252 THEORY or TUB MOTION OF ROCKETS. 



Resistance to the cosine of the angle K T n — — ; (radius being unity 

 a cylinder ♦ r 



tnoTing ob- i„ jjIi ^,3ggg> j^^^^ ]ei z zz FT and x the fluxion of the 

 liquely. ^ i -r * 



same, then the fluxion of the force of the fluid on F T 



will be :z ^ multiplied by the sine of the angle 



P Tn, whereof the angle PT n being composed of the two 

 angles P T Q, Q T n, the^atural sines and cosines of which 

 are represented above; its sine by trig, will be expressed by 



^ +/ll'_Zl!!>i = llJ-il^lZlil^; also i 



T X 



zz -• . Therefore 



* «* /'a ^ 



. sine angle P T w r: 



n t)* 5*/ ' k 



nvp"- r« — a* rx . ex 4- /(r« — J:«)^ 



^ , (r^-x*r- 





4gr' L 



the fluent of which is 



which corrected will, in the ultimate case, where x i= r, be 



which is therefore the cffeaive force of the fluid onthequadran- 

 talarch FTS. Hence Z^l!l . (c + s/) will be the force 



on the semicircum. V F S; and -_'- (c + <lj ) the- 



force on the whole semicylindric surface m Dwr B^; 



or 



