t 



H. A, Newton on the Motion of the Gijroscope. 253 



Example : a crystal of Iceland Spar gave an angle by the two 

 positions of the rule. Each side adjacent is made 1 decimeter 



long. 



'47622 



:mi' 



cos^=-l-0-73811=0-26189. 



The angle corresponding to this cosine is 1^ 60' ; the sui3ple- 

 ment is- 180^-74° 50'=105° 10'. 



Although any rule with a straight edge will answer the pur- 

 pose, a metallic rule is to be preferred, because its weight makes 

 it more steady. Instead of a sheet of paper the top of a white 

 marble mantle-piece may be used. It has the advantage of being 

 immovable, and pencil marks on it are easily erased. 



^Many ways might be proposed for adjusting the 

 stick wax on the ruler and adjust the crystal with the ^xc^ixu^. 

 adheres well to brass, ivory and steel, not so well to wood. 



iL I 

 Wax 



The measurement by a rule is not proposed as better than by 

 a goniometer ; but when the operator has not a good instrument, 

 he will find it a simple and accurate method. An angle can be 

 read to within 15' with a good protractor of 1 decimeter radius, 

 or by measuring the aide opposite to the angle A and calculating 



cos -4. 



Art. XX. — Explanation of the Motion of fJic Gyroscope; by 



H. A. Newton. 



m 



a heavy wheel suspended in a ring. The wheel can revolve on 

 its axis in the ring, and the whole can move in any way about a 

 fixed point in this axis. The instrument differs from Foucault's 

 gyroscope in that its center of gravity and the fixed point do 

 not coincide. In what follows, the ring and the effect of friction 

 are disregarded. 



Let A B C I) be a section of the wheel ^ 

 through its center oi gravity E, and ^ex- y^ ^^^X 

 pendicular to its axis. Designate by / J \ 

 the point of support, OE will be the axis --/ ^X-- .y^ 



of the wheel. »[ (' is ; )b 



If from a state of rest (OE not being I \^^J j 



vertical), the wheel is left to the action of V / 



gi'avity, it will vibrate back and forth like \^^ ^ 



a pendulum. But when a rapid rotation ^'--—.^-^^ 



is given to the wheel, and it is then left to 

 the action of cavity, we find that it no longer swings lilvc a 

 pendulum, but O E commences a slow revolution about a verti- 

 cal line throudi 0. The direction of this motion is the same as 



