224 MAGNUS ON THE DEVIATION OF PROJECTILES, 



account, the body L, though apparently solid, is in fact partly 

 hollow. p.6o 3Ai 



The execution of such an apparatus requires great delicacy 

 and correctness of workmanship, inasmuch as it is essential that 

 the centre of gravity of the body L, in every position, coincide 

 with the common centre of all the rings. Here too it is necessary 

 that the two axes of rotation of the inner rings, AB and EF, as 

 well as the axis ab of the body L, intersect all in one point, and 

 that in this point the centre of gravity be also situated. To 

 secure the last, the points a and i6. can »ker moved backwards: and 

 forwards by means of screws. U^^mr-fi vhn'Aifi noitrfi'n«r3b 3fii 



By this arrangement, as long as no rotation takes place, 

 every ring can be moved with the greatest facility. If the body 

 is made to rotate, however, it requires a very sensible force, in 

 order to change, even slightly, the position of any one of the 

 rings. Consequently the axis a b of the body, during its rotai- 

 tion, retains its direction unchanged. vmi-, 



, .Jf now, during the body's rotation, a force, not passing through 

 the centre of gravity, is applied to the axis ; for example, if^ when 

 the axis of the body is inclined to the horizon, a vertical force 

 act on it, produced by a weight applied to the ring EF near to the 

 extremity of the axis b ; then the latter will not be moved by it 

 in a vertical plane, but will describe a cone, in that it begins 

 thereby to move very slowly and horizontally towards one side. 

 If the force act in a horizontal instead of a vertical direction, 

 the axis describes still a cone, but commences moving, very, 

 slowly and vertically, upwards or downwards. This motion, at 

 the commencement, has always a direction perpendicular, or ap- 

 proximately so, to the plane passing through the direction of the 

 force and axis of rotation. For the following considerations, it 

 is of great importance towards which side of this plane the mo- 

 tion occurs. 



If we suppose that an observer, placed in the production of 

 the axis of rotation through the base, sees the body rotate in the 

 same manner as the hands of a clock, or from left to right, and 

 that the force acts from below upwards on the extremity of the 

 axis of the body L turned from him, i, e. on the apex, then this 

 apex will move towai'ds the right of the observer; if, on the 

 other hand, the force acts from above downwards, the apex will 



