||j|0 rSKORT OF THB MOTION OF ROCKETH. 



Resistance to. ^^'^ ^ = t-^* + ^2)^ ; and y = (2 Tx - a«*)^' by the 

 cylinder moT- . r .» • » .i . r i* ■ — .r jic- 



tng perpcndU Property of the circle; consequently j =: 



thmugba x ^^ 



flttid. and a = (i* + j*)' z: -; (r being the rad. 



(2rx — x*)« 

 of the dr. E S F). Also, by reason ol similar triangles, 



OP LT y ^ ^. QP 



^Tp- = -qTj; == — : whence s, being = ^rp » ^^"t 



also be equal to -^ • Therefore by substitution -— 



-^ / rj_ ^ a^ (2rx — ar*)^ 



r X WW*, -, p 1 • 1 ♦ 



' 1 "~ * [2 rx X -^ X x) ; of which the 



{2rx — a:*)« 4^r 



W V* ^3 T x"^ x^ \ 



fiuentis . ^ % ' ( " / wanting no correction ; so 



that when x = 2 r the fluent will be ^L^LZ ; which is the 



^ effective force of the fluid on the senxicircumference 

 of a section of the cylinder parallel to the base. Conse- 

 quently -- — into the height of the cylinder (k) zz 



' ^ will be the resistance, that the whole cylinder suf* 



fers when it moves in a direction perpendicular to its axis 

 with the velocity v. 



Cor, Because it is found, that a sphere, the radius of 

 which is r, moving in a fluid of the density n, with the velo- 



V city V, is • — ; we shall have the resistance of the 



sphere to the resistance of its circumscribing cylinder as 



*Lf to , or as 1 to (where© r: 3*14 10); 



the latter therefore being resisted more than the former by 

 about '69829 of the former. Whence, the resistance to a 

 sphere being given, the resistance to its circumscribing 

 cylinder will be had by multiplying the former by 1-69829. 



(.EMMA 



