Intelligence and Miscellaneous Articles. 331 



of the distance between the two axes. We will obtain according 

 to this theorem the moment of inertia h' of the wheel in reference to 

 the axis through its centre of gravity : — 



h' = 8-5836-- 178 ' 9 . 5-175 3 ; 



t/O J. 



k' = 3-70. 

 The weight of the heavy mass which at the circumference of a 

 ■wheel opposes to a turning force the same resistance as the mass 

 3*7 at the unit of distance from the rotation-axis which passes 



through the centre of gravity is now found from — ^ — =100*59 



grins. ; and this is the amount' which must be brought into the 

 reckoning in determining the acceleration in the Atwood machine. 

 If in experimenting with the machine we take away the over- 

 weight after the motion has continued a certain time, the entire 

 system must, in consequence of its inertia, move further with a 

 uniform velocity, which depends on the time or the height of the 

 fall and on the acceleration which has been present. Such a uni- 

 form motion, however, will be prevented by the friction of the axle 

 of the wheel, introducing a uniformly retarding motion which, after 

 a time, brings the system to rest. If we regard the friction present 

 as a constant force, under the influence of which a moving body 

 attains the acceleration p, and assume that the motion is produced 

 by an overweight of the mass m and has extended, at the removal 

 of the overweight, to the distance h, in this case the velocity at- 

 tained is 



V 



2g -^— .h~ s/ 2^1, 



where M+m denotes the entire mass set in motion, and g the acce- 

 leration produced by gravity. If from the removal of the over- 

 weight to the resting-point the system advances the distance o-, the 

 calculation of the velocity mentioned can be arrived at by assuming 

 that any body whatever has, under the influence of the acceleration 

 fA, travelled the distance o-. This gives the equation 



V 



,-i — . h— J2nli— J2uff 

 M + m y r r 



or 



gm% 



r (M + w)(Vcr+ SffiT 



Eor this fi we can also form another expression ; for if x denote 

 the mass (or the weight of the mass) which counterbalances the 

 influence of the friction, we have as a second equation 



g 



*+.+; ;•■• (IIL) 



Before I proceeded to the determination of .v, I satisfied myself 

 whether the quantity o- in equation II. could be ascertained with 



