ON CONFINED MOTION. ' 4f 



figures, that is, of the points in which their whole weight may be supposed to 

 be concentrated, with regard to its effect on the times of their vibrations. 



It is remarkable that the isochronism of pendulums, which is a property so 

 important in its application, may still be preserved, notwithstanding the in- 

 terference of a constant retarding force, such as the force of friction is in 

 many cases found to be. It has been shown by Newton, that each complete 

 vibration of a cycloidal pendulum, retarded by a resistance of this nature, will 

 be shorter than the preceding one by a certain constant space, but that it 

 will be performed in the same time. 



There is a great analogy between the vibrations of pendulums, and the re- 

 volution of balls suspended from a fixed point. If a body, suspended by <l 

 -thread, revolve freely in a horizontal circle, the time of revolution will be the 

 same, whenever the height of the point of suspension, above the plane of rcvo>- 

 lution is the same, whatever be the length of the thread. Thus, if a number 

 of balls are fixed to threads, or rather wires, connected to the same point of 

 an axis, which is made to revolve by means of the whirling table, they will so 

 arrange themselves, as to remain very nearly in the same horizontal plane. 

 (Plate II. lig. 26".) lUifjiq 



The time of each revolution of the balls is equal to the time occupied by a 

 double vibration of a pendulum, of which the length is equal to the height of 

 the point of suspension above the plane in which they revolve ; consequently 

 all the revolutions will be nearly isochronous, while the threqds or wires 

 deviate but little from a vertical situation. In fact, we may imagine such a 

 revolution to be composed of two vibrations of a simple pendulum, existing 

 at the same time, in directions at right angles to each other; for while a pen- 

 dulum is vibrating from north to south, it is liable to the impression of any 

 force, capable of causing a vibration from east to west; and the joint result of" 

 both vibrations will be a uniform revolution in a circle, if the vibrations are 

 equal and properly combined; but if they are unequal, the joint vibration will 

 be ultimately an ellipsis, the joint force being directed to its centre, and al- 

 ways proportional to the distance fiom that centre. (Plate II. Fig. 27.) 



The near .approach of these revolutions to isochronism has sometimes been 



