NEWTON S PRINCIPIA. 351 



This gives the variations of/? along any line of motion, 

 and C may vary from one such line to another. By con 

 ceiving all these lines of motion cut by a plane perpen 

 dicular to the axis at a very great distance from the small 

 plane, it will be seen that C is the same for all these lines 

 of motion. 



The theory supposes that the particles of the fluid as 

 they approach the small plane move slower and slower, so 

 that at last their velocity, when in contact with the plane, 

 is so small, that it may be disregarded. The pressure in 

 front is a statical pressure. On the other hand the par 

 ticles in contact with the posterior part of the plane are 

 supposed to move with the general velocity of the fluid in 

 order to fill up the void that would be left by the retreating 

 fluid. The pressure behind is a dynamical pressure. The 

 difference between these two will be the resistance. 



Hence the pressure in front is given by the formula 



that behind by the formula 



/+, rf-i 



The whole resistance will then be 



for every unit of area in the plane. 



It is manifest that this contains a great deal of assump 

 tion in regard to the motion of the fluid. We have been 

 trying to solve a question in Hydrodynamics without 

 making use of all the equations, and each omitted equation 

 has been replaced by an assumption. We should have 

 taken the equation of continuity, and having solved it, 

 we must adapt the solution to the conditions of the 

 question, viz. that the velocity resolved parallel to the 

 axis of x is r, and that perpendicular is nothing at an 



