226 MAGNUS ON THE DEVIATION OF PROJECTILES, 



apparent, and that the hypothesis, that the resultant of re- 

 sistance must cut the axis of the projectile below the centre of 

 gravity, was incorrect. For the apex of the projectile may be 

 made to sink, even when the resultant of resistance acts from 

 below upwards on the part of the axis above the centre of 

 gravity. It is true that in this case the apex will be at first 

 raised, but with a sufficient velocity of rotation this elevation 

 is scarcely perceptible, and instead of it, a motion of the apex 

 towards the right is produced. 



As soon as this motion has commenced, however, the plane 

 passing through the resultant of resistance, i, e, the tangent of 

 the trajectory, and through the projectile's axis, is no longer 

 vertical, and the more this deviation of the apex increases, the 

 inclination of this plane towards the horizon becomes continually 

 greater. But, as we have seen, the apex moves always perpen- 

 dicularly to this plane, or approximately so ; hence from the 

 known direction of this motion, it follows that the apex must 

 be depressed. 



This depression of the apex can extend even so far, that it 

 becomes situated below the tangent through the centre of 

 gravity. Then the resistance of the air, parallel to the tangent, 

 acts from above downwards on the apex — above and below 

 having reference to the before-mentioned observer — and thereby 

 a motion of the apex ensues in a direction opposite to that just 

 mentioned. During the projectile's flight, however, owing to 

 its short duration, so great a depression of the apex is not to be 

 expected ; nevertheless, for the following experiments it is worthy 

 of notice, that when such a depression does take place, the apex 

 must move towards the contrary side. 



In order to discover whether the resultant of resistance passes 

 through the part of the axis before or behind the centre of 

 gravity, the following experiments were made. Against the 

 above-described body L, fig. 6, Plate III., suspended within its 

 three rings, a current of air was directed, equally strong in 

 every part of its transverse section, which was of such a mag- 

 nitude, that the body, whatever position it might assume, re- 

 mained always entirely within the current. 



To produce this current, a strong pair of bellows was employed, 

 by means of which the air was first compressed into a so-called 



