344 THEORY OP THE MOTION OF ROCKITS, 



(t)'+- 



Velocity and 

 space 



scribed by a I -l-T-I i- v—v — ^ : or, putting 



rock' '"' — I >' t -v 1 



the 



its composition 



and resistance /' h \T [hk]'^ 



of the mcdi- ( -7- ) — j and J: — i — — w , we shaU have 



um. \ k / P 



J "^ ^ rr ; and by reducing this equa 



j — V (^— P')"" 



ar 



9 



10 



IV 



. - ^iLjzlSLlLEJL- ; which, when t - a, \s V ^ 



' ^ w . w 



i "^ '^ V ""^ F I tije velocity of the rocket when it just 



ceases burning. Or, restoring the values of j, w, /, /i, &c., 



the velocity of the rocket in thiscase will Tbe expressed by 



1 X 



Aa^d {sneH)^ 4 agd {sne'R)x 



rfj.^^y. ) (ami*) '* -[amb^-acb^) "^ ) 



- - ... - - J 



4a.^d(^neR)^ AagdjsneB.)^ 



. cb - cb 



(amb^) + [amb'^^acb'') 



Now to determine what this velocity is, we must first find 

 the value of R for the given case of velocity b. Now under 

 the conditions, that the p-articles of the medium are perfectly 

 nonelastic, and that the medium is intuiitely comprestied 

 and affords no resistance to the motion of the rocket but what 

 arises from the inertia of its |f)articles, (which is the ground 

 of ourhypptheses concerning the law of resistance), we shall, 

 putting r for the radius of the rocket's base or of the head 

 of the rocket ;y=i the sine of the angle, which the slant 

 side of the head, (supposing it conical) makes with the axis; 

 p =z 3*14l6; S zr the specific gravity of the medium, 

 whichishereconsidered as the atmosphere; and ^ zz l6feet, 



(omitting the tV) ^»ave R zz \__ Z-L- (investigated in 



most woi[ks of fluxions and mechanics). 



Let h zz \y in order to render the expression as simple as 



pos'sible^ 



