Series Spectrum of Mercury, 



641 



These values are not constant, they undergo on the whole 

 a regular progression with m, but if each value be plotted 

 against its distance P(co)— P(ra) from the limit, the extra- 

 polation of this curve to the axis of zero P(oo ) — P(ra) will 

 give an accurate value for the limit, even when the formula 

 itself is quite out in the representation of the lower lines. 

 The extrapolation by a curve is too great unless the lines 

 have been measured close up to the limit, but with the 

 sixteenth line given it is both easy and accurate, aud gives 



P(»)= 21832-5. 



The diffuse series was worked out in a similar way except 

 that a modified formula * which gives a closer representation 

 of the lines was used : 



DM = D (~)-* /(- + -981485-^H||^) 2 . 



The limit D(qo ) calculated for each line of the series from 

 the above formula is shown below : — 



m. 



D(oo). 



m. 



D(oo ). 



4 



401410 



li 





5 



126-2 



12 



40139-2 



6 



35-7 



13 



40-3 



7 



358 



14 



403 



8 



33-8 



15 



39 2 



9 



38-3 



16 



38-8 



10 



393 







Extrapolation is here almost unnecessary, and the value of 

 the limit is 



D(oo) =40139*6. 



This, as may be judged from the table, is probably accurate 

 to less than a unit. The principal limit is not quite so 

 accurately determined owing to the smaller dispersion of 

 the prisms in this region of the spectrum. 



The difference between these limits is 18307*1. The 

 frequency of the first line of the sharp series (\ 5460*97) is 

 18306*8. The agreement is unmistakable. Thus the case 



* This is one of the variations of that used hy Hicks, Phil. Trans 

 vol. ccx. p. 57 (1910). 



Phil. Mag. S. 6. Vol. 20. No. 118. Oct. 1910. 2 U 



