450 



NOTES. 



P Q 



F 



r> 



particles at E, will, in consequence of their gravity, continually descend towards 

 the lower parts at F. 



Again, the greater pressure which obtains among the particles under E, and the 

 lesser under F, will obviously cause the particles at E to descend, and those at F to 

 ascend ; and thus the higher parts of the fluid at E, descending and spreading 

 themselves over the lower parts at F, which at the same time are ascending ; it is 

 obvious, that the surface will at last be reduced to the horizontal position A B ; and 

 having attained that position, it must continually remain in it, for then there is no 

 part higher than another, and consequently, there is no tendency to descend in 

 one part more than in another, and therefore the fluid must rest in a horizontal 

 position. 



Art. 7. If two fluids that do not mix, are poured into the same vessel, and suf- 

 fered to subside, their common surface is parallel to the horizon. 



Let A B D c be the vessel containing the two fluids which do not mix, and let E F 

 denote the common surface, or that in which 

 the fluids come in contact. A a L ft 



The upper surface A B of the lighter fluid is 

 horizontal by art. 6; therefore, let P and Q 

 be two contiguous particles of the heavier ] 

 fluid, equally distant from a horizontal plane, 

 and consequently, equally distant from A B ; if 

 they are not also equally distant from E F the 

 common surface, the vertical pressures upon 

 them will be unequal, for this pressure is made 



up of the weights of two columns, containing different quantities of fluid matter, 

 viz. PC, qd of the heavier fluid, and ca, db of the lighter; consequently, the 

 pressures in opposite directions will be unequal, and motion must take place, which 

 is contrary to the supposition. 



The particles P and Q are therefore equally distant from E F the common surface 

 of the fluids; and the same being true for every other two contiguous particles in 

 the same horizontal plane, it follows, that E F must also be horizontal. 



Art. 8. The particles of fluid situated at the same perpendicular depth below the 

 surface, are equally pressed. 



This is almost self-evident, but nevertheless it may be thus demonstrated ; for 

 let the plane passing through E F, be parallel to the surface 

 AB; then, since the height of the fluid is the same at all the 

 points of E F, it is manifest that the weights of the fluid 

 columns standing upon any equal parts of it, must also be 

 equal, and consequently, the pressure on all the points of the 

 plane passing through EF is the same, since they are all 

 situated at equal depths below the surface AB. 



Art. 9. When a fluid is in a state of rest, the pressure upon 

 any of its constituent elements, wheresoever situated, varies 

 as the perpendicular depth of the particle or element pressed. 

 The demonstration of this principle is evident from that to article 8; for the 

 pressure depends upon the weight of the superincumbent column, and the weight 

 of this column manifestly varies directly as its height ; hence, the pressure upon 

 any particle varies as its perpendicular depth below the surface of the fluid. 



