330 Scientific Intelligence. 



a new higher ordinate. For all observed values of the velocity 

 greater than 1300 ft. per see. the graph is again a horizontal 

 (roughly) straight line. In explanation of the apparently 

 strange course of the gi'aph Preseott says: "It is reasonable 

 that there should be a change in the law of resistance at the 

 velocity of sound, for when the velocity of the projectile is less 

 than that of sound, the particles of air encountered by it at any 

 instant had already been set in motion, before the projectile 

 arrived, by the pressure which was transmitted ahead of it, this 

 pressure being transmitted with the velocity of sound. ■ But 

 when the projectile is travelling with a velocity greater than 

 that of sound no pressure waves are transmitted ahead, so that 

 the projectile meets, and has to set in motion, stationary air par- 

 ' tides. This change in the behaviour of the air is shown in. 

 photographs of flying bullets. ' ' 



Instead of attempting to find a single empirical equation for 

 RV~ 2 as a function of V, the author uses the relations R = A'V- 

 and R = K X V 2 , where K and K r are constants pertaining to the 

 horizontal portions of the graph below and above 1060 ft. per sec. 

 respectively. The formulae for the range, trajectory, etc.. 

 obtained on this hypothesis together with the observed (Bash- 

 forth) fact that the resistance of the air is proportional to the area 

 which the shot presents to the air in its motion, are then derived 

 and are found to give good agreement between the observed and 

 calculated data. Another fact which is taken account of in the 

 derivation of the equations is involved in the following state- 

 ment: "It is known that a rifle jumps up or down on being 

 fired, so that the angle of elevation of the rifle barrel just before 

 firing, which is the angle observed in experiments, is not the 

 same thing as the angle of departure of the bullet ; that is. 

 the axis of the rifle before firing is not a true tangent to the 

 trajectory." 



In the next part of the paper it is shown that the axis of the 

 projectile follows the line of flight while lagging a little behind 

 it, the angle of lag increasing with the range. Also, the action of 

 the air on the side of the shot exposed by the deflection of the 

 axis causes a shot with right-handed spin to veer bodily to the 

 right, giving the deviation known as "drift." It is thus seen 

 that the analogy often drawn between the motion of a projectile 

 and that of a spinning top is not admissible. The fallacy lies 

 in the fact that the external force (gravity) on the top acts in 

 a fixed direction whereas the resistance to a projectile rotates 

 with the line of flight. The precise behaviour of the axis of the 

 shot cannot, therefore, be foreseen from that of the top." 

 "Although the numerical results will have to be modified to 

 suit shells, it is clear from the results worked out that the spin 

 of a shot carries out very faithfully the task of keeping the 

 nose foremost during the flight, and that the deflexion of 



