330 Intelligence and Miscellaneous Articles, 



its introduction into physical cabinets.— -PoggendorfPs Annalen, 

 Erganzung, vol. vi. pp. 334, 335. 



DETERMINATION OE THE FRICTION RESISTANCES IN ATWOOd's 

 MACHINE. BY C. BENDER. 



The determination of the amount of friction in the wheel of the 

 fall-machine is preceded by the determination of its moment of 

 inertia. This can be done by applying a small overweight p to one 

 of the two suspension-weights, determiniug the acceleration y 

 hereby produced, and the unknown moment of inertia from the 

 formula gp 



W+Ic+p' 

 wherein P denotes the suspension-weight, equal on both sides, and 

 g the acceleration of gravity. It is understood that for P and p in 

 this formula their masses must be put. 



The above method cannot give exact results, since in it no ac- 

 count is taken of the friction of the pin in the wheel ; and it is 

 especially useless where the machine worked with has no friction- 

 rollers. Also the method according to which the moment of inertia 

 of a composite body is calculated from that of its separate parts , 

 referred to one and the same axis, cannot be employed here, because 

 the constituent parts of such a wheel but rarely permit a convenient 

 determination of the moment of inertia. 



Very convenient and accurate is the method which relies ou the 

 oscillations of a material pendulum. If h denotes the moment of 

 inertia of a pendulum in reference to its axis of rotation, M its 

 mass, and a the distance of the centre of gravity from the rotation- 

 axis, the oscillation-period of such a pendulum is expressed by 



'=VFi ■;«& 



In an experiment the wheel of the machine was //[\ ^fe 

 placed on a horizontal smooth edge of wood (or 

 of steel), at the point a (see the annexed figure); 

 and then the duration of an oscillation was de- 

 termined very accurately. The experimental 

 data were : — 



Weight of the wheel 173.9 grammes. 



Diameter of the wheel (string-groove) 12 centims. 



Distance of the rotation-axis a from the centre ) „ 



of gravity J S' 1 ? 5 centims. 



•200 vibrations in 60'5 seconds. 



Prom formula I. there results 



£ = 8-5836. 



According to a theorem of mechanics, the moment of inertia of 

 a body, referred to any axis, is equal to its moment of inertia iii 

 reference to an axis through the centre of gravity parallel to the 

 former, added to the product of the mass of the body into the square 



