Chase.] b\J\J [Nov. 4, 



148. The Frmmhofer Harmonies. 

 The general accuracy of Gibbs is confirmed by the fact that his measure- 

 ments indicate harmonies among the principal Fraunhofer lines, as is 

 shown in the following table. They all bear the test of Schuster's crite- 

 rion, with the exception which was stated in the foregoing note. 



The greatest difference is only ^^ of one per cent., in the G line. 

 149. Proper Use of Harononic Tests. 



In systems of waves W'hich are propagated with such frequency as the 

 undulations of light, it may, perhaps, be impossible to devise any criterion 

 which will show whether any two given waves are really harmonic. But 

 if we consider that undulations which are not harmonic are continually 

 tending to destroy each other, various useful tests may be found, which 

 will serve as guides for the approximate determination of harmonies that 

 must really exist. For example, if there are two harmonic light-waves, 

 the slower oscillating 1670 times, while the swifter oscillates 1843 times, 

 there will be more than 300,000,000,000 coincidences of phase per second, 

 and yet Schuster's method would lead us to suppose that there is no har- 

 mony. The ratio f f|f, is equivalent to .906131, which is between f | and ||. 

 29 -^ 32 .906250 



77 -f- 85 . 90588 2 



Difference .000368 



.906250 — .906131 .000119 



Ratio of Differences 119 h-368 .324 



Probable Error .250 



150. Successive Harmonies. 



The following table shows that Angstrom's measurements indicate har- 

 monic undulations, which present more than 600,000,000,000 coincidences 

 of phase per second in successive lines : 



"Wave-length. Log. w. 1. Log. ratio, Ratio. 



A 760.09 2.8808650 T.9755619 • 501 / 530 



a 718.50 2.8564269 • T. 9803266 410 ,/' 429 



B 686.68 2.8367535 T. 9802695 710 / 743 



C 656.18 2.8170230 T.9534617 389 / 433 



Di 589.50 2.7704847 T. 9512343 446 / 499 



