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XXIII. On the Rolling Motion of a Cylinder. By the Rev. Henry Moseley, M.A., 
F.R.S., Corresponding Member of the Institute of France. 
Received March 6, — Read March 13, 1851. 
The oscillatory motion of a heterogeneous cylinder rolling on a horizontal plane 
has been investigated by Euler*. He has determined the pressure of the cylinder 
on the plane at any period of the oscillation, and the time of completing an oscilla- 
tion when the arcs of oscillation are small. 
The forms under which the cylinder enters into the composition of machinery are 
so various and its uses so important, that I have thought it desirable to extend this 
inquiry, and in the following paper I have sought to include in the discussion the 
case of the continuous rolling of the cylinder, and to determine — ■ 
1st. The time occupied by a heterogeneous cylinder in rolling continuously through 
any given space. 
2ndly. The time occupied in its oscillation through any given arc. 
Srdly. Its pressure, when thus rolling continuously, on the horizontal plane on 
which it rolls. 
Under the second and third heads this discussion has a practical application to the 
theory of the pendulum ; determining the time occupied in the oscillations of a pen- 
dulum through any given arc, whether it rests on a cylindrical axis or on knife- 
edges, and the circumstances under which it will jump or slip on its bearings; and 
under the first and third, to the stability and the lateral oscillations of locomotive 
engines in rapid motion, whose driving-wheels are, by reason of their cranked axles, 
untruly balanced. 
Let AMB represent the section of a heterogeneous cylinder through its centre of 
* Nova Acta Acad. Petropol. 1788. “ De motu oscillatorio circa axem cylindricum piano horizontal! incum- 
bentem.” 
4 B 
MDCCCLI. 
