THEORY OF THE MOTION OF ROCKETS. 253 



or the resistance to the cylinder when moving in the fluid Resistance f 

 at rest, so far as relates to that surface. rooving ob- 



To determine what fartlier resistance is opposed to the lil^ely. 

 cylinder by the fluid acting against the top As Br. Let us 

 suppose AV BT (fig. 3) to be the head of the cylinder, and a 

 particle striking it at T ; also let A B be a diameter of the 

 circle perp. to the axis, and draw T Q parallel to A B, and 

 P Q and Q E perp. to T Q and T P respectively. Then 

 P T being considered the representative of the full force of 

 a particle, and to be resolved into the two forces P Q, T Q; 

 the force T.Q, being parallel to the plane A B V, has no 

 effect in causing it to move; but only the force denoted by 

 P Q, which is as the sine (c) of the angle P T Q. There- 

 fore the effective force of a particle in this case will be 



» a 

 ■ : and that of the fluid on the whole circular plane 



— (p being z: 3'14l6). Hence the whole resist- 

 ance to the cylinder is 



Car, 1. When the angle T P Q (fig. 2) is 90% or the so- 



lid moves in a direction perp. to its axis ; then ^^ becoming 



1 ^nd c nothing, the resistance to the cylinder will be 



«v' r h - .1.1^1 

 as determmed m the first lemma. 



^^ 



Cor, 2. The resistance to the cylinder moving in the di- 



rection T P estimated in the direction Q T is 



nv'^J^r h 



(c + 2^), being that arising only from the action of the 

 fluid upon the semisurface of the solid; that on the head or 

 top of the cylinder having no effect to move it inthis direction, 

 but in the direction of its axis. 



For- an example to this proposition in numbers, when 

 the medium is supposed to be that of our atmosphere. Let 

 the angle T P Q (the sine of which is/) — 6o° ; and conse- 

 quently the angle PT Q (the sine of which is c) n 30% 



Then 



