348 THE PRINCIPLES OF SCIENCE. [chap. 



of a second, and remains pretty constant for tlie same 

 observers.^ One practised observer in Sir George Airy's 

 pendulum experiments recorded all his time observations 

 half a second too early on the average as compared witii 

 the chief observer.^ In some observers it has amounted to 

 seven or eight- tenths of a second.^ De Morgan appears to 

 have entertained the opinion that this source of error was 

 essentially incapable of elimination or correction.'* But it 

 seems clear, as I suggested without knowing what had 

 been done,^ that this personal ei'ror might be determined 

 absolutely with any desirable degree of accuracy by test 

 experiments, consisting in making an artificial star move 

 at a considerable distance and recording by electricity the 

 exact moment of its passage over the wire. This method 

 has in fact been successfully employed in Leyden, Paris, 

 and Neuchatel.^ More recently, observers were trained 

 for the Transit of Venus Expeditions by means of a 

 mechanical model representing the motion of Venus over 

 the sun, this model being placed at a little distance and 

 viewed through a telescope, so that diiferences in the 

 judgments of different observers would become apparent. 

 It seems likely tiiat tests of tliis nature might be employed 

 with advantage in other cases. 



Newton employed the pendulum for making experi- 

 ments on the impact of balls. Two balls were hung in 

 contact, and one of them, being di'awn aside through a 

 measured arc, was then allowed to strike the other, the 

 arcs of vibration giving sufficient data for calculating the 

 distribution of energy at the moment of impact. The 

 resistance of the air was an interfering cause wdiich lie 

 estimated very simply by causing one of the balls to 

 make several complete vibrations without impact and then 

 marking the reduction in the lengths of the arcs, a proper 

 fraction of which reduction was added to each of the other 

 arcs of vibration when impact took place.'' 



* Greenwich Observations for 1866, p. xlix. 

 '^ Philosophical Transactions, 1856, p. 309. 



•' Fenny Cyclopaedia, art. Transit, vol, xxv. pp. 129, 130. 



* Ibid. art. Observation-, p. 390. ^ I^ature, vol. i. p. 85. 



* Nature, vol. i. p 337. Ste references to the Memoirs describinf^ 

 the method. 



' I'rincipia, Book I. Law III. Corollary VI. Scholium. Motte'3 

 translation, vol. i. p, 33. 



