1868.] of the Air to Projectiles. 265 



From the above equation the resistance per square inch of sectional area 

 is found, 



■n_. 



log-1 13-0154756' 

 from which the following Table is constructed, the third column showing 

 the resistance, as calculated by Hutton's formula: — 



Table of Resistances to a Rifled Projectile . 



Velocity, 

 feet per 

 second. 



Eesistance, in 

 lbs., per square 

 inch. 



Hutton, 

 p. 218. 



Velocity, 

 feet per 

 second. 



Resistance, in 

 lbs., per square 

 inch. 



Hutton, 

 p. 218. 



1500 



18-89 



18-94 



700 



0-613 



3.12 



1400 



13-87 



16-23 



600 



0-306 



2-20 



1300 



9'94 



13-67 



500 



0-135 



1-49 



1200 



6-92 



11-29 



400 



0-0494 



0-93 



1100 



3-722 



9-14 



300 



0-01354 



0-52 



1000 



3-052 



7-24 



200 



0-00218 



0-23 



900 



1-900 



5-61 



100 



0-0000965 



0-556 



800 



1-118 



4-24 









It is next shown that the hypothesis of the great increase of resistance 

 at velocities exceeding 1100 feet per second being due to the vacuum 

 behind the projectile is untenable, because the actual resistance at 1300 feet 

 per second is only 9-94 lbs. per square inch, whilst, according to that 

 hypothesis, the back resistance alone would be 1 5 lbs. per square inch. 



It is suggested that the true reason of the great increase of resistance 

 may be found in the fact that a wave-impulse cannot be propagated at a 

 greater velocity than 1100 feet per second, and that consequently a great 

 condensation of air must take place in front of the projectile at all velo- 

 cities exceeding this, and the resisting force of such condensed air will in- 

 crease at a greater rate than indicated by Mariotte's law, owing to the 

 evolution of heat due to the condensation. 



A comparison is then instituted between the resistances as ascertained by 

 the above law and those given by Hutton's formula. 



It is stated that in experiments made on May l7th, 1867, the small 

 shot weighing 8*8 lbs., moving with a mean velocity of 986 feet per second, 

 lost 58| feet of velocity in a distance of 900 feet. 



The time of flight being -96 of a second, the resisting force must have 

 been nearly twice the weight of the shot, or more accurately 17*2 lbs. 



Now, according to the formula given in this paper, the resistance is 

 found to be 17*75 lbs., whilst Hutton's formula gives a resistance of 

 46i lbs. 



Having thus obtained a law which gives, with considerable accuracy, the 

 residual velocity at any point of the flight, the corresponding equation to 

 the trajectory is deduced for low degrees of elevation when the length of 



VOL. XVI. 2 B 



