l6 -SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 7I 



The velocities and efficiencies were obtained from the usual expres- 

 sion for the velocity in which a ballistic pendulum, with the bob con- 

 stantly horizontal, is used, namely, 



v=" —- V2p1(i — cos^), 

 m 



where 



M = the total weight of the bob, 



m = the mass ejected; powder plus wadding, 



l=the length of the pendulum, 



^ = the angle through which the pendulum swings, 



g=the acceleration of gravity. 



The cosine of was corrected for friction by observing the two first 

 displacements d^ and do and obtaining therefrom 



It will be noticed that the highest velocity was obtained with 

 " Infallible " powder, and was over 7,000 ft./sec. The corresponding 

 efficiency was close to 50 per cent. In view of the fact that this 

 velocity, corresponding to c in the exponents of equations (6) and 

 (7), is sevenfold greater than for an ordinary rocket, it is easily 

 seen that the employment of a chamber and nozzle such as has just 

 been described must make an enormous reduction in initial mass as 

 compared with that necessary for an ordinary rocket. 



As a matter of possible interest, photographs were taken at night 

 of the flash which accompanied the explosions produced by firing 

 the small chamber. These are given on plates 4 and 5. 

 Plate 3, figure 2, shows the set-up for these experiments ; the camera 

 being in the same position as when the flashes were photographed. 

 The white marks, above the flash, are strips of cardboard, nailed to 

 a long stick at intervals of 10 cm. and constituting a comparison scale, 

 one end of which was directly above the " muzzle " of the gun. This 

 scale was illuminated, before the charge was fired, by a small electric 

 flash lamp held in front of each strip for a moment ; which lamp also 

 illuminated a card bearing the number of the experiment. 



The photographs bring out a curious fact ; i. e, that the " flash " 

 appears in most instances to be at a co'nsiderable distance in front of 

 the nozzle. This is easily understood if we admit that the velocity 

 of the ejected gases is very high just as the gases pass out of the 

 nozzle, but becomes very quickly reduced nearly to zero by the air. In 

 other words we may consider that the gases pass from the nozzle in 



