1903.] The Ultra-violet Spectrum of Radium. 



Wave-lengths of the B-adium Lines continued. 



301 



Measurements are taken of the exact distances apart of the radium 

 lines and certain adjacent iron lines used as standards. By using a 

 formula, first communicated to the British Association by Sir George 

 Stokes, the wave-lengths of the unknown lines can be calculated. At 

 the time the formula was given it was sufficiently accurate for the 

 instrumental means employed for photographing spectra, but the 

 formula only gave approximate results, and the accuracy of determina- 

 tion of wave-lengths has since improved so much that a correction is 

 required to the original formula. Sir George Stokes, before whom I 

 placed the difficulty in June, 1895, quickly solved it in a satisfactory 

 manner. The usual formula requires the positions of two standard 

 lines of known wave-length, n\ and #3, on each side of the unknown 

 line, n>2. To make the small correction, Sir George advised me to take 

 a third line of known wave-length, chosen well removed from the 

 selected known lines n\ and n$. If chosen in the interval 1 3 it had 

 better not be greatly distant from the middle. There is, however, very 

 wide latitude of choice in this respect. All these lines must be photo- 

 graphed and measured in the usual way. Calculate the approximate 

 wave-length of the unknown line by the original formula, and then 

 calculate the approximate wave-length of the third known line by the 

 same formula, as if it were unknown, using the two original standards 

 for this purpose also. We have now the approximate wave-length of a 

 known line, as given by the formula, and also its true wave-length 

 The difference between these two values leads (infra, p. 303) to the 

 correction to apply to the approximate value of the unknown line. 



It often happens that four or more lines are well placed for use as 

 standards. If any three of these be taken, and from them the positions 

 of the other lines be calculated, it will sometimes be found that there is 

 a small residual error in some of them. In such a case the error can 

 be minimised by adjusting the value of the three primary standards so 



VOL LXXII. Y 



