1887.] NEW YORK ACADEMY OF SCIENCES. 131 



ON" CERTAIN LAWS OF GYRATING BODIES. 



Secular Changes in Nutation their Result. 



A gyrating body is one revolving on an axis passing through 

 its centre of gravity, and acted upon by a force — for convenience 

 called herein the second force — tending to make it revolve on 

 another axis at right angles to the first. 



The object of the present paper is to demonstrate, experiment- 

 ally, certain laws or results — not to give their rationale.' 



Apparattis used. — A rather heavy gyroscope, to one side of 

 whose frame was attached, in line with the axis of the wheel, 

 an arm twelve inches long. By adjusting a weight on this arm, 

 the instrument can be balanced, or either end made the heavier. 

 A liook at the opposite side of the frame permits of readily at- 

 taching a weight, or a little pail into which weights can be put. 

 The whole is supported on a fine point a very little above the 

 centre of gravity, and resting in a saucer-like depression, both 

 being of very hard and highly polished steel. This arrange- 

 ment gives great delicacy and freedom of precessional and nu- 

 tational movement. The instrument weighs, complete, about six 

 pounds. 



I. — A gyrating body, not frictionless, yields to the "second 

 force," i. e., tilts in the direction of that force. 



Proof. — I attach a weight to the free end of my balanced gy- 

 roscope, and that end falls. Or, if the weight is attached to the 

 opposite end, the gyroscope rises. The experiment may be 

 varied in all possible ways, with the same result. 



II. — The tilting becomes more rapid as the " second force" is 

 increased, and vice versa. 



Proof. — Attach weights of different sizes, and note the time 

 required to tilt, say 40°. It will be seen that the time dimin- 

 ishes as the weight increases. 



III. — A frictionless gyroscope will not remain in a horizontal 

 position forever. Proved in tioo loays. 



It has been shown that a gyroscope, not frictionless, tilts, or 



• For what seems to me such, see my monograph on Gyrating Bodies; 

 also for description and drawings of both the instruments used in the 

 experiments. 



