60 



PEOF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



To anyone using the form a/m, KYDBERG'S new formula suggests at once the form 

 D = m + /x + a/(m + /i), which only requires three constants. Using the first three 

 lines for these there results 



886213 



n 



= 26617'09-N/ W+-317620+ 



WI+-31762/' 



which reproduces the last three lines well within the limits, as the tahle below shows. 

 I felt no doubt but that this was the true form, until it occurred to me to test the 

 simpler form. 

 The formula 



= 2660974-N/UI+ -345117+ 7235 2 ) 2 

 / \ ml 



n 



reproduces the last three quite as well as the other, and, in addition, possesses all the 

 criteria of a diffuse series. The series is not, therefore, a " new kind of series," as it 

 was called by its discoverer. 



The following table gives the series with the excess of calculated over observed 

 wave-length for each formula, and the limits of observational error : 



* Used to calculate constants. 



An interesting remark may be made here. If a series is represented by 

 I) = m+/i+a/(m+/u,) a slight alteration will represent it equally well by putting D a 

 continued fraction, viz., 



in other words, 



or 



N _N 



n = A 



mf/LiT 

 V 



which looks quite different, and points to the frequencies depending on the roots of a 

 quadratic. 



In RYDBERG'S formula the value of m (or /u) has a certain indeterminateness p 



