221 



The time of a body descending from a point of rest A to the 

 lowest point of the curve at B will be the same from whatever 

 point it start. In other words a pendulum will fall from A to B 

 in precisely the same time it would from C to B, which is about 

 half the distance. Following trom this, a cycloidal pendulum 

 produces unequal arcs in equal t\me, or isochronism. The extreme 

 mechanical difficulty of executing a pendulum that will describe 

 a cycloidal path* during each excursion has lead horologists to 

 originate many ingenious devices to accomplish this end. This 

 pendulum which I show you to-night is constructed so as to 

 cause the center of oscillation to move in a cycloidal path by 

 coming in contact with cycloid cheeks near its point of suspension, 

 but the effects of moisture, friction, dilatation and adhesion of 

 contact against these cheeks would in time give rise to errors as 

 great as those sought to be overcome. 



We therefore must make efforts in another direction. 



The best method of to-day for producing isochronism is to 

 cause the arc of oscillation to be as short as possible, and also 

 have the suspension spring of a given length and given strength 

 in proportion to the length and weight of the pendulum. Then 

 we will only have to deal with the molcular arrangement of the 

 spring which is constantly changing, but this error is very small 

 and exceedingly regular. 



(See Note "A", page 224.) 



THE BAROMETRICAL ERROR. 



A pendulum is effected by the density of the atmosphere, 

 but to a degree that would only be of importance in a precision 

 time piece ; where all the errors are reduced to a minimum. An 

 increase of density of the air is equivalent to reducing the action 

 of gravity, while the inertia of the moving body remains the same. 

 The rule is, that the velocity of the pendulum varies directly as 

 the force of gravity, and inversely as the inertia and it follows 

 then that an increase of density diminishes the velocity and 

 shortens the time of oscillation, causing the clock to gain time. 

 The barometrical error can be reduced to within three to four- 

 tenths of a second in twenty-four hours for each inch rise or fall 

 of the barometer. Short arcs of oscillation are also essential in 

 reducing the barometrical error. An apparatus is sometimes 

 attached to the pendulum to assist in reducing this error. 



