1HEORT O^ THE MOTIOM OF ROCKETS. 24,g| 



Let A BCD (PI. VII, fig. Ijbethecylinder, andETF Resistance to * 

 any ^ection parallel to the base. Let a particle strike this sec- cylinder inoT- 

 ..1 1 T-»rr, 1-1 L 'x.- insf perpendi- 



tion at 1 u) the direction F 1 , ;jerpeudicuiar, by supposition, cularly 



to 13D ; and draw T O to the cti.tre O : draw also the tan- through a * 

 gent T Q to the circle E T F or cylindec at T, upon which 

 let fall the perpendicular P Q, and let fall the perpendicular 

 QRupouTP. 



Then, considering P T to represent the full force of a 

 particle of the fluid, P R will denote that part only, which 

 has eii'ect in raoving the cylinder in the direction PR, 

 For, on account of the obliquity of the surface of the solid, 

 the strcikeof the particle will also be oblique;- and therefore, 

 resolving T P intothe two forces PQand TQ, the forceTQ 

 only wii! be eftective, which, hi the direction P R, will be 

 as P R, or the sine of the angle P Q R, or P T Q } us is evi- 

 dent by considering PQ resolved into the two forces Q R, 

 R P ; whereof ihe former, being parallel to the cylinder, fia« 

 no effect in moving it in a peri)endlcular direction thereto. 



Now by the nature of fluids, the force with which a 

 particle strikes a body perpendicularly is equal to the weight 

 of a line of such particles, the height of which is equal to 

 that which is due to the velocity of its motion, or through 

 which a body must full to acquire that velocity ; therefore, 



calling n the density of the particles or fluid ; (where 



» denotes the velocity, and ^ — 1 6 feet) will be the abso- 

 lute force of a particle moving with the velocify r. And 

 this is represented above by the line PT; therefore, since 

 rad. (1) : TP :: sin. Z P T Q (5) : P Q, the force, de- 



X 2, ■ »■•■ - 



noted by P Q will be ^^-^ , and that by PR*'" 



4g 4g 



Put SL zz X, LT z= y, and S T -= s;- also let Ti» 

 {— z) express the fluxion of the course S T; then, because 

 of the inclination of this line to the direction of the fluid, 

 the number of particles striking it will be diininished in 

 the ratio of T n to no, or of radius to the sine of the 

 angle oTw; consequently the fluxion of the force of 

 the fluid against ST, which would otherwise have beea 



» will be 



Now 



