264 



Mr. Longridge on the Resistance 



[Feb. 27, 



These equations all fail bj x becoming infinite when i? = 1015, 994, and 

 979 respectively. 



It is, however, observed that, in the assumption of the law of the resist- 

 ance, the higher the power of velocity the longer does the corresponding 

 equation give rational results ; and by assuming R=«y^ with the same data, 

 the following equation was obtained, 



which gives consistent results for all values of v. 



The value of p here is 8*747, which would give the resistance varying 

 ' nearly as the ninth power of the velocity. 



This result led the author of the paper to doubt the accuracy of the 

 experiments, and to seek for further and more correct data, which were 

 obtained from a minute (No. 23,351) of the Ordnance Select Committee, 

 dated 21st September 1867, containing the results of experiments show- 

 ing the loss of velocity of two projectiles, one of 8*818 lbs., and the other 

 of 251 lbs., in passing through certain given distances with given initial 

 velocities, varying from about 1500 feet to 600 feet per second. 



From these results a diagram was constructed, and for each projectile an 

 equation was found which agreed tolerably well with the experimental 

 results. 



The form of the equation assumed was 



and the resulting equation was for the small shot 



(a:+665)«^-^=log~^ 10-1473853, 

 and for the large shot 



(^+2032)z;^'=log-^ 12-6696158, 

 the maximum error being about l^ per cent, of the velocity. 



Introducing into these equations the diameter and weight of the re- 

 spective projectiles, and taking the index ?i = 2-5, the values of C were 

 found to be, 



small shot, C=log~i 10-7295585 J, 



1 W 

 large shot, C = log~^ 10'7454405 j^, 



the mean being C=log"' 107375745 ;vr. 

 and the resulting general equation 



. log-M0-7375745.W\ , 

 (^^+-^ ^^^yorr- ) -^=log 10-7375745. 



The maximum error in velocity, as calculated by this formula, v^as for the 

 small shot l^ per cent., and for the large shot 2h per cent. 



