 

 pressures of all the particles above it. This pressure causes 

 the particles to slip away at right angles towards the sides, 

 thereby producing a pressure on the sides which increases with 

 the depth. 



