Nf). 2 



Ml'nilOl) OF KEACIIlNr, KXTRKMI': ALTITUDES 



to show the tremendous importance of efficiency in the attainment of 

 very high altitudes. A statement of the problem will therefore be 

 made, which will lead to the differential equation of the motion. An 

 approximate solution of this equation will be made for the initial 

 mass required to raise a mass of one pound to any desired altitude, 

 when said initial mass is a minimum. 



Fig. I. 



A particular form of ideal rocket is chosen for the discussion as 

 being very amenable to theoretical treatment, and at the same time 

 embodying all of the essential points of the practical apparatus. 

 Referring to figure i, a mass H, weighing one pound is to be raised 

 as high as possible in a vertical direction ^ by a rocket formed of a 

 cone, P. of propellant material, surrounded by a casing K. The 



' See note lo at end of paper. 



