OF SEVENTY-FIVE-MILE RANGE. 375 



Inasmuch as the only thing that has made possible this great 

 ballistic achievement is the taking advantage of the decrease in 

 resistance due to the decreasing density of the air in high altitudes, 

 it is first necessary to make some assumptions as to the law of 

 decrease with the height. I have here assumed that the temperature 

 is constant, giving the isothermal law of Laplace. I accordingly put 



(i) S = S„e- 



iii 



where 80= i.2932kg./meter^, and k is equal to .1251, the altitude y 

 being expressed in kilometers. As the shot rises to a height of 

 about forty kilometers, or twenty-five miles, this results in a diminu- 

 tion of density of about sixteen times. While it is true that for the 

 upper part of the trajectory the form is practically that of the 

 parabola as investigated by Gallileo for the vacuum, it is by no 

 means true, as certain discussions that I have seen would seem to 

 indicate, that there is a region about two miles high at which the 

 effect of the atmosphere suddenly stops. 



The second thing that must be known is the so-called ballistic 

 coefficient of the projectile, involving its mass and diameter, the 

 resistance of the air being supposed to be proportional to the square 

 of the diameter while the acceleration is inversely proportional to 

 the mass. 



For lack of sufficient information at the time that this paper was 

 prepared, it was assumed that the mass of the projectile was 300 

 kilograms and its diameter twenty-two cenitmeters, or eight and 

 one half inches. It is also necessary to know the form factor, which 

 depends upon the sharpness of the projectile. In the calculations 

 made here the number .9, which is that of old-fashioned, rather 

 blunt projectiles, is used. As, however, reports on the shell have 

 shown that it is furnished with a long pointed cap of sheet metal, the 

 form factor should be considerably reduced. If, however, we take 

 a mass of 180 kilograms, or 396.8 pounds, the results given here will 

 be exact if we assume a form factor of .54, which is undoubtedly 

 much nearer the correct value. Finally, if we assume the mass 

 to be 120 kilograms, this will give the same trajectory with a form 

 factor of .36, which is smaller than that of any shot with which I 

 am acquainted. 



