336 THE PRINCIPLES OF SCIENCE. 



There is an exact equation between the intensities of the 

 beams when Newton's rings disappear, the ring created 

 by one ray being exactly the complement of that created 

 by the other*. 



The Method of Repetition. 



The ratio of two quantities can be determined with 

 unlimited accuracy, if we can multiply both the object 

 of measurement and the standard unit without error, and 

 then observe what multiple of the one coincides or nearly 

 coincides with some multiple of the other. Although per- 

 fect coincidence can never be really attained, the error 

 thus arising may be indefinitely reduced. For if the 

 equation py = qx be uncertain to the amount e, so 



IT P 



that py = qxe, then we have p = q~- 9 and 



j J 



as we are supposed to be able to make y as great as we 

 like without increasing the error e, it follows that we 

 can approximate as closely as we like to the required 

 ratio x-^y. 



This method of repetition is naturally employed when- 

 ever quantities can be repeated, or repeat themselves 

 without error of juxtaposition, which is especially the 

 case with the motions of the earth and heavenly bodies. 

 In determining the length of the sidereal day, we really 

 determine the ratio between the earth's revolution round 

 the sun, and its rotation on its own axis. We might 

 ascertain the ratio by observing the successive passages 

 of a star across the zenith, and comparing the interval by 

 a good clock with that between two passages of the sun, 

 the difference being due to the angular movement of the 

 earth round the sun. In such observations we should 

 have an error of a considerable part of a second at each 



* Humboldt's 'Cosmos/ (Bolm), vol. iii. p. 129. 



