138 Mr Sang on the Advantages of a 



pel led to combat error by assertion, and to attempt the removal 

 of one prejudice through the agency of another. 



In the present case, it would be vain to introduce an investi- 

 gation of the law of motion in circular arcs, since no horologist 

 who is able to follow that investigation can be partial to the 

 long sweep. Among those who are unable to follow it, an in- 

 distinct belief prevails that the motions of the pendulum may be 

 subjected to calculation : neither that calculation indeed, nor the 

 principles on which it is founded, have they subjected to exami- 

 nation ; but then the idea of applying the pendulum to the 

 measurement of time was first entertained by one profoundly 

 skilled in science, — the balance- spring, the fusee, and the com- 

 pensations for thermal expansion, were all results of scientific re- 

 search ; and it may not be impossible, say they, that, from the 

 same mysterious source, an exact knowledge of the influence of 

 long and short arcs on the going of a clock, may be obtained. 

 And thus, although they do not fully appreciate the force of 

 theoretical results, they are yet not prepared to contradict them. 

 Such is the kind of argument to which I must appeal in support 

 of the statements I am about to make. 



If, when the pendulum of a clock is making exceedingly minute 

 vibrations, it be adjusted to true time, and if the arc be then 

 lengthened, the duration of the beat will be increased also. At 

 first, this increase will be exceedingly minute, but as the arc en- 

 larges itself, the interval between two beats will augment more 

 and more rapidly, until the slightest change on the arc of vibra- 

 tion will produce a sensible effect on the clock's going. I have 

 computed and arranged, in the annexed tables, the exact amounts 

 of the changes corresponding to each of the first twenty hun- 

 dredth parts of the semicircle ; by the help of these tables, we 

 are enabled readily to compare the performances of pendulums 

 with long or short sweeps. 



Suppose that we had a clock regulated to true time when its 

 pendulum swept an arc of twenty centesimal degrees on each 

 side of the vertical line, and then let the maintaining power, on 

 account of the thickening of the oil, or from any other cause, be 

 reduced by one-twentieth part, the pendulum will, keeping no ac- 

 count of the resistance of the air, vibrate only 19 degrees on each 

 side, and its daily rate will therefore be accelerated 52''^35. 



