472 Prof. W. M. Hicks on 



differences of wave numbers in the same region of the 

 spectrum,, and in this case the probable errors will be 

 far less than those given as all systematic errors will 

 be eliminated. This may be illustrated from the measures 

 for S(2). For Si(2) E.V. and Meissner both agree in 

 making the wave length '04 A larger, whilst in S 2 (2) 

 E. Y. make it 05 larger and Meissner *04. Thus on 

 differences Meissner agrees exactly with Meggers and 

 E.V. make it only '01 less. The true value based on 

 interferential measures to *001 has been found to be 

 248*44, whilst the observers here relied on only read 

 to *01 A. We shall be safe therefore in regarding the 

 probable errors in separations as less than '03 for the poorer 

 measures and '02 for the better, or say possible errors not 

 greater than 'OS and *04. Any calculated displacement 

 effects must therefore agree with observed within these 

 limits. As we have to deal with differences of numbers 

 of seven digits and 7-fig. logariibms have been used, 

 errors of 01 may be introduced on this account also. 

 The limit S^oo) is 31523*48 = N/(r865248) 2 and the 

 8 displacement produces a shift of 4*94. The sequent 

 *i(2) = 31523-48-12352-95 = N/(2'391865) in R.A., and 

 the 8 displacement produces a shift of 2*34. Further a 

 8 on S t (go ) decreases v by "06. These will enable a rough 

 estimate to be made for the displacements required, and 

 actual direct calculation in each case will then be necessary 

 to give the exact values. 



If we attempt to explain the shifts from the Sj lines 

 by displacements on the limits alone, we find that 6J>-S 

 shifts back 32'04, -6f S shifts forward 33*34 and -27 8 

 shifts 134*08. These are not only far from satisfying our 

 present limits of accuracy, but the changes in v called fortli 

 by them are not sufficient to meet the observed amounts. 

 Displacements on both sequents must therefore take place. 

 We begin by finding the displacements on the limits which 

 will reproduce the observed values of v. The results are : 



Displacement 12$"j — 118 -42£ 



v ... 247*74 249*09 250*91 



But since the 8 displacement alters v by *06, i. e. the oun by 

 •015, the actual displacements may differ by one or two ouns 

 and yet give the values of v within our error estimates *. 



* An illustration of the value of accuracy to "001 A. 



