of Fluids, compared with the best Experiments. c 25\ 



9. Of the Minus Pressure. — It is obvious, from the property 

 of figures having parallel sides, that the quantity of fluid re- 

 quired to fill the vacancy left behind the body when it moves, 

 is a constant quantity, whatever be the form of the body ; there- 

 fore the deficiency of pressure will vary only with the velocity 

 the fluid must acquire to follow the retiring surface. But if 

 c be the angle that surface makes with the direction of the 

 motion, the velocity will be v sin c ; consequently, the motion 

 of the fluid being established, the resistance from the defi- 



ciency will be — . 



Combining the two resistances, we have the height of the 



column = - v "— f 2 sin 3 a + sin 2 c) + F = H ; where F is the 



4g N 



friction. When the body is a cube or a cylinder, with the 

 ends perpendicular to the direction of the motion, the angles 



become 90°, and neglecting the friction ~ — = H. 



The height due to the resistance being to the height due to 

 the velocity as 3 : 2. 



10. If the height of a column that would balance the fric- 

 tion be x feet, and H be the height producing the motion, then 



H — <r= -— (2 sin 3 ff + sin 2 c); or x=H — (2 sin 3 a + sin 2 c). 



4g v 4g v 



Assuming that the friction varies as the square of the velo- 

 city, and as the surface of the body; and putting f— the 

 height of a column of water whose weight is equal to the fric- 

 tion of one foot of surface when the velocity is one foot per 



f 

 second ; then — will be the height when distributed over 



the whole section of the moving body, when 5 is the area 

 of that section ; therefore, if Ip be the area of the surface, 



s 



11. There is also the friction of the fluid itself to be consi- 

 dered when the velocity is considerable ; and without being 

 able to assign a satisfactory reason for it, if we consider the 

 length to be increased by a quantity Aw, where A is a coeffi- 

 cient depending on the nature of the fluid, the result agrees 

 nearly with experiment, and the value of x including this effect 



is fp&U -f- Av) , , 



x = * s ; and consequently, 



Before attempting to determine the constant quantities from 

 2 K 2 experi- 



