TBIORT OF THE HOTION OF ROCKCTI* f^ 



Lemma II. 



To determine the same as in the last, when the Cylinder moves Resisttwe* % 



in any Direction oblique to its Axis. * cylinder 



^ > rtioving o©» 



liquely. 

 Let T P (PI. VII, fig. 2) be the direction of the cylinder 

 moving in the fluid, or P T that of the fluid against the 

 cyHader. Let a particle strike the solid at T, at which 

 point draw the tangent T n to the section £ F T, which i» 

 parallel to the base C D: draw L T Q perp. to the diame- 

 ter V O S, which is at right angles to the axis X Y, and 

 P Q and Q R perp. to T Q and T P respectively. Then, 

 denoting the force of a particle of the fluid when in raotioji 

 by P T, and supposing this to be resolved into the twe 

 forces PQ, QT, the latter only, Q T, whicj) varies as the 

 sine of the angle T P Q, will have effect in moving the cj^^* ^ 

 linder; which, in the direction V T, will be as R T, or the 

 sine of the angle T Q tl, or S P Q. Now the elective ferce 

 of a particle in the direction Q T has been shovyu in the 



preceding lemma to be equal to — when the wb^ 



4 or 



force of a particle is represented by Q 1': but in tlie case 

 before us, piittingy for the siye of the angle Q P T, or of 

 the angle of incidence of the irapingeisg fluid against tbe 



. - ' ■ • • ^ wo' 



solid, the efficacy of Q T will consequently be — 



(where s zr sin. of the angle Q Tti) and therefore the effect 

 of a particle to move the cylinder in the direction PT will 



be J^ , 



Put c iz sii). of the angle P T Q, the dosin. being/* 

 r — rad. of the base of the cylindef 

 a: zz G L 

 y = T L 

 Then, by reason of thesimilitiideof the triangles O LT, 



Tn K,. we obviously obtain * zz — iz ■ '^ ■ , and 



tli« 



