C. 13. WARRING. 123 



these reversals of momentum, 1 since it merely intensifies 

 their effect. , 



What this something is I hope soon to show ; but, in 

 order to do so, we must first study the horizontal move- 

 ment, for in that, if I am not mistaken, lies the key to 

 the remaining mystery. 



Returning to our tee-square, or. if you please, to our 

 section, e. g. , in fig. 5, and standing in reference to it as 

 before, we see that when it falls any distance, however 

 small, the upper end acquires motion to the right, while 

 the lower goes to the left. Suppose that at this instant 

 the tee is rotated so that A goes from us. When the 

 arms reach a horizontal, A will still be going to the 

 right, and B to the left, as in the bird's eye view (fig. 15), 

 and this means that the tee is caused to move in the 

 direction of the arrow m ; in other words, around the 

 supporting point c, and in the same direction as that in 

 which the lower end moved from its vertical position. 



As this tee differs in no respect from all other sections 

 of our gyroscope, we are entitled to conclude that each 

 of them will do the same thing. In this is the reason 

 why the gyroscope moves horizontally around the sup- 

 porting point, and why its direction coincides with that 

 of the under side of its wheel. 



It is true that the instrument will at the same time be 

 pulled downward by gravity. But we have already 

 shown how the greatest part of that force is disposed 

 of, and, as for the rest, we will satisfy ourselves for the 

 present with the fact that it is disposed of in some way, 

 and wait till the problem is solved. 



Since these forces, x and y, (fig. 15), are renewed at 

 each reversal, and no force opposes them, the horizontal 

 movement will be a uniformly accelerated one, unless 



1 " Reversals of momentum,'" not that the direction of the momentum is reversed, but 

 only its effect. It is as when a weight is shifted from one pan in a pair of balances to the 

 other. The direction of the downward pull is unchanged, but its effect is reversed. 



107 



