C. B. WARRING. 109 



residuum of what was imparted by the first pull of the 

 string. 



I now vary the experiment. I set the wheel off with a 

 very moderate pull on the string. It revolves only four 

 or five times in a second. I attach my heavy weight. 

 Rapid gyration and rapid descent commence at once. 

 The latter does not need an index to show it. I now 

 wind the wheel up again, and give it the highest speed 

 I can. It goes very fast. I let it out of my hand. 

 Gyration at once is seen, but I need the index to see 

 equally soon the descent. It is there, but is very slow. 

 The conditions may be varied in all possible ways, the 

 result is the same. 



I formulate these results in this law. Increasing the 

 load, or the downward pull, diminishes the time of hori- 

 zontality, and, decreasing the load, increases that time. 

 The opposite is true of the velocity of rotation. 



From all this we must conclude that the time of a gy- 

 roscope' s staying up varies inversely as the load, and, 

 directly as the velocity of the wheel on its axis ; or in 

 mathematical symbols, we have h oc *-, where h=time of 

 horizon tality, and v= angular velocity of wheel, and 

 w=the load. As the two variables, v and w, are inde- 

 pendent of each other, h can become infinite only when 

 v is infinite, or when w is zero. Mere uniformity of ve- 

 locity cannot take the place of either of these. But, 

 uniformity of velocity is the highest effect capable of 

 being produced by absence of friction. 



Hence, in a frictionless gyroscope with any finite ve- 

 locity, h will not "'last forever ;" or, in other words, the 

 gyroscope will fall although all friction be removed. 



It may, perhaps, be thought, the authority is so great 

 on that side, that, in some mysterious way, friction is, 

 nevertheless, the cause of the gyroscope's not remain- 

 ing horizontal. I therefore inquired into the effect of 

 removing or neutralizing all the friction. This mani- 



93 



