THEORY OF THE MOTION OF ROCKETS., 



« r: 230 ozs. the medium pressure of the atmosphere 



on I square inch 



s zz 1000 times tlie pressure of the atmosphere ; or 



force of the inflamed composition 



d zz diameter of the rocket's base 



x — PD the space the rocket describes in the time t, 



and 



V — the acquired velocity in that time. Then, 



ed*" is equal to the area of the rocket's base ( e being '7854 



the area of a circle tbe diameter of which is 1) and ned* the 



pressure of the atmosphere on a surface zz e d\ Hence 



sned^ IS the constant impelling force of the composition. 



Novv the weight of the quantity of rocket matter that is 



c t c t 



fired or consumed in the time <is — ; therefore c is the 



a a 



weight of the part unconsumed ; which added to w gives 



c t c t . 



«?4-c • zz m (by putting w rrtt' + c) for the weight 



a a 



of the whole mass at the end of the time ti or when the 



rocket has ascended to D ; and so far as weight resists the 



motion of the rocket, this muft be deduced from the im* 



pelling force. Hence 5 wed* — ( m j is the motive 



force at D ; and sned* — ( m — ) ,. 



\ a y asned 



^ = — Ithe 



c t a m — c t 



m 



uccelerative force. " 



By the theorj^ of variable forces we have generally v —. 

 ^gft (where f denotes the accelerative force and g zz 



16tV ftV Therftfore df zz tliJJLf — L ^<2g I ;;the fluent 

 ^^ '' am — ct 



of which 18 y= -^ Xhyp.log. t — — « J -* 



2gt. 

 Now when t zz o,v zzo; therefore the fluent corrected will 



<2gasn€d^ /. , am , , am — ct\ 



\)evz- -2 X (hyp. log, hyp. log, — -^ I 



<2agsned^ . , am ^ , . , 



^2gt----^ X hyp. log. ——2§-r; which, 



when 



^79 



