180 Prof. W. Gibbs on the Measurement of Wave-lengths 



the mean of which is 656*28, the error being —0*28. To deter- 

 mine to what extent the method applies when flint-glass prisms 

 are used and the indices are selected from the more refrangible 

 portion of the spectrum, the following data were assumed : — 



F, 



. 1-62917 



486-39 



F andG 



438-88 



+ 0-30 



35 



. 1-63244 



467-00 



F and 39 



438-76 



+ 0-18 



37 



. 1-63828 



438-58 



F and 38 



438-82 



+ 0-24 



38 , 



. 1-63931 



434-28 



G and 35 



438-76 



+ 0-18 



39 . 



. 1-63965 



432-74 



35 and 38 



438-75 



+ 0-17 



G , 



. 1-64006 



431-12 



35 and 39 



438-67 



+ 009 



In this Table line 37 is taken as the middle line in applying 

 formula (2), and the results obtained by combining the other 

 lines in pairs are given in columns 4, 5, and 6. It will be seen 

 that, as in the case of the less refrangible portion of the spec- 

 trum, the results obtained are with this prism always too high. 

 For the purpose of comparison, I have computed the same wave- 

 length from the indices of refraction of the second prism. The 

 data and results are as follows : — 



F 



1-62332 



486-39 



F andG 



439-07 



4-0-49 



35 



1-62657 



467-00 



F and 39 



438-89 



4-0-31 



37 



1-63221 



438-58 



F and 38 



438-92 



-fO-34 



38 



, 1-63324 



434-28 



G and 35 



439-00 



4-0-42 



39 



1-63358 



432-74 



35 and 38 



438-89 



4-0-31 



G , 



1-63400 



431-12 



35 and 39 



438-84 



+ 0-26 



In the case of the first prism the mean of the errors is +0*21, 

 while for the second the mean of the errors is +0-35. From 

 this it appears that in the more refrangible portion of the spec- 

 trum the errors are considerably greater than in the less refran- 

 gible portion, even for equal differences of wave-length, and, 

 further, that the advantage in precision is with the prism having 

 the higher dispersive power. As the probable errors of the 

 measurements of the indices of refraction are not given, it is 

 impossible to determine to what extent the errors in the com- 

 puted wave-lengths are due solely to want of precision in the 

 indices. It is also to be remarked that, while with the second 

 prism the errors in the less refrangible portion of the spectrum 

 are affected with the sign — , in the more refrangible portion 

 they are largely positive. The close agreement in the value of 

 the wave-length of 37, as found by Van der Willigen, with the 



values as found by Ditscheiner and Angstrom (438*27 and 

 438*28), proves that the source of error is not an erroneous de- 

 termination of this quantity. It seems, therefore, certain that 

 the nearly constant errors noted above are due in part to the fact 

 that the indices of refraction are determined only to five places 



