and on the Theory of Escapements. 1 1 7. 



in such a manner as not to alter the time of vibration. Witli 

 this construction a compensated pendulum moving in a cycloidal 

 arc would be isochronous. But the pendulums of clocks swing 

 in circular arcs, and it might therefore appear desirable to make 

 the escapement in such a manner as to correct the difference 

 between the circular and the cycloidal vibration. In this manner 

 the oscillations would always be isochronous, whatever variations 

 the maintaining power and the length of the arc of oscillation 

 might undergo. 



Upon a more accurate examination, however, I believe it 

 will be found much better to lay aside all thoughts of this artifice. 

 The law of the air's resistance when the velocity is so small as 

 that of a pendulum is not known. By observations on detached 

 pendulums of Captain Kater's construction, I have found that it 

 differs very much from that of the square of the velocity. Whether 

 it would be better represented by the simple velocity, or by the 

 square of the velocity increased by a constant, I do not know. 

 Besides this, it is almost impossible to ascertain the effect of the 

 friction upon the pallets, or its proportion to the resistance of 

 the air, &c. Since then we cannot express, in a known function 

 of the length of the arc, the diminution of the arc at each vi- 

 bration, or the quantity which the maintaining force must in- 

 crease it at each vibration, we cannot find what the force must 

 be to maintain a given extent of vibration, and, therefore, we 

 cannot find in what manner it must be applied that its effect 

 on the time of vibration may exactly counteract that of the 

 difference between the circular and cycloidal arcs. It is possible 

 also in pendulums with a spring suspension, to make the vibrations 

 very nearly i.sochronous in different arcs; and in pendulums with 

 knife edge suspensions, it is easy to apply a construction which 

 will have the same effect. I shall, therefore, consider it as the 

 object in the construction of escapements to make them in such 

 a manner that they do not at all affect the time of vibration. 



