Royal Institution of Great Britain, 419. 



This may also be subdivided into two parts : ' ' 



(1) The pendulum, or balance, which governs the rate. 



(2) The escapement, which transmits that government to the train, 

 und in return transmits the impulse of the train to the pendulum. 



In order to understand properly the escapement, we must have 

 gome idea of the properties of the pendulum. 



A body suspended so as to move without friction, and exposed 

 to no resis'tance from the air or other causes, being made by 

 means of equal impulses to perform equal vibrations, would per- 

 form them in equal times, even if we had no better proof of the 

 fact, than the old metaphysical argument, that there is no sufficient 

 reason to the contrary. So also, though there be friction at the 

 point of suspension, and air resisting the vibration, if that friction, 

 and that resistance of the air, be quite invariable, the vibrations 

 would continue invariable both in quantity and time, for the same 

 want of a sufficient reason otherwise. In all this, however, we 

 have assumed three impossible conditions. 



In the first place, it is impossible always to give exactly equal 

 impulses to the pendulum. 



In the second, the friction is likely to vary from temperature, and 

 from the changes which the oil, or other lubricating material, un- 

 dergoes. 



In the third, the resistance of the air changes from temperature, 

 moisture, and other circumstances. 



These causes (with others) preclude the possibility of making a 

 pendulum perform for any length of time exactly equal vibrations ; 

 and since the longer vibrations of a simply suspended pendulum 

 occupy more time than the shorter ones, it becomes an incorrect 

 measure of time. The error produced in this way is very slight, yet 

 enough to be sensible in instruments so perfect as they are now 

 made. The times occupied in describing a complete semi-circle, 

 and the smallest sensible arc, differ only in the proportion of 34 and 

 29 ; and the error becomes much less, in proportion as the differences 

 between the arcs of vibration are less. 



If, however, as is well known, a pendulum could be made to vi- 

 brate, describing the arc called a cycloid, it would perform all its 

 vibrations, whether long or short, in equal times ; and it was, there- 

 fore, proposed by Huygens, to attach to the upper part of the pen- 

 dulum an apparatus which should cause it to describe cycloidal arcs, 

 and thus to free it from the errors arising from changes in the arc of 

 vibration. It was found, however, that this apparatus required an 

 impracticable degree of accuracy in the workmanship ; and therefore 



