SI4.2 THEORY OP THE HOTlOvV OF ROCKETS. ' 



dlums cannot, independent of gravity, describe certain 

 finite spaces but in infipite times, let the velocity of pro- 

 jection be what it may, great or small ; the ratio of the re- 

 sistance of a sphere to that of its circumsciibing cylinder, 

 when this moves in a direction perpendicular to its axis; 

 Itnd many other very curious particulars, as the person who 

 shall read this paper will fmd. The investigations of the re- 

 sistance to cylinders moving in fluids in directions diiferent 

 from that of their axes are new, as far as 1 know. No work, 

 that I am acquainted with, contains a solution to this pro- 

 blem generally, but merely of the common particular case, 

 where the solid is supposed to move in the direction of its axis ; 

 and perhaps the flight of rockets is one out of but very few 

 cases in which the subject is at all applicable. 



With thanks for the attention which you have hitherto 

 paid to my communications, and respect for that impar- 

 tiality and ability, with which your Journal is conducted. 



I am. Sir, 



Your most ebedient servant, 

 IU>i/ah Academy; ~ " W. MOORE. 



JunelSlU 



^ ' t - Prop. 6. 



The motion To determine whether. the Motion of a Rocket ascending ver- 

 of a rocket can tically in the Atmosphere can ever become uniform : the law 

 uliform!'^**™* o/'r^5fs/awc€ being directly as the square of the velocity y as 

 before* 



When the motion of a body becomes uniform, or the ve- 

 locity a maximum, the accelerative force is then nothing: 



^ ^ {sned^ b^—Kv^) a , , , - 



therefore puttms ' , To ' t"^ accelerative 



^ ... ^ .{am — ctj.b* 



force (see ..the last Prop.) — o, and reducing the equation, 



, , /sned^a — «w + c/\4 „,, 

 we have » r= A- t "■''"■ ^R ) * Whence it 



ftppears^ that the velocity, and consequently the motion of 

 the rocket can never become equable ; being in terms of t 

 the time of its burning ; but will be greater and greater unto 

 the end of the time.^, when th^ velocity will continually dc* 

 crease till the whole is destroyed by the retardive force of 

 £ -U gravity. 



