15$ THKORT OF THE MOTION OF ROCKETS. 



4 D <* + 6 E '* + &c. : and substituting these in the {-ven 

 equation it becomes as below ; namely, 



16 =:/A4-2/B<i-3/C/*-f 4/D/*4-5/Ec'*-f &c. 

 — ^J<v=: — p A/ — 2pBi^ — SpCt^ — 4/) D/*— . &c. 

 — qt^^q 



* v*i = — * A* I*~2A- ABi»— (2 A C + B*) 



2gptzz <lgpt 



By adding which we evidently obtain 

 o zz o o 6 



Whence, equating the homologous terms, to find the 

 quantities A, B, C, &c. they become 



A=l 



_ pq^2 gpl 



^ i7^ 



_ p*q^2gp''l+kg* 



T\ -^ P^9 — 2qp^l-\-Qkpq* — Z gkpql 



_ ^5kp*q*'^52gkp^ql-{-Sk^q^+\2g^kl*p*-\'\2p*q'^24lp*q 



&c. &c. 



Therefore the fluent required \svzi-rt 4- ^ - ? / ^U ^4- 



p*q^2glp^+kq* p^q-^<llp^q-\-okpq^~^<2^klpq 



^^ t + — 1 + 



35fepV~32jrA;p^<jr/-f 8A:^9H-12ff*A;/V*+12j0^y— 24/p^7 



l'-4- &c. And hence the space x is readily found zz — t^-\- 



2 » 



pq — ^glp ^f . p''q — ^glp'''\- kq''^^^ p^q^ <2lp^ q-\-<2kpq* 



i — -^*' + &c. ; where, making tZ2a\n both expres- 



sions, the values of t> and x as required by the proposition 

 will be determined. 



Scholium. 



