248 



THEORY OP THE MOTION OF ROCKETS. 



»— 1 



RtJ* 



fluent of which is < ~ 



-J- (substituting for / as before) the 



Now when t zz 0,v zz a, 



1 



2gliv 

 therefore the correct fluent of the time is ^ ~ 

 1 



2 g- R w 



which, on v becoming nothing, will be infinite. 



A projected 

 body cannot 

 lose all its mo- 

 tion ill any 

 finilQ time. 



Resistance to 



a cylinder 

 rnoving per- 

 pendicularly 

 through a 

 fluid. 



2glla 



So that it appears, that the rocket will not describe the 

 above space but in an infinite tiaae. 



Supposes =: 1 foot; then ^ = - "^^ — 133-344 se- 



2giia 



conds or 2 min. 13 seconds. That is, the rocket will only- 

 have been in motion 2 min. 13 sec. after it has acquired the 

 greatest velocity from its burning before the celerity of its 

 motion will be reduced to 1 foot per second ; and yet, not- 

 withstanding this great annihilation of velocity in so short a 

 time, the remaining small part will not in any finite time 

 be destroyed, though we know the limit at which the rocket 

 would attain a state of quiescence. 



And from the result here determined we conclude, that 

 into whatever medium a body is projected with any given 

 velocity, great or small, it will in no finite time lose all its 

 motion. So that, if the planetary bodies were moving in 

 a resisting medium, and gravity should suddenly be de- 

 stroyed ; the bodies would all pursue rectilinear paths (that 

 would be tangents to their orbits) to certain finite distances, 

 which would not be wholly described by them but in infi- 

 nite times. 



Lemma I. 



To determine the Resistance a Cylinder meets with in a Fluid 

 when moving in a Direction perpendicular to its Axis. 



It is universally allowed, and indeed is evident, that the 

 resistance to a body moving through an infinite fluid at rest 

 (such as is here supposed) is the same in eflect as the force 

 of the fluid in motion with equal velocity on the body at 

 rest: therefore, as it will be somewhat more convenient tocon- 

 sider the fluid in motion, and the body quiescent, we shall 

 pursue the solution of the problem upon this hypothesis. 



