and on the Theory of Escapements. 125 



in the dead-beat escapement) lasts for a very short time. It is, 

 therefore, in the power of the artist to construct it in such a manner 

 that the action shall take place equally before and after the time 

 at which the balance reaches the middle of its vibration. In this 

 manner the quantities c and c', in the investigation for the dead- 

 beat escapement, would be equal, and the effect of the maintaining:;- 

 power on the rate of the chronometer would be absolutely nothing-. 

 It appears to be owing to this that the duplex escapement is found 

 to be so good. The only point in which the detached escape- 

 ments of Arnold and Earnshaw appear to be superior (which is, 

 however, a jioint of importance) is the almost perfect absence of 

 friction. As the wheel touches the balance only once in two 

 vibrations, the latter may be so adjusted that the time of vibration 

 shall be perfectly independent of the maintaining power. If the 

 slight resistance offered by the springs be taken into account, the 

 same is true. When to this consideration we add that the motion 

 of the balance is not clogged by any friction, except that of its 

 own pivots and spring, it does not appear possible to form an 

 escapement more perfect in theory than these. The reasons which 

 determine the form of the teeth of the wheel in these two escape- 

 ments are entirely practical : provided the action takes place during 

 a small part only of the vibration, it is indifferent whether the 

 force be uniform or not. 



We have seen that the rank which is assigned to the different 

 escapements by theory is precisely the same as that which is given 

 by experience: and this circumstance seems to justify us in the 

 presumption that nothing imjjortant is omitted in the view that 

 we have taken of this theory. Perhaps then I may be allowed 

 to suggest, on mere theoretical considerations, a form for the 

 escapement of clocks : similar in its principles to the best detached 

 e.scapements of chronometeis, and apparently likely to possess 

 the same advantages. In fig. 1, A is the wheel whose axis 



