Abstract
The time occupied by a heterogeneous cylinder in oscillating upon a horizontal plane through a small arc has been investigated by Euler; and he has determined the pressure of the cylinder upon the plane when oscillating through any arc, applying the formula he has arrived at to find the pressure upon the plane at the highest and lowest points of oscillation. It is the object of the present paper to endeavour to extend this investigation to the continuous rolling of the cylinder, under which more general form its oscillation is obviously included as a particular case. In the first part of the paper, the time of rolling through any angle, and therefore of completing any given number of revolutions, is investigated ; and in the second, the conditions of the pressure upon the plane at any period of a revolution.
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