OgQ THEORY OP THE MOTION OF ROCKETS. 



, , . <2agsned'^ , , m 



vrhetif becomes a, IS vrz — X hyp- log* 



m- — c 



, ...,,, 2 as: sned'^ 

 lag'y or, because m zz w ■\- c^ \i will hev zz X 



byp. log. • — 2 a g" ; \vhich therefore is the velocity 



of the rocket when all the matter of inflammability in its 

 body is just consumed. 

 'rWs exempli- For an example in numbers, suppose the weight, di- 

 fied 111 nutn- tensions, &c. to be as below ; namely, 

 *^'* * =: 1000 



n =. 230 ozs. 

 MJ = 18 lbs. = 288 ozs. 

 c rr IQ lbs. z: l6o ozs, 

 o rr 3 sec. 

 d =z 3 in. 3: I ft. 

 gzz 16 ft. 

 e =7854 



Then the above expression for v, namely — £.- ^^ — X 



c 



- , W -\- C ^ 2X3Xl6x 1000 X 230 X 



hyp. log. ' — . 2 a ff r: -^— -Tl— 



^^ ° w ^ 160 



448 

 •7854 X tV X hyp. log. ~^g6~ 6774-075 X hyp. log. 



?i ^ 96 - 2992-9895 — 96 - 2896-9895 feet, the velocity 



pf the rpcljiet per second at the instant of exhaustion of 

 the wildfire. 



To find the space or, we have by the doctrinp of variable 



forces X zz p f — b t* X hyp. log. — . 2 c < i' 



am — c t ° 



( whefe b represents the fraction — 2_!! \ 



Method of Now to find the fluent of this equation, we must first de.p 



Jinding the flu- ^ am . 



ent for the termine the log. of ; which is done by first puttino" 



time of the as- am^ct J f o 



cent of. the jt \^iq fluxions, and then finding its fluent in a series. Thus, 



the flu;!{ion of the log. being , we shall 



° am^ct *^ am-^ct 



by 



