1881.] 



599 



[Chase. 



sons, are far more significant tlian any conclusions that can be drawn 

 from more restricted investigations. 



Whatever test may be applied, it should always be remembered that the 

 failure to discover a harmonic influence between any two given lines does 

 not affect, in the slightest degree, the evidences of harmonic influence be- 

 tween other lines. The failing cases are entitled to no weight in drawing 

 the final conclusion. We should, therefore, have been justified in stopping 

 our examination of the observed lines in the hydrogen spectrum, as soon 

 as we found that « is harmonically connected with (3 and d, and that y is 

 similarly connected with d- Even if subsequent discussions had fiiiled to 

 show any probable evidence of harmony between /9 and y^ /5 and 3^ « and 

 ;', the fact that there are such harmonies operating through the relations 

 of the intermediate to the extreme wave-lengths, Avould have been unshaken . 



147. Uncertainties of Measurement. 



The influence of probable errors of observation upon the validity of 

 Schuster's criterion may be illustrated by applying it to two of tlie different 

 values which have been found for the Fraunhofer lines A, B and C. 

 Angstrom's measurements are taken from Schellen's' Spectrum Analysis, 

 p. 168 ; Gibbs's, from Am. Jour. Science, [2] xliii, 4. 



Gibbs. 

 761.20 

 687.49 

 656.77 

 1.107216 

 1.107143 

 1.107692 

 ,000549 

 .000073 

 73 -- 549 

 137 -^ 549 

 1.046776 

 1.046513 

 1.046875 

 .000363 

 .000109 

 109 ^ 863 

 90 H- 368 



Hence the criterion indicates a harmony of vibration, both between the 

 A and B lines, according to Uibbs, and between the B and C lines, accord- 

 ing to Schellen. The « ^;?-iori probability or certainty that there must be 

 such a harmony, lends confidence to the greater accuracy of Gibbs's meas- 

 urement of the A line, and of Schellen's measurement of the C line. If 

 such allowance as I have proposed is made for that probability, the har- 

 mony is shown by Gibbs in both comparisons. 



A 

 B 

 C 



A-v-B:=« 



h = 81 ^ 28 

 c =r 72 -- 65 



c —b = d 

 a — 6 = e 

 e ~~ d 



Probable error 

 C = «! 

 6j = 45 -4- 48 

 Ci = 67 -- 64 

 Ci — &i = di 



e, -V- d, 

 Probable error 



B 



