ANALYSIS OF QUANTITATIVE PHENOMENA. 403 



difference between the judgment of observers at the 

 Greenwich Observatory usually varies from -^ to ^ of 

 a second, or even a little more, and remains pretty con- 

 stant for the same observers 11 . In some observers it has 

 amounted to seven or eight-tenths of a second x . De 

 Morgan appears to have entertained the opinion that 

 this source of error was essentially incapable of elimina- 

 tion or correction y. But it seems clear that this personal 

 error 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 z . 



Newton employed the pendulum for making experi- 

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

 contact, and one of them, being drawn 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 which he 

 estimated very simply by causing one of the balls to 

 make several complete vibrations and then marking the 

 reduction in the length of the arcs, a proper fraction 

 of which reduction was added to each of the other ob- 

 served arcs of vibration a . 



In the modern use of the pendulum, to measure 

 terrestrial gravity, it is not found convenient to annul 



11 'Greenwich Observations for 1866,' p. xlix. 



x 'Penny Cyclopaedia,' art. Transit, vol. xxv. pp. 129, 130. 



y Ibid. art. Observation, p. 390. 



z 'Nature,' vol. i. pp. 85, 337. See references to the Memoirs de- 

 scribing the method. 



a 'Principia,' Book I. Law III. Corollary VI. Scholium. Motte's 

 translation, vol. i. p. 33. 



D d 2 



