NEWTON S TRINCIPIA. 169 



1. The pressure of the fluid upon any element of a 

 surface exposed to it is normal to that surface. 



2. Any pressure communicated to a fluid mass in 

 equilibrium is equally transmitted through the whole fluid 

 in every direction. 



Consider any point in a fluid, and let an indefinitely 

 small plane pass through it ; by the second law the pres 

 sure is the same, whatever be the inclination of the plane 

 to the horizon; by the first it is normal, and proportional 

 to the area of the plane. Let this area be ; then the 

 pressure may be represented by p . This quantity p is 

 therefore what we seek to find. It is what the pressure 

 would be if the area were unity, and the pressure constant 

 over that area. It is therefore called the &quot; pressure referred 

 to a unit of area.&quot; 



The law expressing the equality of pressures in all direc 

 tions is true in viscous as well as perfect fluids. The dif 

 ference is this, that in the latter the transmission of the 

 pressure is effected in a moment, in the former it takes 

 time. During this interval the law is not true ; but when 

 a short time has been allowed to pass, the fluid takes up its 

 form of equilibrium, and the pressure becomes equal in all 

 directions. 



These two laws are not independent. The first con 

 tains the second. For, let the fluid contained within the 

 pyramid O A B C in the interior c 



of the fluid become solid. This 

 is allowable, for, the fluid being in 

 equilibrium, the pressure on the 

 solidified element will be borne 

 and resisted in exactly the same 

 way that it was while still fluid. Let p be the pressure 

 referred to a unit of area on the plane C O A at O, q 

 that on a plane parallel to B C A through O. Let the 



