166 



THEORY OF THE MOTrON OF ROCKETS. 



Again, by the nature of the parabola V E : V F : ; E H« 

 :FL« zz^^l^ ^('IJ^l+kx^gtA', and F Lit 



^ ^(V""*" ^^ "~ 5^''0 Whence A L the entire 



range (:rFL+ B F + AB) =: ^(^^ + A;x— ^/'V 



+ •\- I X which vras required. 



For an example in numbers : suppose the engine from 

 whence the rocket is thrown to make an angle with the 

 horizon zi 45° : and let all other things remain as in the first 

 proposition. Then w, the velocity of the rocket in the 



curve at the end of its burning n (/« Z)^ x (hyp. log. 



m 



m 



Vx (^A:Z»4-Hyp. og. J^^— 6 ^yy = v/ 4479024 



+ 4080400 zz -v/8559424 zz 2925*6 ; and sine angle I DB 



= — X co-sin. Z C A B = 



2993 



X co-sin. Z C A B 



2925-0 



= 134* 6' 38". Whence angle I D H =z 44* 6 38"; the 

 Tjat. sin. and CO - sin. of which are '6960172 and '7180251 

 rz ^and w respectively : and the values of the letters in the 

 above expression for the range collectively qreas under. 



Whence the range itself is 

 readily found zi 273116-2$ 

 feetor 51*72657 miles. 



On the ^fotioHi S^c. of Rockets in a resisting Medium. 

 Prop. V. 



Motion of a •^'^'^ Strength or first force of the gas from the infiamed 



rocket in a fomposttlon of a rocket being given, as also the weight of the 

 resisting me- quantiti/ of composition thf rocket contains, together with 



