62 SMITHSONIAN MISCELLANKOUS COLLECTIONS VOL. J I 



from the trace on the smoked glass tube, we have, by the principle of 

 the Conservation of Linear Momentum, for the momentum per unit 

 area produced by the gaseous rebound, 



_!_ _ nicYc _ mcV2gs 



Ac Ac" Ac 



Hence the momentum communicated to the suspended system by the 

 gaseous rebound is 



mcAgy2g^s 



'"Ac " ' 



and calling O the ratio of the momentum given the gun by gaseous 

 rebound to the observed momentum of the suspended system, we 

 have 



Q^ mcAgy2gs 

 ^ m,jAcV 



APPENDIX D 

 THEORY OF SPRING IMPULSE-METER 



The theory of the spring impulse-meter is as follows : If we use 

 the sartle notation as in the preceding case, calling, in addition, the 

 mass of the spring nig, and the mass required for unit extension of 

 the spfing, m,, we have, by the same theory as that for the gun 

 suspended by a spring, 



Vm7g 



V.= 



Vmc+^nia 



Hence the momentum per unit area, communicated to the upper 

 cap of the 12-inch pipe, when the chamber is fired, is 



_L — (mc + Mms)Vc _ Vmc+JnisVmjgs 



Ac '^ a;^^ " Ac' 



Hence the momentum that would be communicated to the suspended 

 system by the gaseous rebound, provided the system were at the top 

 of the 12-inch pipe, would be 



AgVmc -l-^msVm^gs 

 Ac 

 and the percentage, O, of the momentum communicated by the gas- 

 eous rebound to the observed momentum of the suspended system, is 



Q _ AgVmc-l-^m"sVm tg 

 ^ A.m„v 



I 



