C. B. WARRING. 165 



through a similar round, and aids in producing the same 

 result. 



In fig. 40 we have the same thing. A B represents a 

 section of the wheel with its axle M N, and standing so 

 that the eye is supposed to be in the plane of the wheel. 

 The centre, c, is immovable, while permitting freedom of 

 all other parts. The dark lines represent a section 

 while the axle is horizontal. The dotted lines repre- 

 sent the same after reversal. The arrows denote the di- 

 rection of the different motions. 



The momentum which B gets from the pulling of w, 

 would, when B is on the upper side (at B'), push it back 

 to the vertical, but it has to meet the continued action 

 of gravity on w as well as its (w's) momentum. It can 

 overcome only one ; consequently, the other carries it 

 down. 



There is the same struggle between the action of 

 gravity and the momentum of the previous instant, as 

 in case of the gyroscope, resulting for the same reasons 

 in a uniform and very slow rate of fall ; and this, in its 

 turn, is reduced to almost zero by the acceleration of the 

 lateral or gyrating motion. 



It is found also, that the " time of staying up " varies 

 directly as the angular velocity of the wheel, and, in- 

 versely, as the load. Conseqently, whatever the velocity, 

 short of infinite, the weight descends. Any other con- 

 clusion would bring the same absurd result that we 

 found in case of the gyroscope ; to wit, infinite power 

 of resistance so long as the rotation continued uniform. 



If, while the Bohnenbergher is in operation, the finger 

 be pressed with some force upon the upper side of the 

 axle, the side which is pressed down will rise even 

 though a considerable load is attached. It is another 

 paradox ; pressing down either side makes it rise. It 

 does apparently just what it ought not to do. 



The explanation is this. In the first case the reaction 



149 



