350 NEWTON S PRINCIPIA. 



equations by replacing -=+-, the first by 

 d x 



^P - A ( d&amp;lt;1 u ^ u - 2 u } 

 Tx~ (d^ + 5V + dz*) 



-B 



J 



d y 

 d fd u d v 



fd u d v dw\ 

 \d~^ + T* d*J 



and making similar changes in the second and third. The 

 investigation of Professor Stokes makes A = 3 B, and he 

 has shown that this relation must exist even on Poisson s 

 own principles. The coefficient B is some constant depend 

 ing on the &quot; internal friction &quot; of the fluid. 



Such are the equations giving the motion in the interior 

 of any mass of fluid. But we have still to consider the 

 equation expressing the effect of boundaries to the fluid. 

 In the case of ordinary hydrodynamics the condition is 

 manifestly that along &free surface p is constant, whereas 

 along a surface bounding the fluid, the normal motion of 

 the fluid must be the same as that of the surface. But 

 when we consider the fluid as possessing internal friction, 

 the last condition must be changed. The motion of the 

 fluid in contact with the surface will clearly be in every 

 way the same as that of the surface. 



(2.) The whole theory of the resistance of bodies is in 

 cluded in the equations of fluid motion as enunciated above. 

 It is therefore both interesting and important to deduce 

 from them the law of resistance. 



It is manifestly the same thing whether we conceive the 

 body to be at rest, and the fluid to impinge on it, or the 

 body to move with the same velocity through the fluid. 

 Conceive then the fluid to be moving in a horizontal 

 direction parallel to the axis of x, and let z be the altitude 

 of the surface of the water above the axis. Let a small 

 plane be fixed in the axis of x, and perpendicular to it. 



Following the usual notation, the equation of motion 

 will be 



