chap, xix.] PRINCIPLE OF ARCHIMEDES. 195 



disturbance of it, a continuous flow takes place from 

 one end to the other of the series of vessels. 



-The principle of Archimedes. - - When a 

 solid body is immersed in a liquid, in accordance with 

 Pascal's law the liquid exerts pressure upon it in all 

 directions, and the pressure at each point of its sur- 

 face will be equal to the column of liquid above the 

 point. Thus, the body ABCD (Fig. 96) plunged in 

 the liquid is pressed on every side. Sup- 

 pose it to be a cube, then it is evident 

 that the pressures on the four sides of 

 the cube being directed perpendicularly 



to the surfaces, equalise one another, Fig. 96. The 

 and all that is left for consideration 23BSL? 

 is the pressure on the upper surface 

 AB, which is directed downwards, and the pressure 

 on the under surface CD, which is directed upwards. 

 The downward pressure is equal to a column of the 

 liquid whose base is AB and whose height is AN, the 

 upward pressure is a column whose base is CD and 

 whose height is ex. These two partly destroy one 

 another. The column ABXN is common to both, and 

 its downward pressure is, therefore, counterbalanced 

 by its upward pressure. There remains, then, only 

 the difference between the two, an upward pressure 

 equal to a column of water whose base is CD and 

 whose height is CA ; in other words, a column of 

 water represented by the cube. The body is therefore 

 pressed upward by a force exerted by a column of the 

 liquid equal to the bulk of fluid which it displaces. 

 The weight of the body tends to make it sink, and 

 to this downward tendency is opposed an upward 

 one represented by the quantity of fluid displaced. 

 Thus every body plunged into a liquid loses weight 

 equal to that of the displaced liquid. Suppose the 

 weight of the displaced liquid is just equal to 

 the weight of the body, then the body will float in 



